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Class X - science: Light - Reflection and Refraction
One Word Answer Questions:
Q) Name the mirror which has curved and reflecting surface?
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Q) Name the mirror that can give an erect and enlarge image of the object?
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Q) What is the SI unit of power of lens?
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Q) Which mirror has a curved surface whose inner side is capable of reflection?
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Q) Which miror is used in a solar furnace?
    
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Q) What is the form of energy, which enables us to interact with our surroundings in a most effective way?
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Q) What are two major phenomena of light?
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Q) In Laws of Reflection of light, the angle of incidence and angle of reflection is?
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Q) Mirrors having curved reflecting surfaces are called?
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Q) The diameter of reflecting surface of a spherical mirror is called?
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Q) What are the two major phenomena of light that takes place?
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Q) The change of direction of light because of change of medium is known as?
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Q) A mirror having a flat surface is called?
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Q) What is the form of energy, which enables us to interact with our surroundings in a most effective way?
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Q) What are the two major phenomena of light?
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Q) How the angle of incidence is denoted?
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Q) An object that reflects 100% of the incident light is called?
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Q) What is an optical device which converges or diverges the rays of light before transmitting?
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Short Answer Questions:
Q) State the basic laws which determine the reflection of light by mirrors?
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Q) What impact does atmospheric refraction have on sunrise and sunset?
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Q) Why are reflecting prisms used in periscopes?
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Q) Define refractive index in terms of velocity and mass density?
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Q) Differentiate between real image and virtual image?
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Q) What is Reflection?
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Q) What is the Mirror?
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Q) What is the Concave Mirror?
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Q) Describe curved mirrors?
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Q) What is the Reflection Of Light?
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Q) What is Mirror?
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Q) What is Optical Density?
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Q) What is the Refractive Index?
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Q) What is the Absolute Refractive Index?
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Q) What is Reflection of light?
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Q) What is Concave lens?
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Q) What is convex lens?
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Q) What is convex mirror?
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Q) What is Spherical Lens?
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Long Answer Questions:
Q) Why does a light ray incident on a rectangular glass slab immersed in any medium emerges parallel to itself? Explain with a diagram.
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Q) State Snell's Law? Give its uses?
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Q) Can the laws of plane refracting surfaces be applied to spherical refracting surfaces? State the laws of refraction of light?
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Q) What is lateral inversion? Explain with a suitable example?
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Q) Define principal focus of concave and convex mirrors? Give any two uses of these mirrors?
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Q) Explain the Spherical Mirror?
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Q) Explain about the Sign convention for the parameters related to the mirror equation?
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Q) Explain about the Magnification?
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Q) Explain about Reflection of light by plane mirrors?
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Q) Explain the Derivation of formula for curved mirrors?
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Q) Explain the Refraction Of Light?
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Q) Explain about the Mirages?
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Q) Explain the Applications of total internal reflection?
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Q) Explain the Laws of Refraction?
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Q) Explain the Laws of Reflection of light?
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Q) Explain about Image formation by spherical mirrors?
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Q) Explain about Refraction by Spherical Lenses?
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Q) Explain the Image formation in lenses using ray diagrams?
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Introduction

Light is the form of energy, which enables us to interact with our surroundings in a most effective way. Light causes the sensation of vision.
There are two major phenomena of light that takes place in the process of seeing. They are:

  • Reflection
  • Refraction.
Reflection Of Light
Reflection:

Reflection is one of the unique properties of light. It is the reflection of light, which enables us to see any object.
Reflection of light:
The bouncing back of rays of light from a polished and shiny surface is called reflection or reflection of light. It is similar to bouncing back of a football after colliding with a wall or any hard surface.

Mirror:

Most of the objects reflect the light incident on them to different extent. Some of the objects which have a smooth surface reflect the incident light to the maximum extent. "An object that reflects 100% of the incident light is called a mirror". If the surface of the mirror is plane, it is referred to as a plane mirror. Other types of mirrors are curved mirrors.
We find our images in proper proportions in plane mirrors due to regular reflection.
We cannot observe our images formed by plane mirrors on a screen as they are virtual images unlike those which are formed on a screen and termed as real images. The reflection that takes place on other surfaces other than plane mirrors is irregular reflection. Irrespective of the type of reflection, the light ray (which is the path of light) follows two laws of reflection.

Laws of Reflection of light

  • The angle of incidence and angle of reflection is equal.
  • The incident ray, reflected ray and normal to the point of reflection lie in the same plane.
Reflection And Refraction

The angle of incidence is denoted by 'i' and angle of reflection is denoted by 'r'. The law of reflection is applicable to all types of reflecting surface.


Spherical Mirror

Plane mirror:A mirror having a flat surface is called plane mirror.

Formation of image in plane mirror

Reflection And Refraction
Image Formation In Plain Mirror
  • A plane mirror always forms virtual and erect image.
  • The distance of image and that of object is equal from the mirror.
  • The image formed by a plane mirror is laterally inverted.
Spherical Mirror:

Mirrors having curved reflecting surface are called spherical mirrors. A spherical mirror is a part of a sphere.

Types of Spherical Mirror

Concave Mirror:

Spherical mirror with reflecting surface curved inwards is called concave mirror. If a part of a hollow glass sphere is cut and the cut part of the sphere is coated outside with silver or similar material, then its inner surface reflects the entire light incident on it, and thus, forms a mirror.
Since the inner surface is a concave surface, the mirror so formed is called a concave mirror. Concave mirrors converge the light incident on them and hence are called converging mirrors. We can observe ourselves magnified when the mirror is placed close to our face. This is due the position of the object between the focus and the pole.
As the object moves away from the mirror, the size of its image reduces along with its distance from the 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. Due to this property, concave mirrors are used as shaving mirrors, and by dentists to view clearly the inner parts of the mouth.

Convex Mirror:

Spherical mirror with reflecting surface curved outwards is called convex mirror. If the cut part of the glass sphere is coated from inside with silver or a similar material, then its outer surface reflects the entire light incident on it, and thus forms a mirror. Since the outer surface is a convex surface, the mirror so formed is called a convex mirror.

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 produced 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.

Reflection And Refraction
Concave Mirror and Convex Mirror

Terms Associated with Spherical Mirrors

  • Centre of curvature (C) is the centre of the sphere, of which the mirror is a part.
  • Radius of curvature (R) is the radius of the sphere, of which the mirror is a part.
  • Pole (P) is the geometric centre of the spherical mirror.
  • Principal axis is the line joining the pole and the centre of curvature.
  • 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.
Reflection And Refraction

Concave Mirror At Infinity

Reflection And Refraction

Convex Mirror At Infinity

In the case of a concave mirror, parallel rays coming from infinity converge after reflection in front of the mirror. Thus, the focus lies in front of a concave mirror. In the case of a convex mirror, parallel rays coming from infinity appear to be diverging from behind the mirror. Thus, the focus lies behind the convex mirror.

  • Focal length (f) is the distance of the principal focus from the pole of the mirror. Focal length is equal to half of the radius of curvature.
  • i.e., f = R/2 or R = 2f

    Reflection And Refraction

    Aperture: The diameter of reflecting surface of a spherical mirror is called aperture.

Image formation by spherical mirrors
Rules for Construction of Ray Diagrams for Spherical Mirrors

Rule 1: A light ray incident parallel to the principal axis, after reflection, either actually passes through the principal focus or appears to pass through the principal focus.
Rule 2:A light ray which first passes through the principal focus or appears to pass through the principal focus, after reflection, will travel parallel to the principal axis.
Rule 3: A light ray which first passes through the centre of curvature or appears to pass through the centre of curvature, after reflection, retraces its initial path.

Image Formation by Concave Mirror

Depending on the position of the object in front of the concave mirror, the position, size and the nature of the image varies.

1. Object at infinity: A real, inverted, highly diminished image is formed at the focal point F, in front of the concave mirror.

Reflection And Refraction

2. Object beyond C: A real, inverted, diminished image is formed between C and F, in front of the concave mirror.

Reflection And Refraction

3. Object at C: A real, inverted, same sized image is formed at C, in front of the concave mirror.

Reflection And Refraction

4. Object between C and F: A real, inverted, enlarged image is formed beyond C, in front of the concave mirror.

Reflection And Refraction

5. Object at F: A real, inverted, highly enlarged image is formed at infinity, in front of the concave mirror.

Reflection And Refraction

6. Object between F and P: A virtual, erect and enlarged image is formed behind the concave mirror.

Reflection And Refraction

The table below shows the image formation for different positions of the object

Position of the object Position of the image Size of the image Nature of the image
At Infinity At the focus F Highly-diminished,
point sized image
Real and inverted
Beyond C Between F and C Diminished Real and inverted
At C At C Same size Real and inverted
Between C and F Beyond C Enlarged Real and inverted
At F At Infinity Highly enlarged Real and inverted
Between F and P Behind the Mirror enlarged Virtual and erect

Representation of images formed by spherical mirrors using ray diagrams
Reflection of Rays parallel to Principal Axis

In the case of concave mirror: A Ray parallel to principal axis passes through the principal focus after reflection from a concave mirror.

Reflection And Refraction
Ray Parallel To Principal Axis

Similarly, all parallel rays to the principal axis pass through the principal focus after reflection from a concave mirror. Since, a concave mirror converge the parallel rays after reflection, thus a concave mirror is also known as converging mirror.

In the case of convex mirror: A ray parallel to principal axis appears to diverge from the principal focus after reflecting from the surface of a convex mirror.

Reflection And Refraction
Ray Parallel To Principal Axis

Similarly, all rays parallel to the principal axis of a convex mirror appear to diverge or coming from principal focus after reflection from a convex mirror. Since, a convex mirror diverges the parallel rays after reflection, thus it is also known as diverging mirror.

Reflection of ray passing through the Principal Focus

In the case of concave mirror: Ray passing through the principal focus goes parallel to principal axis after reflection in the case of concave mirror.

Reflection And Refraction
Ray Passing Through Principal Focus

In the case of convex mirror: A ray directed towards principal focus goes parallel to principal axis after reflecting from the surface of a convex mirror.

Reflection And Refraction
Ray PassingThrough Principal Focus
Ray passing through the Centre of curvature

In the case of concave mirror: Ray passing through the centre of curvature returns at the same path after reflecting from the surface of a concave mirror.

Reflection And Refraction
Ray passing through C

In the case of convex mirror: Ray appears to passing through or directed towards the centre of curvature goes parallel to the principal axis after reflecting from the surface of a convex mirror.

Reflection And Refraction
Ray Passing Through C
Ray incident obliquely to the principal axis:

Ray obliquely to the principal axis goes obliquely after reflecting from the pole of the both concave and convex mirror and at the same angle.

Ray Passing Obliquely To Principal Axis

Reflection And Refraction
Concave Mirror
Reflection And Refraction
Convex Mirror
Image Formation by Concave Mirror

Formation of image depends upon the position of the object. There are six possibilities of the position of object in the case of concave mirror.
1. Object at infinity
2. Object between infinity and centre of curvature (C)
3. Object at centre of curvature (C)
4. Object between centre of curvature (C) and Principal focus (F)
5. Object at Principal Focus (F)
6. Object between Principal Focus (F) and Pole (P)

Object at infinity

Since parallel rays coming from the object converge at principal focus, F of a concave mirror; after reflection. Hence, when the object is at infinity the image will form at F.

Reflection And Refraction
Object At Infinity

Properties of image


  • Point sized
  • Highly diminished
  • Real and inverted
Object between infinity and Centre of Curvature

When object is placed between infinity and centre of curvature of a concave mirror the image is formed between centre of curvature (C) and focus (F).

Reflection And Refraction
Object Between Infinity And C

Properties of image

  • Diminished compared to object
  • Real and inverted
Object at Centre of Curvature (C)

When the object is placed at centre of curvature (C) of a concave mirror, a real and inverted image is formed at the same position.

Reflection And Refraction
Object At C

Properties of image

  • Same size as object
  • Real and inverted
Object between Centre of curvature (C) and Principal Focus (F)

When the object is placed between centre of curvature and principal focus of concave mirror, a real image is formed beyond the centre of curvature (C).

Reflection And Refraction
Object Between C and F

Properties of image

  • Larger than object
  • Real and inverted
Object at Principal Focus (F)

When the object is placed at principal focus (F) of a concave mirror, a highly enlarged image is formed at infinity.

Reflection And Refraction
Object At F

Properties of image

  • Highly enlarged
  • Real and inverted
Object between Principal Focus (F) and Pole (P)

When the object is placed between principal focus and pole of a concave mirror, an enlarged, virtual and erect image is formed behind the mirror.

Reflection And Refraction
Object Between F and P

Properties of image

  • Enlarged
  • Virtual and erect
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 the back of the tooth.
  • 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, search lights 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.
Image formation by a convex mirror

There are only two possibilities of position of object in the case of a convex mirror, i.e. object at infinity and object between infinity and pole of a convex mirror.

Object at infinity:

When the object is at the infinity, a point sized image is formed at principal focus behind the convex mirror.

Reflection And Refraction
Object At Infinity

Properties of image

Image is highly diminished, virtual and erect.
Object between infinity and pole:
When the object is between infinity and pole of a convex mirror, a diminished, virtual and erect image is formed between pole and focus behind the mirror.

Reflection And Refraction
Object Between Infinity and P

Properties of image:Image is diminished, virtual and erect.

Positions and Nature of Image in Convex Mirror
Position of ObjectPosition of ImageSize of ImageNature of Image
At infinity At F,behind mirrorHighly diminishedVirtual and erect
Between infinity
and P
Between F and P,
behind mirror
DiminishedVirtual and erect
Uses of Convex Mirrors
  • Used as rear view mirrors in automobiles as it covers wide area behind the driver.
  • Used as reflectors for street light bulbs as it diverges light rays over a wide area.
Sign Convention for Spherical Mirror
Cartesian Sign Convention:

In the case of spherical mirror all signs are taken from Pole of the spherical mirror, which is often called origin or origin point.
"This sign convention is known as New Cartesian Sign Convention".
Sign is taken as – (negative) from pole of a spherical mirror towards object along the principal axis.
This means sign is always taken as -(negative) in front of a spherical mirror.
For example; the distance of object is always taken as - (negative) in case of both types of spherical mirror, i.e. concave and convex mirrors.

  • Sign is taken as + (positive) behind the spherical mirror. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis.
  • The height is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis.
Reflection And Refraction
Cartesian Sign Convention
Sign in the case of concave mirror
  • Since, object is always placed in front of the mirror hence the sign of object is taken as negative.
  • Since, the centre of curvature and focus lie in front of the concave mirror, so signs of radius of curvature and focal length are taken as negative in the case of concave mirror.
  • When image is formed in front of the mirror, the distance of image is taken as – (negative) and when image is formed behind the mirror, the distance of image is taken as + (positive).
  • Height of image is taken as positive in the case of erect image and taken as negative in the case of inverted image.

Sign in the case of a convex mirror

  • Since, object is always placed in front of the mirror hence the sign of object is taken as negative.
  • Since, the centre of curvature and focus lies behind the convex mirror, so sign of radius of curvature and focal length are taken as + (positive) in the case of convex mirror.
  • In the case of convex mirror, image always formed behind the mirror, thus the distance of image is taken as positive.
  • In the case of a convex mirror, always an erect image is formed, thus the height of image is taken as positive.
Mirror Formula and Magnification

Mirror formula shows the relation among distance of object, distance of image and focal length in case of spherical mirror. All distances are measured from pole of the mirror.

The distance of object is denoted by 'u'
The distance of image is denoted by 'v'
Focal length is denoted by f

 1     1       1
--- + ---  =  --- (mirror formula)
 v     u       f

By knowing any two, the third can be calculated using the mirror formula.

Magnification:

Magnification is the relative ratio of size of image formed by a spherical mirror to the size of object. Magnification is generally denoted by letter 'm'.

                  Height of image(h')                h'
magnification(m)=---------------------    (or)  m = ----
                  Height of image(h)                 h

Relation among magnification, distance of object and distance of image:

                  Height of image(h')                h'
magnification(m)=---------------------    (or)  m = ----
                  Height of image(h)                 h

Where; m = magnification
h' = height of image
h = height of object
v = image distance and
u = object distance.

Refraction Of Light

"The change of direction of light because of change of medium is known as Refraction or Refraction of Light".

The ray of light changes its direction or phenomenon of refraction takes place because of difference in speed in different media.
The light travels at faster speed in rare medium and at slower speed in denser medium. The nature of media is taken as relative. For example air is a rarer medium than water or glass. When ray of light enters from a rarer medium into a denser medium, it bends towards normal at the point of incidence. On the contrary, when ray of light enters into a rarer medium from a denser medium it bends away from the normal.

  • Ray emerging after the denser medium goes in the same direction and parallel to the incident ray.
  • If the light ray retraces its path while travelling from denser to rarer, the angle of incidence is lesser than that of the refraction. This is the principle of reversibility.
  • The angle between incident ray and normal is called Angle of Incidence and it is denoted as 'i'.
  • The angle between refracted ray and normal is called the Angle of Refraction. Angle of refraction is denoted by 'r'.
Reflection And Refraction
Refraction of Light Through A Rectangular Glass Slab

When a light ray, incident at an angle, passes through a glass slab, the emergent ray is shifted laterally. The lateral shift depends on the thickness and refractive index of the glass slab.

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.

Laws of Refraction:
  1. The incident ray, refracted ray and normal to the interface of given two transparent media, all lie in same plane.
  2. The ratio of sine of angle of incidence and sine of angle of refraction is always constant for the light of given colour and for the pair of given media.

The Second Law of Refraction is also known as Snell's Law of Refraction.

sin i/sin r = Constant

The constant is called refractive index of the second medium in relation to the first medium.

Refractive Index:

A ray of light changes its direction when it enters from one medium to another medium. This happens because speed of light is different in different media.

Example: The speed of light is 3 * 108 m/s (2.99 *108 m/s) in vacuum and it is 2.98 * 108 m/s in air.

Refractive Index is the extent of change of direction of light in a given pair of media. The refractive index is a relative value of speed of light in the given pair of media. Thus, to calculate the refractive Index the speed of light in two media is taken.
Let the speed of light in medium 1 is v1 and in medium 2 is v2
Therefore; refractive index of medium 2 with respect to medium 1,
(n21)

n21=v1/v2
Above expression gives the refractive index of medium 2 with respect to medium
1. This is generally denoted by n21.
Similarly, the refractive index of medium 1 with respect to medium 2 is denoted by n12.
n12 = Speed of light in medium2 /Speed of light in medium1
n12 = v2/v1

Absolute Refractive Index:

When one medium is taken as vacuum and speed of light is taken in it, then the refractive index of second medium with respect to vacuum is called Absolute Refractive Index and it is generally denoted by n2.
thus n2 = Speed of light in vaccum/Speed of light in given medium

The speed of light in vacuum is slightly faster than in air. Let speed of light in air is ‘c’ and the speed of light in given medium is 'v'.
Therefore, refractive index of the given medium:
nm = Speed of light in air/Speed of light in given medium

Since, Refractive Index is the relative value of the speed of light of a medium with respect to the speed of light in vacuum, thus light will travel faster in the medium having lower value of refractive index.

Optical Density: Medium having greater value of refractive index is called optically denser medium, this means light will travel at slower speed in optically denser medium compared to an optically rarer medium.

Refraction by Spherical Lenses:

Lens:Lens is an optical device which converges or diverges the rays of light before transmitting. A lens has similar shape to lentils and genus of lentil is called Lens, thus a lens got its name after the shape and name of genus of lentils. A lens is made by combining at least one part of sphere made of transparent material, generally glass.

Spherical Lens: Most of the lenses are made by the combination of parts of transparent sphere. Concave and Convex lens are most commonly use spherical lens.

Convex lens is the most commonly used lens in our day to day life.

Convex lens:

A lens having two spherical surface bulging outwards is called Convex Lens. It is also known as biconvex lens because of two spherical surface bulging outwards.

Convex lenses converge the light and hence are called the converging lenses. You can observe the magnified image of your palm when the lens is placed close to your palm. This is due the position of the object between the focus and the optic centre. As the object moves away from the lens, the size of its image reduces along with its distance from the lens. Convex lenses form erect, virtual, magnified images or inverted, real, diminished/magnified images depending on the position of the object.

Concave lens:

A lens having two spherical surface bulging inwards is called Concave Lens. It is also known as biconcave lens because of two spherical surface bulging inwards.

Concave lens diverge the light incident on it. Hence, called the diverging lens. Due to this these 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.

Reflection And Refraction

Spherical Lens

Differences Between Convex Lens and Concave Lens

Convex Lens Concave Lens

1. It is thick in the middle and thin at the edges.
2. It converges the incident rays towards the principal axis.
3. It has a real focus.

1. It is thin in the middle and thick at the edges.
2. It diverges the incident rays away from the principal axis.
3. It has a virtual focus.

Important terms for spherical lens:

Reflection And Refraction
Convex Lens

Centre of curvature: The centre of sphere of part of which a lens is formed is called the centre of curvature of the lens. Since concave and convex lenses are formed by the combination of two parts of spheres, therefore they have two centres of curvature.

One centre of curvature is usually denoted by C1 and second is denoted by C2.

Focus: Point at which parallel rays of light converge in a concave lens and parallel rays of light diverge from the point in a convex lens is called Focus or Principal Focus of the lens.

Reflection And Refraction
Converging Convex Lens
Reflection And Refraction
Diverging Concave Lens

Similar to centres of curvature; convex and concave lenses have two Foci. These are represented as F 1 and F2.

Principal Axis: Imaginary line that passes through the centres of curvature of a lens is called Principal Focus.

Optical centre: The central point of a lens is called its Optical Centre. A ray passes through optical centre of a lens without any deviation.

Radius of curvature: The distance between optical centre and centre of curvature is called the radius of curvature, which is generally denoted by R.

Focal Length: The distance between optical centre and principal focus is called focal length of a lens. Focal length of a lens is half of the radius of curvature.

i.e. 2f = R or f = R/2

This is the cause that the centre of curvature is generally denoted by 2F for a lens instead of C.

Image formation by lenses:

A lens is a piece of transparent optical material with one or two curved surfaces to refract light rays. It may converge or diverge light rays to form an image.

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 a lens is a bi-concave lens that has two inward bent surfaces. It is generally referred to as a concave lens.

Convex and concave lenses are important as they are more commonly used than the other types of lenses.

Convex Lens:

  • A lens in which both the surfaces are convex, is known as convex lens.
  • Light rays incident on a convex lens get converged at its focus.
  • Used by palmists and fingerprint experts.
  • If an incident ray passes through a focus and its emergent ray passes parallel to the principal axis, then that focus is called the first principal focus.
  • If an incident ray passes parallel to the principal axis, and its emergent ray converges at a focus, then that focus is called the second principal focus.
  • The distance between the optic centre and the focal point is called the focal length.
Behaviour of Light Rays Propagating Through a Convex Lens
Incident Ray Emergent Ray
Is parallel to principal axis Passes through focus
Passes through optic centre Passes without deviation
passes through focus Passes parallel to principal axis
Location and Characteristics of Images Formed by a Convex Lens
Object LocationImage LocationNature of Image
InfinityAt F2Real
Inverted
Highly Diminished
Beyond 2F1Between F2
and 2F2
Real
Inverted
Diminished
At 2F1At 2F2Real
Inverted
Equal in size
to that of
the object
Between 2F1
and F1
Beyond 2F2 Real
Inverted
Magnified
At F1InfinityReal
Inverted
Highly Magnified
Between F1 and OOn the same side of lens as the objectVirtual
Erect
Magnified
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

Incident RayEmergent Ray
Is parallel to principal axisAppears to pass through focus
Passes through optic centrePasses without deviation
Is directed towards focusPasses parallel to principal axis

Location and Characteristic of the Images Formed by a Concave Lens

Object Location Image LocationNature of Image
InfinityAs a point at F1 Virtual
Erect
Highly Diminished
Beyond 2F1Between F1 and O Virtual
Erect
Diminished
Image formation in lenses using ray diagrams
Refraction through Lens

Refraction of parallel ray
A parallel ray converges at focus of a convex lens and diverges from the focus of a concave lens.

Reflection And Refraction
Ray Parallel To Principal Axis (Converge)
Reflection And Refraction
Ray Parallel To Principal Axis (Diverge)
Refraction of ray passing through the Principal focus

A ray passing through principal focus emerges parallel to the principal axis after refraction from a convex lens.

Reflection And Refraction
Ray Passing Through Focus

A ray passing through the principal focus emerges parallel to the principal axis after diverging from a concave lens.

Reflection And Refraction
Ray Passing Through Focus
Ray passing through the optical centre of lens:

Ray passing through the optical centre of convex and concave lens emerges in same direction without any deviation.

Reflection And Refraction
Ray Passing Through Optical Centre
Reflection And Refraction
Ray Passing Through Optical Centre

Converging lens: A convex lens is known as converging lens because parallel rays converge at its focus.

Reflection And Refraction
Converging Lens

Diverging lens: A concave lens is known as diverging lens because parallel rays appear to diverge from the focus after refraction.

Reflection And Refraction
Diverging Lens
Image Formation by Convex Lens:

There are six possibilities of position of object in the case of convex lens:
1. Object at infinity
2. Object beyond centre of curvature, C
3. Object at centre of curvature, C
4. Object between centre of curvature, C and principal focus, F
5. Object at principal focus, F
6. Object between principal focus, F and optical centre, O

Object at infinity:
Convex lens converge parallel rays coming from objet at infinity and a highly diminished - point sized, real and inverted image is formed at principal focus F2.

Reflection And Refraction
Object At Infinity

Properties of Image: Image is highly diminished, real and inverted.

Object beyond centre of curvature, C1 or 2F1:

A diminished, real and inverted image is formed between principal focus, F2 and centre of curvature, C2 at the opposite side when an object is placed beyond C1 of a convex lens.

Reflection And Refraction
Object Beyond 2F

Properties of Image: Image is diminished, real and inverted.

Object at centre of curvature, C1 or 2F1:

A same sized, real and inverted image is formed at centre of curvature, C2 when object is placed at centre of curvature, C1 of a convex lens.

Reflection And Refraction
Object At 2F

Properties of Image: Image is same size as object, real and inverted.

Object between centre of curvature, C1 and principal focus, F1:

An enlarged, real and inverted image is formed beyond centre of curvature, C2 when an object is placed between centre of curvature, C1 and principal focus, F1 of a convex lens.

Reflection And Refraction
Object between 2F and F

Properties of Image: Image is enlarged, real and inverted.

Object at principal focus, F1:

An infinitely large, real and inverted image is formed at infinity when object is placed at principal focus, F1 of a convex lens.

Reflection And Refraction
Object At F

Properties of Image: Image is highly enlarged, real and inverted.

Between principal focus, F1 and optical centre, O:

A virtual, erect and enlarged image is formed at the same side of lens, when an object is placed between principal focus, F1 and optical centre, O of a convex lens.

Reflection And Refraction
Object Between F and O

Properties of Image: Image is enlarged, virtual and erect.

Image Formation by Concave Lens

There are only two possibilities of position of object in the case of a concave lens:
1. Object is at infinity
2. Object is between optical centre, O and infinity
Object is at infinity:
A highly diminished point sized, virtual and erect image is formed when object is at infinity by a concave lens at principal focus F1.

Reflection And Refraction
Object At Infinity

Properties of Image: Image is point sized, highly diminished, virtual and erect.

Object is between optical centre, O and infinity:

A diminished, virtual and erect image is formed between principal focus F1 and optical centre, O; when object is placed between optical centre and infinity of a concave lens.

Reflection And Refraction
Object Between Infinity And O

Properties of Image: Image is diminished, virtual and erect.

Sign convention for spherical lenses:
  • 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 incident rays are taken as positive and all the distances measured in the direction opposite to that of the incident rays are taken as negative.
  • All distances on the principal axis are measured from the optic center.
Lens Formula and Magnification:

The relation between distance of object, distance of image and focal length for a lens is called lens formula.

1/v -1/u = 1/f
Where, v is the distance of image, u is the distance of object, and f is the focal length of lens.
Distance of object and image is measure from the optical centre of the lens. The sign for distance is given as per convention.
The lens formula is valid for all situations for spherical lens.
By knowing any of the two the third can be calculated.

Magnification:

The ratio of height of image and that of object or ratio of distance of image and distance of object gives magnification. It is generally denoted by 'm'.

m= Height of Image(h')/Height of the Object(h)
m=Distance of Image(v) /Distance of Object(u)

The positive (+) sign of magnification shows that image is erect and virtual while a negative (-) sign of magnification shows that image is real and inverted.

Power of a lens:

A convex lens with short focal length converges the light rays with greater degree nearer to principal focus and a concave lens with short focal length diverges the light rays with greater degree nearer to principal focus.
The degree of divergence or convergence of ray of light by a lens is expressed in terms of the power of lens. Degree of convergence and divergence depends upon the focal length of a lens. The power of a lens is denoted by 'P'. The power of a lens is reciprocal of the focal length.

Power(p) = 1/ focal length(f) = 1/f
The SI unit of Power of lens is dioptre and it is denoted by 'D'.
Power of a lens is expressed in dioptre when the focal length is expressed in metre. Thus, a lens having 1 metre of focal length has power equal to 1 dipotre.
Therefore,
1 D = 1 m−1 A convex lens has power in positive and a concave lens has power in negative.

Power of optical instruments having multiple lenses:

If there is more than one lens used, then total power of lenses is equal to the sum of power of all individual lenses.

Example: If there are three lenses used in an optical device having powers equal to 1.0 D, 0.25D and 0.5 D respectively,
Therefore, the total power of the optical device = 1.0 D + 0.25D + 0.5D = 1.75D

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