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CBSE 10 PHYSICS
Light – Reflection And Refraction
_____________________________________________
Full Notes
Introduction To Reflection and Refraction of Light
Light travels in a straight path in a uniform medium.
The light that bounces back when it strikes a smooth or rough Opaque surface is called reflection of light.
Light bends when it travels from one transparent medium to the other transparent medium at the surface that separates the two transparent media. Such a phenomenon is called Refraction of light.
Reflection of light
Reflection of light is of two types they are;
(i) Specular or Regular
(ii) Diffused or Irregular Reflection.
(i) Specular or Regular
(ii) Diffused or Irregular reflection
Laws of Reflection
In the case of reflection, The light obeys two laws of reflection as follows.
(i) angle of incidence, i is equal to the angle of reflection, r. Mathematically, it is represented as: ∠i = ∠r
(ii) The incident ray, The normal ray and reflected ray lie in the same plane.
The image formed by a mirror, such as a plane mirror and a spherical mirror are due to regular reflection of light.
Based on the nature of images formed by the mirrors, the images are of two types they are:
- Real images
- Virtual Images
Real images are the images which can be captured onto a screen.The real images are formed when the light rays really meet at a point.
Example, Slide projector in a cinema hall forms an image on the screen.
Virtual images are the images which cannot be caught on a screen.
The virtual images are formed when the light ranys really do not meet at a point.
But they appear to be images formed by the meeting of light rays.
Note:
- The virtual images can be viewed with our naked eyes.
For example, the images formed due to reflection of light by a plane mirror of a dressing table and parking (convex) mirror.
Types of Mirrors
Generally the mirrors are classified into the following two types as:
- Plane mirrors
- Curved mirrors.
Generally mirrors refer to plane mirrors. But if the surface of a mirror is curved it is said to be a curved mirror.
Examples:
Concave mirror, convex mirror and Elliptical mirror etc.,
If the curvature of a mirror is a huge sphere, the mirror is said to be a spherical mirror.
Examples:
Concave mirror, convex mirror
Spherical mirrors are a special type of curved mirror.
Characteristics of Image Formed By A Plane Mirror
*The image formed by a plane mirror is unmagnified, virtual and erect.
*The image formed by a plane mirror has right-left reversal known as lateral Inversion.
*Focal length of a plane mirror is infinite.
*Power of a plane mirror is zero.
*If a plane mirror is turned by an angle, θ , the reflected ray turns by 2θ .
*The least size of a plane mirror to view an object is equal to half the size of the object.
Curved – Mirrors
A mirror that has a curved reflecting surface is said to be a curved mirror.
Spherical Mirrors
If the curvature of a mirror is a huge sphere, the curved mirror is said to be a spherical mirror.
The reflecting surface of a mirror can be curved inwards or curved outwards.
Curved mirrors and Spherical mirrors are classified into the following two types:
- Concave mirrors
- Convex mirrors.
A curved mirror or a spherical mirror whose reflecting surface is curved inward is known as a concave mirror.
Conversely, A curved mirror or a spherical mirror whose reflecting surface is outward curved is known as a convex mirror.
Terms Associated with Spherical Mirrors
*Pole – The geometric centre of the reflecting surface of a spherical mirror is its pole. It is represented by P.
*Centre of curvature – The centre of the curvature of the reflecting surface of a spherical mirror is known as centre of curvature. It is represented by C.
*Centre of curvature in a convex mirror lies behind the mirror.
*But it lies in front of the mirror in a concave mirror.
*Radius of curvature – The radius of the reflecting surface of the spherical mirror is known as radius of curvature. It is represented by R.
*Principal axis – Straight line passing through the pole and centre of curvature in a spherical mirror is known as principal axis.
*Principal focus – The reflected rays appear to come from a point on the principal axis, known as principal focus. Principal focus (F) is the point on the principal axis, where a parallel beam of light, parallel to the principal axis after reflection converges in the case of a concave mirror and appears to diverge from in the case of a convex mirror.
*Focal length – The distance between the pole and the principal focus in a spherical mirror, known as focal length and it is represented by f.
*Note: Radius of curvature is twice the focal length (R=2f). In other words, The focal length is half the radius of curvature.
*Focal plane: A plane, drawn perpendicular to the principal axis such as it passes through the principal focus is called the focal plane.
*Aperture – The diameter of the reflecting surface is known as its aperture. The size of the mirror is called its aperture. In other words It is also defined as the effective diameter of the light reflecting area of the mirror.
Image Formation by Spherical Mirrors
Rules for Construction of Ray Diagrams for Spherical Mirrors
Rule 1: An incident light ray parallel to the principal axis, passes through the principal focus or appears to pass through the principal focus after reflection.
Rule 2: An incident light ray that passes through the principal focus or appears to pass through the principal focus, travel parallel to the principal axis after reflection.
Rule 3: An incident light ray that passes through the center of curvature or appears to pass through the center of curvature, after reflection and retraces its initial path.
Rule 4: A ray incident obliquely to the principal axis towards the pole, P of the curved mirror (concave mirror and convex mirror) is reflected obliquely.
Note:
The incident and reflected rays always follow the laws of reflection at the point of incidence (P) making equal angles with the principal axis.
that passes through the center of curvature or appears to pass through the center of curvature, after reflection and retraces its initial path.
Reflection By Concave Mirrors
Incident Ray Reflected Ray Parallel to principal axis Passes through focus Passes through C Retraces its path Passes through focus parallel to principal axis Strikes the pole at an angle with principal axis Makes the same angle with the principal axis. Reflection by Convex Mirror
Incident Ray Reflected Ray Parallel to principal axis Appears to pass through focus Directed towards the focus Appears to pass parallel to principal axis Strikes the pole at an angle with principal axis Makes the same angle with principal axis Concave Mirror
A spherical mirror whose reflecting surface is curved inward is known as a concave mirror.
Terms Associated With Concave Mirror
The geometric centre of a concave mirror is called its pole.
The centre of the sphere from which the concave mirror was cut is called the centre of curvature of the concave mirror.
The centre of curvature of the reflecting surface of a concave mirror is called the centre of curvature of the concave mirror.
The distance from any point on the concave mirror to its center of curvature is called the radius of curvature of the concave mirror.
An imaginary line passing through the center of curvature and the pole of the concave mirror is called the principal axis of the concave mirror.
The area of a concave mirror that is exposed to incident light is called the aperture of the concave mirror.
The length along the principal axis from the pole to the principal focus is called the focal length of the concave mirror.
If an object is placed close to a concave mirror such that the distance between the mirror and the object is less than its focal length, then a magnified and virtual image is formed.
This property of the concave mirror is used in many applications such as a dentist mirror to view the inner parts of the mouth clearly and a shaving mirror.
Concave mirrors converge the light incident on them and hence are called converging mirrors.
Image Formation by Concave Mirror
Location of an image of an object formed by a concave mirror by drawing the ray diagrams.
*We can locate the image of an object formed by a concave mirror by drawing the ray diagrams.
*The intersecting point of at least two reflections will give the position of image of the point object.
*The following rays can be used to draw the ray diagrams.
*A ray parallel to the principal axis of a concave mirror.
*A ray passing through the focus of the concave mirror
*A ray which is passing through the centre of curvature of a concave mirror
*A ray incident obliquely to the principal axis on a concave mirror.
Rules for Drawing Ray Diagrams in Spherical Concave Mirrors
A ray parallel to the principal axis of a concave mirror.
*A ray parallel to the principal axis of the concave mirror reflects through its focus.
A ray passing through the focus of the concave mirror.
*A ray passing through the focus of the concave mirror reflects parallel to the principal axis.
A ray which is passing through the centre of curvature of a concave mirror
*A ray which is passing through the centre of curvature of a concave mirror reflects back on the same path.
*A ray incident obliquely to the principal axis on a concave mirror.
A ray when incident obliquely to the principal axis on a concave mirror also reflects obliquely.
Concave Mirrors – Ray Diagrams
Depending on the position of the object in front of the concave mirror, the position, size and the nature of the image varies.
We can represent the images formed by a Concave Mirror using Ray Diagrams.
Object at infinity
A real, inverted, highly diminished image is formed at the focus, F, in front of the concave mirror.
Object beyond C
A real, inverted, diminished image is formed between C and F, in front of the concave mirror.
Object at C
A real, inverted, same sized image is formed at C, in front of the concave mirror.
Object between C and F
A real, inverted, enlarged image is formed beyond C, in front of the concave mirror.
Object at F
A real, inverted, highly enlarged image is formed at infinity, in front of the concave mirror.
Object between F and P
A virtual, erect and enlarged image is formed behind the concave mirror.
Image Formation by a Concave Mirror
Object Location Image Location Nature of Image Infinity At F Real, InvertedHighly DiminishedMagnification<<1 Beyond C Beyond F and C Real, InvertedDiminishedMagnification<1 At C At C Real, InvertedEqual to size of objectMagnification=1 Between C and F Beyond C Real, InvertedMagnifiedMagnification>1 At F Infinity Real, InvertedHighly MagnifiedMagnification>>1 Between F and P Behind the mirror Virtual, ErectMagnifiedMagnification>1 Uses of Concave Mirrors
- Concave mirrors are used as shaving mirrors to see a larger image of the face.
- Dentists use concave mirrors to view a magnified view of the interior parts of the mouth.
- ENT doctors use them for examining the internal parts of the ear, nose and throat.
- They are used as reflectors in the headlights of vehicles, searchlights and in torch lights to produce a strong parallel beam of light.
- Huge concave mirrors are used to focus sunlight to produce heat in solar furnaces.
Convex Mirror
A spherical mirror whose reflecting surface is curved outward is known as a convex mirror.
Terms Associated With Convex Mirror
The geometric centre of the curvature of the convex mirror is called its pole.
The centre of curvature of the reflecting surface of a convex mirror is called the centre of curvature of the convex mirror.
The distance from any point on the reflecting surface of a convex mirror to its centre of curvature is called radius of curvature of the convex mirror.
An imaginary line passing through the centre of curvature and the pole of the convex mirror is called the principal axis of the convex mirror.
The reflected rays, when projected backwards, appear to meet at a point on the principal axis. This point is called the principal focus. The length along the principal axis from the pole to the principal focus is called the focal length of the concave mirror.
The area of a convex mirror that is exposed to incident light is called the aperture of the convex mirror.
If the aperture of a convex mirror is small, then Convex mirrors, such as the rear view mirrors of cars and bikes, always form erect, virtual, and diminished images.
The location of the object does not affect the characteristics of the image formed by a convex mirror.
When an object approaches a convex mirror, the image formed by the mirror also approaches the mirror, but not proportionately. Because of this it is mentioned as “Objects seen in the mirror are closer than they appear” on the outside rear view mirrors of vehicles.
Image Formation by Concave Mirror
ray diagrams –
- We can locate the image of an object formed by drawing a ray diagram.
- The intersecting point of at least two reflections will give the position of image of the point object.
The two rays that can be used to draw the ray diagram are:
- A ray parallel to the principal axis.
- A ray parallel to the principal axis reflects
- It passes through the focus in case of a concave mirror.
- A ray parallel to the principal axis. On reflection it appears to diverge from principal focus after reflection in case of a convex mirror.
- A ray passing through the focus of the concave mirror. On reflection it becomes parallel to the principal axis due to reflection.
- A ray directed towards the focus of convex mirrors. On reflection it becomes parallel to the principal axis due to reflection.
- A ray which is passing through the centre of curvature of a concave mirror. It reflects back on the same path.
- A ray which is directed towards the centre of curvature of a convex mirror. It reflects back on the same path.
- A ray when incident obliquely to the principal axis on a concave x mirror is also reflected obliquely.
- A ray when incident obliquely to the principal axis on a convex mirror is also reflected obliquely.
Reflection by Convex Mirror
Incident Ray Reflected Ray Parallel to principal axis Appears to pass through focus Directed towards the focus Appears to pass parallel to principal axis Strikes the pole at an angle with principal axis Makes the same angle with principal axis Image Formed By A Convex Mirror
Irrespective of the position of the object, a virtual, erect and diminished image is formed between F and P, behind the convex mirror.
Uses of Convex Mirrors
Convex mirrors are used as:
- rear view mirrors in automobiles and in ATM centres as it covers a wide area behind the driver.
- reflectors in street light bulbs as it diverges light rays over a wide area.
- Rear view mirrors of vehicles and the ones used.
Sign Convention for Spherical Mirrors
- Object is always considered at the left side of the mirror
- Distances measured in the direction of the incident ray are taken as positive.
- Distances measured in the direction opposite to that of the incident rays are taken as negative.
- All distances are measured from the pole of the mirror.
- Distances measured along the y-axis above the principal axis are taken as positive.
- Distances measured along the y-axis below the principal axis are taken as negative.
Table Showing Sign Convention
Type of Mirror Object Distance, u Image Distance, v Focal length, f Radius of Curvature, R Height of the Object, hO Height of the Image, hi Real Virtual Real Virtual Concave mirror –Ve –Ve +Ve –Ve –Ve +Ve –Ve +Ve Convex mirror –Ve Virtual image +Ve +Ve +Ve +Ve Virtual image +Ve Mirror Formula
The relation between the focal length (f), object distance (u) and the image distance (v) is given by:
Magnification
The ratio of the height of the image in a spherical mirror, to the height of the object is called magnification (m)
Magnification,m = Height of Image, HHeight of Object, i= Image Distance, HObject Distance, i
The distance from the principal focus to the pole of the mirror is the focal length of the mirror and is equal to half the radius of curvature, which is the distance between the centre of curvature and the pole.
For a real image object distance (u) and the image distance (v) are negative and the magnification is negative.
If the magnification of an image is negative it does mean that the image is real and inverted.
On the other hand for a virtual image object distance (u) is negative and image distance (v) is positive and hence the magnification is positive, i.e., the image is erect.
If the magnification of an image is positive it does mean that the image is virtual and erect.
- If the magnification is less than 1 The image formed is diminished in size.
- If the magnification is more than 1 The image formed is magnified in size.
- If the magnification is equal to 1 The image formed is equal to the object in size.
Convex mirrors diverge the light incident on them and hence they are called the diverging mirrors.
Due to this they always form diminished, virtual and erect images irrespective of the position of the object in front of them.
Thus, the magnification caused by these mirrors is always less than one.
The field of view for a convex mirror is greater than that for a plane mirror, the aperture being the same.
Hence, convex mirrors are used as rear-view mirrors in vehicles.
It is also installed behind automated teller machines as a security measure.
The field of view for a convex mirror is greater than that for a plane mirror, the aperture being the same.
Hence, convex mirrors are used as rear-view mirrors in vehicles. It is also installed behind automated teller machines as a security measure.
The images formed by convex mirrors are always diminished, virtual and erect, irrespective of the position of the object.
Differences Between Convex Mirror and Concave Mirror
Convex Mirror Concave Mirror Convex mirror is curved outwards. 1. Concave mirror is curved inwards. The focal point of the convex mirror is behind the mirror. 2. The focal point of the concave mirror is in front of the mirror. In convex mirrors the image is always virtual, upright and smaller than the object. 3. In the case of concave mirrors different types of images are formed on different locations of the object. The image is upside down (inverted) and far away but if we bring the object close to the mirror then the image will be larger and upright. Convex mirrors are used in cars (as passenger-side mirrors since they provide upright and wide view), they are also used in camera phones, for safety measures there are also used in roads and driveways.Besides these convex mirrors are found in many hospitals, schools etc. as hallway safety mirrors. 4. Concave mirrors are used in telescopes. These are also used as make up and shaving mirrors since these provide larger images.
Besides these concave mirrors are used by dentists and also used in headlights of cars, solar devices, satellite dishes etc.Refraction Of Light At Plane Surfaces
Introduction
Light bends while traveling from one medium to another. Since the refraction of light occurs at the surface joining two media, the refraction is a surface phenomenon.
The bending of light when it travels from one medium into another is called refraction of light.
The reason for refraction of light is the change in speed of light.
The speed of light in an optically rarer medium is more than that in an optically denser medium.
- Light rays passing from rarer to denser medium bends towards the normal. This makes the angle of incidence (angle between the incident ray and the normal at the point of incidence) more than that of the angle of refraction (angle between the normal and the refracted ray).
- Light rays passing from denser to rarer medium bends away from the normal. This makes the angle of incidence (angle between the incident ray and the normal at the point of incidence) less than that of the angle of refraction (angle between the normal and the refracted ray).
- The extent to which a light ray bends depends on the refrangibility of the ray with respect to the medium.
- In other words, the extent to which a light ray bends depends on the refractive index of the respective medium.
- The ratio of velocity of light in vacuum to that in a medium is termed as the absolute refractive index (m) of the medium or simply termed as the refractive index of the medium.
- Refractive index (m) of the medium is the measure of the ability of light to get bent in the given medium.
- Measuring the speed of light is difficult.
- We can determine the refractive index using Snell’s law
- According to Snell’s law,
- The refraction of light obeys the following two laws:
- The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
- The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. This constant is called the index of refraction or refractive index.
Mathematically, (sin i)/(sin r)= (n2/n1) (Or)
(sin i)/(sin r)= (1n2), where (1n2), is the refractive index of the medium 2, in which the refracted ray travels, with respect to medium 1, in which the incident ray travels.
This law is credited to Willebrord Snell and is, therefore, called Snell’s law.
If wng is the refractive index of glass w.r.t. water, ang be the refractive index of glass w.r.t. air and anw be the refractive index of water w.r.t. air ,then
wng= ang/anw
- If the light ray retraces its path while traveling from denser to rarer, the angle of incidence is lesser than that of the refraction. This is the principle of reversibility.
The extent to which a light ray bends depends on the refrangibility of the ray with respect to the medium.
The ratio of velocity of light in vacuum to that in a medium is termed as the absolute refractive index (m) of the medium. Absolute refractive index (m) of the medium is the measure of the ability of light to get bent in the given medium.
Measuring the speed of light is difficult.
We can determine the refractive index using Snell’s law
According to Snell’s law,
Refraction of Light At A plane Surface
The bottom of a water glass appears to rise upwards when viewed normally. This is due to the vertical shift of the bottom of the glass, which takes place because of refraction.
Refraction of Light At Glass Slab
When a light ray, incident at an angle, passes through a glass slab, the emergent ray shifts laterally, known as lateral shift.
The lateral shift depends on the thickness and refractive index of the glass slab.
If the angle of incidence increases gradually, the angle of refraction also increases.
But, at a particular angle of incidence in the denser medium, the refracted ray emerges along the surface. That particular angle is known as the critical angle.
If the angle of incidence is greater than the critical angle, the ray undergoes Total Internal Reflection.
The formation of Mirages in deserts is due to total internal reflection of light.
n=cv
n=(Speed of light in vacuum)/( speed of light in the medium)
As light travels from one medium to another, the frequency of light does not change.
Lenses
A lens is a piece of transparent optical material with one or two curved surfaces to refract light rays.
The simplest lens has two spherical surfaces close enough together that we can neglect the distance between them. Such a lens is called a thin lens.
The two common types of lenses are Converging lens or Convex lens.
It should be noted that, if the above lenses are surrounded by a material with a refractive index greater than that of the lens, the convex lens gets converted into a concave lens and vice versa.
A lens may converge or diverge light rays to form an image.
Types of Lenses
A bi-convex lens is one with a surface that is bulged outwards on both the sides. It is generally referred to as a convex lens.
Another type of lens is a bi-concave lens that has two inward bent surfaces. It is generally referred to as a concave lens.
A Plano-convex lens has a convex surface on one side and a plane surface on the other.
A Plano-concave lens is the one that has a concave surface on one side and a plane surface on the other.
A concavo-convex lens has a concave surface on one side and a convex surface on the other.
Convex and concave lenses are important as they are more commonly used than the other types of lenses.
Terms Used for Lens
Center of Curvature: The center of the imaginary glass sphere of which the lens is a part, is called center of curvature.
Principal Axis: An imaginary line joining the centers of curvature of the two spheres, of which lens is a part, is called Principal Axis.
Optic Center: A point within the lens, where a line drawn through the diameter of lens meets the principal axis, is called the optic center.
Principal Focus for Convex Lens: It is a point on the principal axis of a convex lens, where parallel beams of light rays, traveling parallel to the principal axis, after passing through the lens actually meet.
Principal Focus for Concave Lens: It is a point on the principal axis of a concave lens, from where a parallel beam of light rays, traveling parallel to the principal axis, after passing through the lens, appears to come.
Focal Length: The distance between principal focus and optical centre is called focal length.
Aperture: The effective diameter of the lens through which refraction takes place is called aperture of lens.
Optic centre is a point on the axis of a lens such that any light ray passing through this point emerges without refraction.
• Principal focus is a point on the axis of a lens.
• Principal focus is also known as the focal point.
Spherical Lenses
Convex Lense
A lens in which both the surfaces are convex, is known as convex lens.
Since the convex lens converges the light incident on it. It is called the converging lens.
The convex lenses form different types of images depending on its relative position with respect to the position of the object in front of them.
Thus, the magnification produced by these lenses varies.
Concave Lense
A lens in which both the surfaces are concave, is known as a concave lens.
Since the concave lens diverges the light incident on it. It is called the diverging lens.
Due to this the concave lenses always form diminished, virtual and erect images irrespective of the position of the object in front of them.
Thus, the magnification produced by these lenses is always less than one.
Image Formation by Refraction Of Light Through Spherical Lenses
Behaviour of Light Rays Propagating Through a Convex Lens
Rules for Construction of Ray Diagrams for Convex Lens
Rule 1: All rays parallel to the
principal axis of a convex lens passes through the principal focus after refraction.
Rule 2: A ray of light passing through the focus of a convex lens becomes parallel to the principal axis after refraction.
Rule 3: A ray of light passing through the optical center of a convex lens passes un deviated after refraction.
Rule 4:
Note: A convex and a concave lens can be supposed to be made-up of prisms.
Image Formation by a Convex Lens
Object Location Image Location Nature of Image Uses Infinity At F2 • Real• Inverted• Highly Diminished Telescopes Beyond 2F1 Between F2 and 2F2 • Real• Inverted• Diminished In a camera, In eye while reading At 2F1 At 2F2 • Real• Inverted• Equal to size of object Photocopier Between 2F1 and F1 Beyond 2F2 • Real• Inverted• Magnified Projector, Microscope objective At F1 Infinity • Real• Inverted• Highly Magnified Spotlights Between F and O On the same side of lens as the object • Virtual• Erect• Magnified Magnifying glass, eye lenses spectacles for short distances. Concave Lens:
A lens, in which both the surfaces are concave, is known as a concave lens.
An image formed by a concave lens is always diminished due to the divergence of rays. This is why concave lenses are widely used to correct eye defects such as myopia.
A concave lens is also known as a diverging, reducing, negative and myopic or minus lens.
Behaviour of Light Rays Propagating Through a Concave Lens.
Behaviour of Light Rays Propagating Through a Concave Lens
Rules for Construction of Ray Diagrams for Concave Lens
Rule 1: All rays parallel to the principal axis of a concave lens diverge such that they are coming from the principal focus after refraction.
Rule 2: A ray of light directed towards the focus of a concave lens becomes parallel to the principal axis after refraction.
Rule 3: A ray of light passing through the optical center of a concave lens passes un deviated.
Note: A convex and a concave lens can be supposed to be made-up of prisms.
The lens formula defines the relationship between the focal length of the lens (f), the distance of the object from the optic center (u) and the distance of the image from the optic center (v):
Location and Characteristic of the Images Formed by a Concave Lens
Sign convention for spherical lenses:
- All distances on the principal axis are measured from the optic center of the lens.
- All distances measured above the principal axis are taken as positive. Thus, height of an object and that of an erect image are positive and all distances measured below the principal axis are taken as negative.
- The distances measured in the direction of the incident light are taken as positive (+)
- The distances measured in the direction opposite to that of the incident light are taken as negative (-).
Table Showing Sign Convention In Concave & Convex Mirrors & Lenses
Type of Mirror Object Distance, u Image Distance, v Focal length, f Radius of Curvature, R = f/2Power = 1/P Height of the Object Height of the Image Real Virtual Real, Inverted Virtual, Erect Concave Mirror -Ve +Ve -Ve -Ve +Ve -Ve +Ve Convex Mirror -Ve +Ve -Ve +Ve +Ve -Ve +Ve Convex Lens -Ve +Ve -Ve +Ve +Ve -Ve +Ve Concave Lens -Ve +Ve -Ve -Ve +Ve -Ve +Ve Lens Formula and Sign Conventions
Magnification of lens (m)
Magnification is the ratio of the image size to the object size. It is also measured as the ratio of image distance to object distance.
m = Size of the image / Size of Object
Or
m = Image distance / Object distance
If m = 1; image size = object size
If m > 1: image size > object size
If m < 1: image size < object size
Power of Lens (P)
• The converging or diverging capacity of a lens is ascertained by its power
• Power of a lens is the reciprocal of its focal length expressed in meter.
P=1f
( measured in meters).
• SI Unit of power of a lens is dioptre (D).
• Power of a convex lens is positive and that of a concave lens is negative.
Differences Between Convex Lens and Concave Lens:
Formulae:
- Magnification = Image distance / Object distance
m=vu
- Magnification = Image Height / Object Height
- Image distance / Object distance = Image Height / Object Height
- If magnification is <1, the image is Diminished or minimised or shrunk.
- If magnification= 1, the size of the image is equal to the size of the object.
- If magnification is >1, the image is Magnified or enlarged or bigger.
- If magnification is <1, the image is Diminished or Shrunk or Smsller.
- ⇒ m=vu ⇒ u=vm
- ⇒ m=vu ⇒ v=mu
- ⇒ 1f=1v1(vm) ⇒ 1f=1v-mv ⇒ 1f=1-mv
- ⇒ f=v1-m
- ⇒ f=mu1-m
- ⇒ Power of lens=1Focal Length
- ⇒ Power of lens x Focal Length =1
- ⇒ P=1f
For Spherical Mirrors :
P= 2R=1f=1v+ 1u=1-mv =(m-1)mu-(m-1)-mu
For Spherical Lenses :
P= 2R=1f= 1v-1u=1-mv = 1-mmu
- For Spherical Mirrors :
- R2=f= uvu+v
- 2R=1f= 1v + 1u
- m=-vu
- If m > 1, Image is magnified
- If m < 1, Image is diminished
- If m = 1, Image is Equal to size of object
- Sign of magnification, m is negative for real image.
- Sign of magnification, m is positive for virtual images.
- The number indicates how many times magnification.
- Where the sign indicates whether the image is virtual erect or real inverted.
- v=-mu
- m=hih0
- For Spherical Lenses :
- R2=f= uvu-v
- 2R=1f= 1v – 1u
- m=vu
- m=hih0
- If m > 1, Image is magnified
- If m < 1, Image is diminished
- If m = 1, Image is Equal to size of object
- Sign of magnification, m is negative for a real, Inverted image.
- Sign of magnification, m is positive for virtual, Erect image.
- The number indicates how many times magnification.
- Where the sign indicates whether the image is virtual erect or real inverted.
- P= 2R=1-mv = 1-mmu
- 1f= 1v+1u
- If m is Negative image is real
- If m is Positive image is Virtual
- If height of the image is equal to height of the object m = 1, that is image height is equal to the object height
- If height of the image is greater than height of the object, then m > 1. That is, the image is enlarged.
- If height of the image is less than height of the object then m<1, That is, the image is diminished.
- Magnification of a Plane mirror is always +1.
- Positive Sign of the magnification indicates Virtual, erect image.
- Negative Sign of the magnification indicates Real , Inverted image.
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The Human Eye and the Colourful World | Study
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Electric Current | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Electricity Electricity is a branch of physics that deals with the study of phenomena associated with stationary or moving electric charges. Therefore, the various manifestations of electricity are the result of the accumulation or motion of electrons. Electricity is classified into two types. They are Static… readmore
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Electricity
Electricity is a branch of physics that deals with the study of phenomena associated with stationary or moving electric charges.
Therefore, the various manifestations of electricity are the result of the accumulation or motion of electrons.
Electricity is classified into two types. They are Static Electricity and Current Electricity. (Scroll down to continue …)
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ELECTRICITY
V-Lab Book Slides V-Class Quiz Solutions Resources of Electricity Static Electricity
Static Electricity is a branch of physics that deals with the study of phenomena associated with stationary electric charges.
Current Electricity.
Current Electricity is a branch of physics that deals with the study of phenomena associated with moving electric charges.
Electric Charge
Electric charge is a fundamental property of matter.
Though we can’t say what is charge with certainty, we can study the properties and behaviour of charge.
Charge is defined as the property associated with matter due to which it produces and experiences electrical and magnetic effects.
The electric charge is caused by the elementary particles, electrons and protons.
Protons possess positive charge, electrons possess negative charge and Neutrons do not possess any charge.
Laws of Electric Charges:
Similar electric charges repel each other
Dissimilar (opposite) electric charges attract each other.
Conductors And Insulators
Conductors are the materials in which electrons move freely.
Example: All metals.
Insulators are the materials which do not have any free electrons to move.
Example: Wood and plastic.
Electric Circuit:
The path of flow of current is known as electric circuit.
Electric Potential Energy
Electric potential energy of a group of charges is defined as the amount of work done in bringing the charges to their respective positions in the system.
Electric Potential At A Point
The electric potential at a point, in an electric field, is defined as the amount of work done in moving a unit + ve charge from infinity to that point, without acceleration or without a change in K.E., against the electric force due to the electric field.
The potential at a point is given by the expression V = W/q
The S.I Unit of potential is mathematically written as 1 volt = 1 joule/1 coulomb.
Potential is a scalar quantity, therefore it is added algebraically.
For a positively charged body, potential is positive and for a negatively charged body potential is negative.
Electric current flows through a conductor only if there is a potential difference across its ends.
Work done in moving a charge in the electric field of another charge is given by:
W = Vq
More is the charge on a body, the more is its potential due to it.
Electric current flows through a conductor only if there is a potential difference across its ends.
Positive charge flows from a body at higher potential to a body at lower potential and negative charge flows from a body at a lower potential to a body at higher potential.
Potential difference
The work done in moving a unit positive charge from one point to another is known as Potential Difference between those points.
Example
The work done in moving a unit positive charge from point A to another point B is known as Potential Difference between the points A and B.
SI Unit: volt
The unit of potential difference is volt (V).
Volt
In other words, Volt is defined as the potential difference between two points, if 1 Joule of work is done in moving 1 coulomb charge from one point to another.
Potential difference between two points across a conductor is measured by using a voltmeter.
Voltmeter is always connected in parallel to the points across which potential difference is to be measured.
Battery:
Battery is an arrangement that creates a constant potential difference between its terminals.
Battery is defined as a combination of a number of cells in series.
Electric Current
The literary meaning of Electric Current is flow of electric charge.
Definition
Electric current is defined as the amount of charge passing a cross section of conductor per a unit time (second in SI Units).
Electric current is expressed mathematically in terms of rate of flow of charges as:
Electric Current =(Net Charge, Q)/(Time,t)
i =n.et , Where n = number of electrons, e = charge of one electron, t= time taken to flow,
Q = charge through the crosssection of the conductor.
The SI unit of electric current is Ampere (A).
- Direction of electric current is the same as the direction of positive charges But it is opposite to the direction of flow of negative charges.
Ohm’s Law
Potential difference, V between two points at a constant temperature is directly proportional to the current, I.
V ∝ I
⇒ V = lR
Where, R is a constant termed as Electric Resistance.
The SI unit of resistance is ohm (Ω)
Q.1. State Ohm’s law. How can it be verified?
Answer: It states “Physical conditions’ remaining same, the current flowing through a conductor is directly proportional to the potential difference across its two ends”.
i.e., V∞ I
or
V = IR, where, R is the constant of proportionality.
R is called the electrical resistance or resistance of the conductor.
Verification:
V∞ I or V = IR, where the constant of proportionality R is called the electrical resistance or resistance of the conductor.
The following circuit diagram is used to verify Ohm’s law.
Take a few cells; connect one cell across a nichrome wire AB, along with an ammeter and a voltmeter as shown in figure. Note the voltage and the current from the voltmeter and the
ammeter.
Now, connect two cells and again note the voltage and the current. Repeat the procedure for three cells and four cells. Calculate the ratio for each set.
You will find the ratio is nearly the same in all cases. If a graph of current against voltage is plotted, it will turn to be a straight line as shown in figure. This shows that the current is directly proportional to the potential difference.
Laws of Electric Resistance
Or
Factors Affecting Resistance
Resistance is directly proportional to length of conductor.
- Resistance is inversely proportional to the area of cross-section.
- Resistance is directly proportional to the temperature.
- Depends on the nature of the material. This is determined by the resistivity of material.
Laws of Electric Resistance
The resistance of any substance depends on the following factors,
Length of the substance.
Cross sectional area of the substance.
The nature of material of the substance.
Temperature of the substance.
There are mainly four (4) laws of resistance from which the resistivity or specific resistance of any substance can easily be determined.
The resistance of a substance is directly proportional to the length of the substance. Electric resistance, R of a substance is written as
Where L is the length of the substance.
The resistance of a substance is inversely proportional to the cross-sectional area of the substance. Electrical resistance R of a substance is
Where A is the cross-sectional area of the substance.
Resistivity
Combining these two laws we get,
Where, ρ (rho) is the proportionality constant and known as resistivity or specific resistance of the material of the conductor or substance.
Now if we put L = 1 and A = 1 in the equation, we get, R = ρ.
That means resistance of a material of unit length having unit cross – sectional area is equal to its resistivity or specific resistance.
Resistivity of a material can alternatively be defined as the electrical resistance between opposite faces of a cube of unit volume of that material.
Unit of Resistivity
The unit of resistivity can be easily determined form its equation
The unit of resistivity is Ω – m in the MKS system and Ω – cm in the CGS system and 1 Ω – m = 100 Ω – cm.
Resistivity
Resistivity is the property of the material. It does depend on the length and area of the conductor.
Resistance = (Resistivity) x (Length of Conductor) / (Cross Sectional Area)
The SI unit of resistivity is ohm-metre.
- Resistivity of metals varies from 10-8 to 10-6.
- Resistivity of insulators varies from 1012 to 1017
- Copper and aluminium are used in electrical transmission due to their low resistivity.
Net Resistance in Resistors In Series
When several resistors are joined in series, the resistance of the combination Rs equals the sum of their individual resistances, R1, R2, R3
It is mathematically expressed as: RS = R1 + R2 + R3
Thus greater than any individual resistance.
Derivation of Net Resistance of Resistors In Series
When two or more resistors are joined in series, then their total resistance is given by the formula:
⇒ RS = R1 + R2 + R3
The current will remain the same through all resistors.
Total voltage is given by: V = V1 + V2 + V3
Voltage across each resistor is given as: V1 = IR1, V2 = IR2, V3 = IR3
⇒ V = V1 + V2 + V3
But Total Voltage V = I × R, Here I = Current in electric circuit and R = Net Resistance in the circuit.
⇒ IR = IR1 + IR2 + IR3 ⇒ IR = I(R1 + R2 + R3) ⇒ R = R1 + R2 + R3
Resistors In Parallel
The reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
(V/Rp) = (V/R1) + (V/R2) + (V/R3)
Derivation of Net Resistance of Resistors In Parallel
In this case, voltage is the same across each resistor and is equal to applied voltage.
Total current is given as:
I = I1 + I2 + I3
It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.
I = I1 + I2 + I3 ————– (i)
Let Rp be the equivalent resistance of the parallel combination of resistors.
By applying Ohm’s law to the parallel combination of resistors, we have: I = V/Rp ————– (ii)
On applying Ohm’s law to each resistor, we have
I1= V /R1; I2= V /R2; and I3= V /R3 —————– (iii)
From Eqs. (ii) to (iii), we have
(V/Rp) = (V/R1) + (V/R2) + (V/R3)
⇒ V(1/Rp) = V[(1/R1) + (1/R2) + (1/R3)]
⇒ (1/Rp) = [(1/R1) + (1/R2) + (1/R3)] ————– ()
Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
Advantages of Parallel Combination over Series Combination:
If one component fails in series, then the complete circuit is broken and no component can work properly. Different appliances need different current, this can be met through parallel.
Heating effects of Electric Current
When charge Q moves against the potential difference V in time t, the amount of work is given by-
Joule’s Law of Heating
- Heat produced in a resistor is directly proportional to square root of current.
- It is also directly proportional to resistance for a given current.
- Also, directly proportional to time
⇒ H = l2 Rt
Filament of an electric bulb is made up of tungsten because it has a very high melting point and also does not oxidise readily at a high temperature.
Electric fuse is a safety device to protect the electrical appliance from short circuits.
Electric Power
The rate at which electric energy is dissipated or consumed in an electric current. The SI unit of power is Watt.
⇒ P = Vl
⇒ P = l2 R = V2/R
The commercial unit of electric energy is kilowatt hour (KWh).
Formulae:
Cylindrical Conductor:
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Magnetic Effects Of Electric Current | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Content Study Tools MAGNETIC EFFECTS OF ELECTRIC CURRENT | ELECTROMAGNETISM | FULL NOTES Chapter At A Glance Interactive Notes E-Book L-Plan Solutions Assessment (Quiz Time) Assignment (Worksheet/QB) Summary Interactive Notes Summary L-Plan Q-Bank E-Book Assessment V-Lab Video Key Assignment Magnetic Effects of… readmore
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MAGNETIC EFFECTS OF ELECTRIC CURRENT | ELECTROMAGNETISM | FULL NOTES
Chapter At A Glance
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Interactive Notes Summary
Magnetic Effects of Electric Current – Electromagnetism
- Electromagnet
- Solenoid
- Electric Motor
Electromagnetic Induction
Electric Effects of Changing Magnetic Fields –
- Electric generators
- Transformer
Electricity and magnetism are linked to each other.
Electric current through conducting wire produces a magnetic field known as electromagnetic induction.
In other words, Generation of magnetic fields due to electric current is known as electromagnetic induction.
Relative motion of a conductor with respect to a magnetic field generates electricity in it.
Magnetic Effects of Electric Current
Accidentally, Oersted discovered that a magnetic field is produced around a current carrying conductor.
Oersted Experiment
Hans Christian Oersted, one of the leading scientists of the 19th
century, played a crucial role in understanding electromagnetism.
In 1820 Oersted accidentally discovered that a compass needle got deflected when an electric current passed through a metallic wire placed nearby.
Through this observation Oersted showed that electricity and magnetism were related phenomena.
His research later created technologies such as the radio, television and fibre optics.
The unit of magnetic field strength is named the Oersted in his honour.
Magnetic Field And Magnetic Lines
The iron filings arrange themselves in a pattern when they are sprinkled around a magnet.
Why do the iron filings arrange in such a pattern?
What does this pattern demonstrate?
The iron filings experience a magnetic force in its surroundings due to the magnetic field.
The force makes iron filings to arrange in a pattern.
The region surrounding a magnet, in which the force of the magnet can be detected, is known as a magnetic field.
The lines along which the iron filings align themselves represent the lines of magnetic field or magnetic field lines.
Are there other ways of obtaining magnetic field lines around a bar magnet?
Yes, we can draw the field lines of a bar magnet using a magnetic compass.
Magnetic Compass
- Magnetic compass is a device used to find the Geographic south and north direction.
- Compass needle gets deflected when brought near a magnet.
- The ends of the compass needle point approximately towards Geographic north and south directions.
- The end pointing towards Geographic north is called the north seeking pole or north pole.
- The other end that points towards south is called south seeking pole or south pole.
- Like magnetic poles repel, while unlike magnetic poles attract each other.
Magnetic field
A magnetic field exists in the region surrounding a magnet, in which the force of the magnet can be detected.
The region surrounding a magnet, in which the force of the magnet can be detected, is said to have a magnetic field.
Magnetic field has both direction and magnitude. Therefore the magnetic field is a vector quantity.
The direction of the magnetic field is taken to be the direction in which the north pole of the compass needle moves inside it.
Therefore it is taken by convention that the field lines emerge from the north pole and merge at the south pole.
Inside the magnet, the direction of field lines is from its south pole to its
north pole.
Thus the magnetic field lines are closed curves.
The relative strength of the magnetic field is shown by the degree of
closeness of the field lines.
The field is stronger, that is, the force acting on the pole of another magnet placed is greater where the field lines are crowded.
No two field-lines are found to cross each other.
If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible.
Magnetic Field lines
- A magnetic field line is the path along which a hypothetical free north pole would tend to move.
- Field lines are used to represent a magnetic field.
- The direction of the magnetic field at a point is given by the direction that a north pole placed at that point would take.
- Field lines are shown closer together where the magnetic field is greater.
MAGNETIC FIELD DUE TO A CURRENT-CARRYING CONDUCTOR
A conductor carrying an electric current has a magnetic field associated with it.
The pattern of the magnetic field around a conductor due to an electric current flowing through it depends on the shape of the conductor.
- Straight Current Carrying Conductor
- Circular loop
- Coil
- Electromagnetic Induction By A Coil
- Solenoid
- Electromagnet
MAGNETIC FIELD DUE TO A STRAIGHT CURRENT-CARRYING
CONDUCTOR
Take a battery (12 V), a variable resistance (or a rheostat), an ammeter (0–5 A), a plug key, connecting wires and a long straight thick copper wire.
Insert the thick wire through the centre, normal to the plane of a rectangular cardboard.
Take care that the cardboard is fixed and does not slide up or down.
Connect the copper wire vertically between thepoints X and Y, as shown in Fig. 13.6 (a), in series with the battery, a plug and key.
Sprinkle some iron filings uniformly on the cardboard. (You may use a salt sprinkler for this purpose.)
Keep the variable of the rheostat at a fixed position and note the current through the ammeter.
Close the key so that a current flows through the wire. Ensure that the copper wire placed between the points X and Y remains vertically
straight.
Gently tap the cardboard a few times. Observe The pattern of the iron filings. You would find that the iron filings align themselves showing a pattern of concentric circles around the copper wire.
What do these concentric circles represent?
They represent the magnetic field lines.
How can the direction of the magnetic field be found? Place a compass at a point (say P) over a circle.
Observe the direction of the needle.
The direction of the north pole of the compass needle would give the direction of the field lines produced by the electric current through the straight wire at point P. Show the direction by an arrow.
Does the direction of magnetic field lines get reversed if the direction of current through the straight copper wire is reversed? Check it out.
Finding Direction of Magnetic Field
Right Hand Thumb Rule Or Right Hand Grip Rule
Imagine that you are holding a current-carrying straight conductor in your right hand such that the thumb points towards the direction of current.
Then your fingers will wrap around the conductor in the direction of the field lines of the magnetic field, as shown in Figure known as the right-hand thumb rule*.
The field lines about the wire consist of a series of concentric circles whose direction is given by the right-hand rule.
Right Hand Thumb Rule
Right hand thumb rule states that if we hold the conductor in the right hand such that the thumb points in the direction of electric current, then the direction in which the fingers curl gives the direction of the magnetic field
If we point the thumb downwards in the direction of the current, the magnetic field would be represented by the curled fingers as the circles around the conductor.
So, if it is viewed from the above plane these field lines will be clockwise circles, but the direction of the magnetic field at any point on these circular magnetic lines is in the direction of the tangent drawn to the circular magnetic lines at the desired points.
Example:
A current through a horizontal power line flows in an east to west direction. What is the direction of the magnetic field at a point directly below it and at a point directly above it?
Solution
The current is in the east-west direction. Applying the right-hand thumb rule, we get that the magnetic field (at any point below or above the wire) turns clockwise in a plane perpendicular to the wire, when viewed from the east end, and anti-clockwise, when viewed from the west end.
Maxwell’s Cork-Screw Rule:
Maxwell’ cork screw rule is also known as maxwell’s right hand thumb rule Maxwell’s right hand thumb rule states that, if the head of a cork-Screw is rotated such that the tip of the screw advances in the direction of electric current, then the direction of rotation of the head of the screw represents the direction of the magnetic field around the conductor.
A magnetic field caused by a current-carrying conductor consists of sets of concentric lines of force. The direction of the magnetic field lines depends on the direction of the current passed through the conductor.
Example 13.1
A current through a horizontal power line flows in east to west
direction. What is the direction of magnetic field at a point directly
below it and at a point directly above it?
Solution
The current is in the east-west direction. Applying the right-hand
thumb rule, we get that the magnetic field (at any point below or
above the wire) turns clockwise in a plane perpendicular to the wire,
when viewed from the east end, and anti-clockwise, when viewed
from the west end.
Clock-S Rule
Clock-S rule is a rule which helps us to find the formation of magnetic South Pole due to electromagnetic induction in a current carrying conducting coil.
According to clocks rule if one face of a current carrying conducting coil is placed such that one face of the coil is faced to us and current is moving in the clockwise direction with respect to us then the face of the coil which is faced to us becomes as a magnetic south pole and the other face behaves as the north magnetic pole.
A current carrying conductor in the form of a rectangular loop behaves like a magnet and when suspended in an external magnetic field experiences force.
*SNOW Rule
Case 1
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of west.
Case 2
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of east.
Case 3
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of east.
Case 4
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Above the conducting wire, the needle of the compass deflects in the direction of west.
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of east.
Current Direction Compass Position N – of Compass Deflection S – of Compass Deflection South to North Above SNOWWest East North to South Above East West South to North Below East West North to South Below West East Magnetic Field due to a Current through a
Circular Loop
We have so far observed the pattern of the magnetic field lines produced around a current-carrying straight wire.
Suppose this straight wire is bent in the form of a circular loop and a current is passed through it.
What would the magnetic field lines look like?
We know that the magnetic field produced by a current-carrying straight wire depends inversely on the distance from it.
Similarly at every point of a current-carrying circular loop, the concentric circles representing the magnetic field around it would become larger and larger as we move away from the wire (Fig. 13.8). By the time we reach the centre of the circular loop, the arcs of these big circles would appear as straight lines.
Every point on the wire carrying current would give rise to the magnetic field appearing as straight lines at the centre of the loop.
By applying the right hand rule, it is easy to check that every section of the wire contributes to the magnetic field lines in the same direction
within the loop.
We know that the magnetic field produced by a current-carrying
wire at a given point depends directly on the current passing through it.
Therefore, if there is a circular coil having n turns, the field produced is
n times as large as that produced by a single turn.
This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up.
Factors affecting magnetic field of a circular current carrying conductor-
- Magnetic field is directly proportional to the current passing through the conductor.
- Magnetic field is inversely proportional to the distance from the conductor.
- Magnetic field is directly proportional to number of turns in coil.
Solenoid
The solenoid is an electromagnet which is a long cylindrical coil of wire consisting of a large number of turns bound together very tightly.
Note: The length of the coil should be longer than its diameter. (Or)
Solenoid is a coil of a number of turns of insulated copper wire closely wrapped in the shape of a cylinder.
When a soft iron rod is placed inside the solenoid, it behaves like an electromagnet.
The use of soft iron as core in the solenoid produces the strongest magnetism.
A solenoid consists of an insulated conducting wire wound on a cylindrical tube made of plastic or cardboard.
Magnetic Field due to a Current in a Solenoid
The magnetic field of a solenoid carrying a current is similar to that of a bar magnet.
Compare the pattern of the field with the magnetic field around a bar magnet.
Do they look similar?
Yes, they are similar.
In fact, one end of the solenoid behaves as a magnetic north pole, while the other behaves as the south pole.
The field lines inside the solenoid are in the form of parallel straight lines.
This indicates that the magnetic field is the same at all points inside the solenoid.
That is, the field is uniform inside the solenoid.
These appear to be similar to that of a bar magnet.
One end of the solenoid behaves like the North Pole and the other end behaves like the South Pole.
Magnetic field lines inside the solenoid are in the form of parallel straight lines.
This means that the field is the same at all the points inside the solenoid.
Electromagnet
An electromagnet consists of a core of soft iron wrapped around with a coil of insulated copper wire.
An electromagnet is a magnet made up of a coil of insulated wire wrapped around a soft iron core that is magnetised only when current flows through the wire.
A strong magnetic field produced inside a solenoid can be used to magnetise a piece of magnetic material, like soft iron, when placed inside the coil.
It is a temporary magnet that can be easily demagnetized.
In this type of magnet, polarity can be reversed and strength can be varied. They are very strong magnets.
Magnetic Field of An electromagnet
Force on A current-carrying conductor placed in a magnetic field
Placing a current-carrying conductor in a magnetic field experiences a force.
Finding direction of force on a current-carrying conductor placed in a magnetic field Using Fleming’s left-hand rule
If the direction of the magnetic field and that of the current are mutually perpendicular to each other, then the force acting on the conductor will be perpendicular to both and will be given by Fleming’s left-hand rule.
Flemings Left Hand Rule
Stretch the thumb, forefinger and middle finger of the left hand such that they are mutually perpendicular. If the forefinger is in the direction of the magnetic field, Central finger in the direction of current, then the thumb will point in the direction of motion or force.
Rules & Laws of Electromagnetism
Clock-S Rule
Clock-S rule is a rule which helps us to find the formation of magnetic South Pole due to electromagnetic induction in a current carrying conducting coil.
According to clocks rule if one face of a current carrying conducting coil is placed such that one face of the coil is faced to us and current is moving in the clockwise direction with respect to us then the face of the coil which is faced to us becomes as a magnetic south pole and the other face behaves as the north magnetic pole.
A current carrying conductor in the form of a rectangular loop behaves like a magnet and when suspended in an external magnetic field experiences force.
SNOW Rule
Case 1
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of west.
Case 2
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Over the conducting wire, the needle of the compass deflects in the direction of east.
Case 3
The SNOW rule states that if the current is flowing in an electric circuit from South to North direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of east.
Case 2
The SNOW rule states that if the current is flowing in an electric circuit from North to South direction and a magnetic compass is placed Below the conducting wire, the needle of the compass deflects in the direction of west.
Current Direction Compass Position N – of Compass Deflection South to North Above SNOWWest North to South Above East South to North Below East North to South Below West Maxwell’s cork-screw rule:
Maxwell’ cork screw rule is also known as maxwell’s right hand thumb ruleIf the head of a cork-Screw is rotated such that the tip of the screw advances in the direction of electric current, then the direction of rotation of the head of the screw represents the direction of the magnetic field around the conductor.
A magnetic field caused by a current-carrying conductor consists of sets of concentric lines of force. The direction of the magnetic field lines depends on the direction of the current passed through the conductor.
Ampere Right Hand Thumb Rule
Right hand thumb rule states that if we hold the conductor in the right hand such that the thumb points in the direction of electric current, then the direction in which the fingers curl gives the direction of the magnetic field
If we point the thumb downwards in the direction of the current, the magnetic field would be represented by the curled fingers as the circles around the conductor.
So, if it is viewed from the above plane this field lines will be clockwise circles, but the direction of the magnetic field at any point on this circular magnetic lines is in the direction of the tangent drawn to the circular magnetic lines at the desired points.
Example 13.1
A current through a horizontal power line flows in east to west
direction. What is the direction of magnetic field at a point directly
below it and at a point directly above it?
Solution
The current is in the east-west direction. Applying the right-hand
thumb rule, we get that the magnetic field (at any point below or
above the wire) turns clockwise in a plane perpendicular to the wire,
when viewed from the east end, and anti-clockwise, when viewed
from the west end.
Fleming’s Right Hand rule (Working Principle of Transformer and generator )
Fleming’s right hand rule gives the direction of the induced current in a conductor when it is moved in a magnetic field.
Transformers are based on this principle, which consist of a primary coil and a secondary coil.
The number of turns in the coils is selected based on the type of the transformer to be made, namely, step-up or step-down.
Magnetic Field Due to An Electric Conducting Coil (Motor Working Basics)
Electric Motor
Electric Motor
An electric motor is a device that converts electrical energy into mechanical energy.
Fleming’s left-hand rule is the basis of an electric motor.
A rotating device that converts electrical energy to mechanical energy.
Working Principle: The Working Principle of Electric motor is Fleming’s Left Hand Rule.
Construction of Electric Motor:
It consists of a rectangular coil ABCD made up of insulated copper wire.
The coil is placed perpendicular to the magnetic field.
There are two conducting brushes X and Y.
Current in coil ABCD enters through a source battery through conducting brush X and flows back to the battery through brush Y.
The split ring acts as a commutator.
It reverses the direction of flow of current in a commutator.
They are used in electromagnets, as soft iron core on which coil is wound.
Armature enhances the power of the motor.
Electric Motor
Working Principle
Working Principle of electric motors is Fleming’s left hand rule.
The direction of the force is given by Fleming’s left hand rule. This gives the basis for an electric motor.
An electric motor essentially consists of a coil as an armature, a split ring commutator for changing the direction of the current in the coil.
There are two brushes linked with the split rings that maintain the contact with the armature for the current flow.
Electric motor converts electrical energy to mechanical energy.
A number of such loops form a coil and the coil is termed solenoid.
If there is a soft iron core in the solenoid, it behaves like a magnet as long as there is current through the coil. Thus it is an electromagnet.
When an electric current passes through a conductor, a magnetic field is created around the conductor. This phenomenon is known as the magnetic effect of electricity.
A magnetic field is the extent of space surrounding a magnet where the magnet’s effect can be felt.
Magnetic field lines represent the lines of action of the force acting on a unit North Pole placed in a magnetic field.
Electromagnetic Induction
Electromagnetic Induction – Electric Effects of Changing Magnetic Field
The phenomenon of electromagnetic induction is the production of induced current in a coil placed in a region where the magnetic field changes with time.
The magnetic field may change due to a relative motion between the coil and a magnet placed near to the coil.
If the coil is placed near to a current-carrying conductor, the
the magnetic field may change either due to a change in the current through the conductor or due to the relative motion between the coil and conductor.
The direction of the induced current is given by the Fleming’s right-hand rule.
Fleming’s Right Hand Rule
A generator converts mechanical energy into electrical energy. It works on the basis of electromagnetic induction.
Electromagnetic Induction is the electric effects of relative motion between magnetic field and electric conductor.
When we place a conductor in a changing magnetic field, some current is induced in it. This current is known as Induced Current and the phenomenon is known as Electromagnetic Induction.
Faraday’s Experiment
The working principle of electric generators and Transformers is Fleming’s right hand rule.
Faraday’s experiment proved that the strength of the induced current depends on several factors like the strength of the magnet, the speed of motion of the magnet, its orientation, the number of turns in the coil and the diameter of the coil. The induced current can be detected by a galvanometer.
Electric Generator
An electric device that converts mechanical energy into electrical energy is called an electric generator.
Working Principle: Fleming Right Hand Rule
Fleming Right Hand Rule
Hold the forefinger, middle finger and thumb of your right hand at right angles to each other. Forefinger points towards the direction of the magnetic field, thumb points in the direction of motion of conductor and middle finger shows direction of induced current.
Electric Energy is a device used to convert mechanical energy into an alternating form of electrical energy. It consists of insulated copper wire, magnetic poles, split rings, axle, brushes and galvanometer.
The axle is rotated so that it moves clockwise, that is AB moves up and CD moves down. After half rotation, CD starts to move up and AB moves down. After every half rotation current changes its direction, this is called AC current.
Electric generators work on the same principle.
They have an armature which is free to rotate in a magnetic field.
Its terminals are connected to two slip rings, which are further connected to two brushes and they are connected across a load resistance through which the generated electricity can be trapped.
The rotation of the armature in the magnetic field changes the magnetic flux in the coil of the armature and an electric current is induced.
As the direction of the induced current changes for every half rotation, it is called alternating current.
The current at the power plants is distributed through transmission lines at a high voltage and hence the lines are referred to as high tension power lines.
At the substations these are stepped down to a lower voltage and supplied to houses at a low voltage.
A domestic electric circuit essentially contains mains, a fuse, live or line, neutral and earth wires.
From the poles supply cables bring the current to the mains.
Within the house, all the equipment is connected in parallel.
Electromagnetic induction (EMI) is the process of generating an electromotive force by moving a conductor through a magnetic field.
The electromotive force generated due to electromagnetic induction is called induced emf. The current due to induced emf is called induced current.
Alternating current (AC) is the current induced by an AC generator. AC current changes direction periodically. Direct current (DC) always flows in one direction, but its voltage may increase or decrease.
An electric motor is different from an electric generator. A generator converts mechanical energy (Kinetic energy) into electrical energy while an electric motor converts electrical energy into mechanical energy (Kinetic energy).
AC Generator:
Principle: It works on the principle that when a coil rotates in a uniform magnetic field, a current is induced in the coil. The direction of induced current is determined by Fleming’s right hand rule.
Construction: An ac generator consists of the following components as shown in figure.
(i) Armature coil: It consists of a large number of turns of a rectangular coil ABCD made of copper wire wound over a soft iron laminated core.
(ii) Strong field magnets: Two concave poles (NS) of permanent magnets between which the armature coil is rotated.
(iii) Slip-rings: The two ends of the coil are welded to two different circular metallic rings R, and R,. These rings are called the slip-rings. The function of the slip-rings is to ensure that the ion of current flowing through the coil after each half rotation.
A schematic diagram of common domestic circuit is as shown below
(iv) Brushes : Two carbon brushes B, and B2 make a contact with the slip-rings R, and R2
An electric generator is as shown in fig. 7.7.
Domestic Electric Circuit
HouseHold Electric Circuits
In our houses we receive AC electric power of 220 V with a frequency of 50 Hz. One of the wires in this supply is with red insulation, called live wire.
The other one is of black insulation, which is a neutral wire. The potential difference between the two is 220 V.
The third is the earth wire that has green insulation and this is connected
to a metallic body deep inside earth. It is used as a safety measure to ensure that any leakage of current to a metallic body does not give any severe shock to a user.
Fuse is the most important safety device, used for protecting the circuits due to short-circuiting or overloading of the circuits.
Electrical components and wires fitted in a household to supply electricity to various appliances form a domestic electric circuit.
The old colour convention of the three wires used in household electrical circuits was Red, called live wire, Black, called neutral wire and Green, called earth wire. Now, this colour convention has changed.
The new colour convention is Brown, called live wire, Light blue, called neutral wire and Green or Yellow, called earth wire.
In our houses, we receive AC electric power of 220 V with a frequency of 50 Hz. One of the wires in this supply is with red insulation, called live wire.
The other one is of black insulation, which is a neutral wire. The potential difference between the two is 220 V.
The third is the earth wire that has green insulation and this is connected to a metallic body deep inside earth.
It is used as a safety measure to ensure that any leakage of current to a metallic body does not give any severe shock to a user.
Earthing
Earthing of an electrical appliance is very important.
Suppose, a conductor is exposed to the appliance due to bad insulation.
If a person touches such an appliance, he will receive a severe shock.
If the metal casing of the appliance is connected to the earth with the help of a conductor, the metal casing will be then at the same potential as the earth i.e., zero volt.
If there is a leakage of current, the current will safely flow to the earth.
The earth connection can also save the appliance from the damage.
Fuse
Fuse is the most important safety device, used for protecting the circuits due to short-circuiting or overloading of the circuits.
It is a safety device to limit the current in an electric circuit.
It prevents the electric appliances from damage.
It is made up of material which has high resistivity and low melting point.
Exam Revision
Magnetic Compass
A compass needle is a small magnet. Its one end, which points towards north, is called a north pole, and the other end, which points towards south, is called a south pole.
Magnetic Field
A magnetic field exists in the region surrounding a magnet, in which the force of the magnet can be detected.
Field lines
Field lines are used to represent a magnetic field. A field line is the path along which a hypothetical free north pole would tend to move. The direction of the magnetic field at a point is given by the direction that a north pole placed at that point would take. Field lines are shown closer together where the magnetic field is greater.
Magnetic Effects of Electric Current
A metallic wire carrying an electric current has a magnetic field associated with it.
The field lines about the wire consist of a series of concentric circles whose direction is given by the right-hand rule.
Right Hand Rule
Magnetic Field Around a Conductor Due to An Electric Current
The pattern of the magnetic field around a conductor due to an electric current flowing through it depends on the shape of the conductor.
Magnetic Field of a solenoid
The magnetic field of a solenoid carrying a current is similar to that of a bar magnet.
Magnetic Field of An electromagnet
An electromagnet consists of a core of soft iron wrapped around with a coil of insulated copper wire.
Force on A current-carrying conductor placed in a magnetic field
O placing a current-carrying conductor in a magnetic field experiences a force.
Direction of Force on A current-carrying conductor placed in a magnetic field Using Fleming’s left-hand rule
If the direction of the magnetic field and that of the current are mutually perpendicular to each other, then the force acting on the conductor will be perpendicular to both and will be given by Fleming’s left-hand rule.
Electric Motor
An electric motor is a device that converts electric energy into mechanical energy.
Fleming’s left-hand rule is the basis of an electric motor.
Electromagnetic Induction – Electric Effects of Changing Magnetic Field
The phenomenon of electromagnetic induction is the production of induced current in a coil placed in a region where the magnetic field changes with time.
The magnetic field may change due to a relative motion between the coil and a magnet placed near to the coil.
If the coil is placed near to a current-carrying conductor, the
magnetic field may change either due to a change in the current through the conductor or due to the relative motion between the coil and conductor.
The direction of the induced current is given by the Fleming’s right-hand rule.
Fleming’s Right Hand Rule
A generator converts mechanical energy into electrical energy. It works on the basis of electromagnetic induction.
HouseHold Electric Circuits
In our houses we receive AC electric power of 220 V with a frequency of 50 Hz. One of the wires in this supply is with red insulation, called live wire.
The other one is of black insulation, which is a neutral wire. The potential difference between the two is 220 V.
The third is the earth wire that has green insulation and this is connected
to a metallic body deep inside earth. It is used as a safety measure to ensure that any leakage of current to a metallic body does not give any severe shock to a user.
Fuse is the most important safety device, used for protecting the circuits due to short-circuiting or overloading of the circuits.
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Mind Map Overal Idea Content Speed Notes Quick Coverage Euclid’s Division Lemma/Euclid’s Division Algorithm : Given positive integers a and b, there exist unique integers q and r satisfying a=bq+r, 0 r<b. This statement is nothing but a restatement of the long division process in which q is called the quotient and r is called… readmore
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Euclid’s Division Lemma/Euclid’s Division Algorithm :
Given positive integers a and b, there exist unique integers q and r satisfying a=bq+r, 0 r<b.
This statement is nothing but a restatement of the long division process in which q is called the quotient and r is called the remainder. (Scroll down to continue …)
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Introduction:
Euclid’s Division Lemma/Euclid’s Division Algorithm:
Given positive integers a and b, there exist unique integers q and r satisfying a=bq+r, 0 r<b.
This statement is nothing but a restatement of the long division process in which q is called the quotient and r is called the remainder.
NOTE:
1. Lemma is a proven statement used for proving another statement.
2. Euclid’s Division Algorithm can be extended for all integers, except zero i.e., b 0.
HCF of two positive integers :
HCF of two positive integers a and b is the largest integer (say d ) that divides both a and b(a>b) and is obtained by the following method :
Step 1. Obtain two integers r and q, such that a=bq+r, 0r<b.
Step 2. If r=0, then b is the required HCF.
Step 3. If r0, then again obtain two integers using Euclid’s Division Lemma and continue till the remainder becomes zero. The divisor when remainder becomes zero, is the required HCF.
The Fundamental Theorem of Arithmetic :
Every composite number can be factorised as a product of primes and this factorisation is unique, apart from the order in which the prime factors occur.
Irrational Number :
A number is an irrational if and only if, its decimal representation is non-terminating and non-repeating (non-recurring).
OR
A number which cannot be expressed in the form of pq , q 0 and p, qI, will be an irrational number. The set of irrational numbers is generally denoted by Q.
NOTE:
1. The rational number pq will have a terminating decimal representation only, if in standard form, the prime factorisation of q, the denominator is of the form 2n5m, where n, m are some non-negative integers.
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Mind Map Overal Idea Content Speed Notes Quick Coverage Any expression of the form a0xn+a1xn-1+a2xn-2+….an is called a polynomial of degree n in variable x ; a0≠0, where n is a non-negative integer and a0, a1, a2, ….., and are real numbers, called the coefficients of the terms of the polynomial. (Scroll down to continue …)… readmore
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Any expression of the form a0xn+a1xn-1+a2xn-2+….an is called a polynomial of degree n in variable x ; a0≠0, where n is a non-negative integer and a0, a1, a2, ….., and are real numbers, called the coefficients of the terms of the polynomial. (Scroll down to continue …)
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A polynomial in x can be denoted by the symbols p(x), q(x), f(x), g(x), etc.
Degree Of Polynomial: The highest power of x in p(x) is called the degree of the polynomial p(x).
Linear Polynomial : A polynomial of degree one is called a linear polynomial.
Quadratic Polynomial :
A polynomial of degree two is called a Quadratic Polynomial.
Generally, any quadratic polynomial in x is of the form ax2+bx+c, a ≠ 0 and a, b, c are real numbers.
Cubic Polynomial :
A polynomial of degree three is called a Cubic Polynomial.
Generally, any cubic polynomial in x is of the form ax3+bx2+cx+d, a≠0 and a, b, c, d are real numbers.
Value of a Polynomial :
If we replace x by ‘ -2’ in the polynomial p(x) = 3x3-2x2+x-1
we have p(-2) =3(-2)3-2(-2)2+(-2)-1
= -24-8-2-1 =-35
Thus, on replacing x by ‘ -2 ‘ in the polynomial p(x), we get -35, which is called the value of the polynomial.
Hence, if k is any real number, then the value obtained by replacing x by k in p(x), is called the value of the polynomial p(x) at x=k, and generally, denoted by p(k).
Zeros of a Polynomial :
A real constant, k is said to be a zero of a polynomial p(x) in x, if p(k)=0
For example, the polynomial p(x) = x2+x-12 gives p(3)=32+3-12=0 and p(-4)=(-4)2+(-4)-12=0.
Thus, 3 and -4 are two zeroes of the polynomial p(x).
A linear polynomial (degree one) has one and only one zero, given by;
Zero of the linear polynomial = -(constant term )coefficient of x
Geometrical Representation of the Zeroes of a Polynomial :
Let us consider a linear polynomial p(x)=3x-6.
We know that, graph of a linear polynomial is a straight line.
Therefore, graph of p(x)=3x-6 is a straight line passing through the points (1,-3),(3,3),(2,0).
Table for p(x)=3x – 6
From the graph of p(x)=3x-6, we observe that it intersects the x-axis at the point (2,0).
Zero of the polynomial [p(x)=3x-6] = -(-6)3 = 63 = 2.
Thus, we conclude that the zero of the polynomial p(x) = 3x – 6 is the x-coordinate of the point where the graph of p(x) = 3x – 6 intersects the x-axis.
Similarly, the zeroes of a quadratic polynomial, p(x) = ax2+bx+c, a≠0, are the x-coordinates of the points where the graph (parabola) of p(x)=ax2+bx+c, a≠0, intersects the x-axis.
Graph of p(x) = ax2+bx+c, a≠0 intersects the x-axis at the most in two points and hence the quadratic polynomial can have at most two distinct real zeros.
A cubic polynomial can have at most three distinct real zeros.
Relation between Zeroes and Coefficients of a Polynomial :
Let the quadratic polynomial be p(x) = ax2+bx+c, a≠0 and having zeroes as α and β, then
Sum of the zeroes = α + β
= -(coefficient of x) /(coefficient of x2) = -b/a
Product of the zeroes = αβ
Let the cubic polynomial be p(x) = ax3+bx2+cx+d, a≠0 and having zeroes as α , β and γ, then Sum of the zeroes = α + β + γ
α + β + γ = -(coefficient of x2 )/(coefficient of x3)= -b/a
αβ = (constant term) /(coefficient of x2) = c/a
Sum of the products of zeroes taken two at a time αβ+βγ+γα
αβ+βγ+γα = (coefficient of x) /(coefficient of x3)= c/a
and
Product of the zeroes = αβγ
αβγ = (constant term) /(coefficient of x3)= -d/a
Division Algorithm for Polynomials :
For any two polynomials p(x) and g(x) ; g(x) ≠0, we can find two polynomials q(x) and r(x), such that p(x)=g(x) × q(x)+r(x).
Where r(x)=0 or degree of r(x) is less than the degree of g(x). Here, q(x) is called quotient, r(x) is called remainder, p(x) is called dividend and g(x) is called divisor. This result is known as a division algorithm for polynomials.
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