Unit 1: Light - Reflection and Refraction

Introduction

Light is a form of energy due to which we are able to see the objects.

Light rays basically consist of electromagnetic waves which do not require any material medium (like solid, liquid or gas) for their propagation.

The wavelength of visible light waves is very small and is of the order of 4×10−7m to 8×10−7m .

Speed of light waves depends on the medium through which they pass as speed of light in air is slightly less than the speed of light in vacuum (3×108m/s)  When light falls on the surface of an object it can either be

1. Absorbed:- If an object absorbs all the light falling on it , then it will appear perfectly black for example a blackboard
   
   
2. Transmitted: - An object is said to transmit light if it allows light to pass through itself and such objects are transparent.
   
   
3. Reflected:- If an object sends back light rays falling on its surface then it is said to have reflected the light
   
   

Reflection of Light

The process of sending back light rays which falls on the surface of an object is called REFLECTION of light

Silver metal is one of the best reflectors of light..

A ray of light is the straight line along which the light travels and a bundle of light rays is called a beam of light.

Laws of Reflection of light

1. The angle of incidence is equal to the angle of reflection, and
   
   
2. The incident ray, the reflected ray and the normal to the mirror at the point of incidence all lie in the same plane.
   
   

These laws of reflection are applicable to all types of reflecting surfaces including spherical surfaces

Real and Virtual images

An image is formed when the light rays coming from an object meet at a point after reflection from a mirror (or refraction from lens).

The images are of two types

1. Real Images:- Real images are formed when rays of light that comes from an object (or source) meets at a point after reflection from a mirror (or refraction from a lens). Real images can be formed on a screen and can be seen with the eyes.
   
   
2. Virtual images:- Virtual image is an image in which the outgoing rays from an object do not meet at a point. It will appear to meet at a point in or behind the optical device (i.e., a mirror) but they do not actually meet after reflection from a mirror (or refraction from a lens). A plane mirror always forms virtual images.
   
   

Characteristics of images formed by mirrors:-

(a) Images formed by mirrors are always virtual and erect
(b) Size of image is always equal to the size of the object and the image is laterally inverted.
(c) The images formed by the plane mirror are as far behind the mirror as the object in front of the mirror.

Lateral inversion:- If an object is placed in front of the mirror, then the right side of the object appears to be the left side and left side of the object appears to be the right side of this image. This change of sides of an object and its mirror image is called lateral inversion.

SPHERICAL MIRRORS

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

The reflecting surface of a spherical mirror may be curved inwards or outwards. Spherical mirrors are of two types

1. Concave mirror: - In a concave mirror reflection of light takes place at the concave surface or bent-in surface as shown below in the figure. 

2. Convex mirror:- In a convex mirror reflection of light takes place at the convex surface or bent out surface as shown below in the figure.

Commonly used terms about Spherical mirrors :-

Centre of curvature: - The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C. Please note that the centre of curvature is not a part of the mirror. It lies outside its reflecting surface. The centre of curvature of a concave mirror lies in front of it. However, it lies behind the mirror in case of a convex mirror.

Radius of curvature: - The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror. It is represented by the letter R.

Pole: - The center of a spherical mirror is called its pole and is represented by letter P.

Principle axis: - Straight line passing through the pole and the centre of curvature of a spherical mirror is called principle axis of the mirror.

Focus or Principal Focus: Point on principal axis at which parallel rays; coming from infinity; converge after reflection is called the Focus or Principal Focus of the spherical mirror. Focus is represented by letter ‘F’.

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.

Fig: Converging 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.  Fig: Diverging Mirror

Focal length: The distance from pole to focus is called focal length. Focal length is denoted by letter ‘f’. Focal length is equal to half of the radius of curvature.

Aperture of the mirror: - Portion of the mirror from which reflection of light actually takes place is called the aperture of the mirror. Aperture of the mirror actually represents the size of the mirror.

IMAGE FORMATION BY SPHERICAL MIRRORS

• The nature, position and size of the image formed by a concave mirror depend on the position of the object in relation to points P, F and C.
  
  
• The image formed can be real as well as virtual depending on the positions of the object.
  
  
• The image is either magnified, reduced or has the same size, depending on the position of the object.
  
  

Rules for obtaining images formed by spherical mirrors

(1) Rule 1

A ray of light which is parallel to the principle axis of the mirror passes through its focus after reflection from the mirror as shown below in the figure

From the figure given above it can be clearly seen that the light rays pass through principle focus in case of concave mirrors and appears to diverge from principle focus in case of concave mirror.

(2) Rule 2

A ray of light passing through the centre of curvature of the concave mirror or directed in the direction of the centre of curvature of a convex mirror, is reflected back along the same path as shown below in the figure.

This happens because the incident rays fall on the mirror along the normal to the reflecting surface.

(3) Rule 3

A ray passing through principle focus of a concave mirror or a ray which is directed towards the principal focus of a convex mirror, becomes parallel to the principle axis after reflection and is shown below in the figure

(4) Rule 4

A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror or a convex mirror, is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal angles with the principal axis.

Image formation by concave mirror

The type of image formed by a concave mirror depends on the position of the object kept in front of the mirror. We can place the object at following places:

1. Between pole P and focus F
   
   
2. At the focus
   
   
3. Between focus F and centre of curvature C
   
   
4. At the centre of curvature
   
   
5. Beyond center of curvature
   
   
6. At far off distances called infinity and cannot be shown in the figures
   
   
1. Image formation by a concave mirror for different positions of the object is shown below in the table:
   
   

 

Uses of concave mirrors:

• Concave mirrors are used as shaving mirrors, reflectors in car headlights, hand torch and table lamps.
  
  
• Large concave mirrors are used in field of solar energy to focus sun rays on objects to be heated.
  
  

IMAGE FORMATION BY CONVEX MIRRORS

•    A ray of light parallel to the principle axis of a convex mirror appears to be coming from its focus after reflection from the mirror.

•    A ray of light going towards the centre of curvature of convex mirror is reflected back along its own path.

•    Whatever be the position of object in front of convex mirror, the image formed by a convex mirror is always behind the mirror, virtual, erect and smaller than the object.

•    Nature, position and relative size of the image formed by a convex mirror is given below in the table:

Uses of convex mirrors:

•    Convex mirrors are used as rear view mirrors in automobiles to see the traffic at back side as they give erect images and also highly diminished one giving the wide field view of traffic behind.

SIGN CONVENTION FOR REFLECTION BY SPHERICAL MIRRORS

Reflection of light by spherical mirrors follow a set of sign conventions called the New Cartesian Sign Convention. In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X) of the coordinate system. The conventions are as follows –

•    The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

•    All distances parallel to the principal axis are measured from the pole of the mirror.

•    All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.

•    Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.

•    Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.

These new Cartesian sign convention for spherical mirrors are shown below in the figure:

Mirror formula and magnification

Mirror formula:-

It gives the relationship between image distance (v) , object distance (u) and the focal length (f) of the mirror and is written as

1/v+1/u=1/f

Where v is the distance of image from the mirror, u is the distance of object from the mirror and f is the focal length of the mirror. This formula is valid in all situations for all spherical mirrors for all positions of the object.

Magnification

Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as the ratio of the height of the image (h1) to the height of the object (h2). It is usually represented by the letter m. So,  

m=h1/h2

The magnification m is also related to the object distance (u) and image distance (v) and is given as

m=h1/h2=−v/u

REFRACTION

We know about light and also know that light travels in a straight path in a medium or two different mediums with same density.

Now a question arises what happens when light travels from one medium to another with different densities for example from air to glass.

When light ray is made to travel from one medium to another say from air to glass medium then light rays bend at the boundary between the two mediums.

So, the bending of light when it passes from one medium to another is called Refraction of light.

The refraction of light takes place on going from one medium to another because the speed of light is different in two media.

Medium in which speed of light is more is called optically rarer medium and medium in which speed of light is less is known as optically denser medium. For example glass is an optically denser medium than air and water.

NOTE:- When light goes from rarer medium to denser medium it bends towards the normal and when it goes from denser medium to rarer medium it bends away from the normal.

Laws of refraction of light

Refraction is due to change in the speed of light as it enters from one transparent medium to another.

Experiments show that refraction of light occurs according to certain laws.

So Laws of refraction of light are

1. The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
   
   
2. The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given color and for the given pair of media. This law is also known as Snell’s law of refraction.
   
   

If i is the angle of incidence and r is the angle of refraction then

sin-i/sin-r=constant
This constant value is called the refractive index of the second medium with respect to the first.

REFRACTION THROUGH A RECTANGULAR GLASS SLAB:

To understand the refraction of light through a glass slab consider the figure given below which shows the refraction of light through a rectangular glass slab.

•    Here in this figure AO is the light ray travelling in air and incident on glass slab at point O.

•    Now on entering the glass medium this ray bends towards the normal NN’ that is light ray AO gets refracted on entering the glass medium.

•    After getting refracted this ray now travels through the glass slab and at point B it comes out of the glass slab as shown in the figure.

•    Since ray OB goes from glass medium to air it again gets refracted and bends away from normal N1N'1 and goes in direction BC.

•    Here AO is the incident ray and BC is the emergent ray and they both are parallel to each other and OB is the refracted ray.

•    Angle of incidence and angle of emergence are equal as emergent ray and incident ray are parallel to each other.

          Refraction of light occurs through a glass slab due to change in the speed of light as it enters from one medium into another. When light enters from a rarer medium to a denser medium that is from air to glass it bends towards the normal. When light enters from a denser medium to a rarer medium that is from glass to air it bends away from the normal.

The Refractive Index

We now know about refraction of light and the extent of the change in direction that takes place in a given pair of media it is  is expressed in terms of the refractive index,

Consider the figure given below

Let v1 be the speed of light in medium 1 and v2 be the speed of light in medium 2 then the refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2. So,

where n21 is the refractive index of medium 2 with respect to medium 1.

The refractive index of medium 1 with respect to medium 2 is represented as n12. It is given by

If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium.

If c is the speed of light in the air and v is the speed of light in any medium then refractive index nm of the medium would be

Refraction by Spherical Lenses

A lens is a piece of transparent glass bound by two spherical surfaces.

There are two types of lens

• A convex lens bulges outward and is thick at the center and thinner at the edges. Convex lens converges the light rays as shown below in the figure 1(a). 
   Hence convex lenses are called converging lenses.
  
  

 

• A concave lens bulges inward and is thinner in the middle and thicker at the edges. Such lenses diverge light rays as shown in Figure 1(b)
   Such lenses are called diverging lenses.
  
  
• 

A lens, whether it is a convex lens or a concave lens, has two spherical surfaces which form a part of a sphere. The centers of these spheres are called centers of curvature of the lens usually represented by the letter C.

• Since there are two centers of curvature, we may represent them as C1 and C2.
  
  
• An imaginary straight line passing through the two centers of curvature of a lens is called its principal axis.
  
  
• The central point of a lens is its optical centre. It is usually represented by the letter O.
  
  
• Letter f is usually used to represent principal focus. A lens has two principal foci.
  
  

The distance of the principal focus from the optical centre of a lens is called its focal length represented by letter f.

Image Formation in Lenses Using Ray Diagrams

The ray diagrams for the image formation in a convex lens for a few positions of the object are summarized below in the table

The ray diagrams for the image formation in a concave lens for a few positions of the object are summarized below in the table

Lens Formula and Magnification

Lens Formula gives the relationship between object distance (u), image image-distance (v) and the focal length (f ) and is expressed as

1/v−1/u=1/f

This formula is valid in all situations for any spherical lens.

The magnification produced by a lens is defined as the ratio of the height of the image and the height of the object.

Magnification produced by a lens is also related to the object-distance u, and the image-distance v and is given by

m=v/u

POWER OF A LENS

The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given by

P=1/f

Power of a convex lens is positive and that of a concave lens is negative.

The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D.

1 dioptre is the power of a lens whose focal length is 1 meter.