Light Reflection and Refraction

Introduction to Reflection of Light

• Light is a form of energy due to which we are able to see the objects which emits light for example objects like sun, lamp, candle emits light of their own and thus they are known as luminous objects.
• There are objects like table , chair etc. which are not luminous objects and still we are able to see them and this happens because they reflects lights which falls on them from a luminous object like sun, lamp etc. and when this reflected light reaches our eyes we are able to see such non luminous 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 8×108m/s same way speed of light in water and glass is much less than that in air.
• 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

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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.
• Mirrors we use on our dressing tables in our home are plane mirrors.
• A ray of light is the straight line along which the light travelled 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

• 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 :-
  
1. 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 as shown above in the figure 2.
2. 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.
3. Pole: - The center of a spherical mirror is called its pole and is represented by letter P as can be seen in figure 2.
4. Principle axis: - Straight line passing through the pole and the centre of curvature of a spherical mirror is called principle axis of the mirror.
5. 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.

Principle focus and focal length of a Spherical Mirrors

• For understanding about principle focus and focus length of a spherical mirror first consider the figure given below
  
• From figure 3a we see that a number of rays parallel to the principal axis are falling on a concave mirror. If we now observe the reflected rays we see that they are all intersecting at a point F on the principal axis of the mirror. This point is called the principal focus of the concave mirror.
• In case of convex mirror rays get reflected at the reflecting surface of the mirror and these reflected rays appear to come from point F on the principle axis and this point F is called principle focus of convex mirror.
• The distance between the pole and the principal focus of a spherical mirror is called the focal length. It is represented by the letter f.
• There is a relationship between the radius of curvature R, and focal length f, of a spherical mirror and is given by R=2f which means that that the principal focus of a spherical mirror lies midway between the pole and centre of curvature.

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 passes 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 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 and is shown below in the figure

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
• Image formation by a concave mirror for different positions of the object is shown below in the table 
• 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

• In order to construct a ray diagram to find out the position, nature and size of image formed by convex mirror we should remember following path of rays of light.
• 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.
• Convex mirrors have its focus and center of curvature behind it and no light can go behind the convex mirror and all the rays that we show behind the convex mirror are virtual and no ray actually passes through the focus and center of curvature of the convex mirror.
• 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 
• 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
1v+1u=1f
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 to the height of the object. It is usually represented by the letter m. So, 
or,
m=h1h2
The magnification m is also related to the object distance (u) and image distance (v) and is given as 
m=h1h2=−vu