Image Formation by Spherical Mirrors

Find out approximate focal length of a concave mirror.

Mark 3 parallel lines P, F & C on a table such that the distance between any two successive lines is equal to the focal length of the mirror.

Place a stand with concave mirror over the line P such that its pole lies over the line.

Keep a bright object (e.g. burning candle) at a position far beyond C. Place a paper screen and move it in front of the mirror to obtain a sharp bright image of the candle flame.

Repeat the activity by placing the candle (a) just beyond C, (b) at C, (c) between F & C, (d) at F and (e) b/w P & F.

Nature, position and size of the image formed by a concave mirror depends on the position of the object in relation to points P, F & C.

Representation of Images Formed by Spherical Mirrors Using Ray Diagrams

In an extended object, each small portion acts like a point source. An infinite number of rays originate from each point. But it is easier to consider only two rays, for the clarity of the ray diagram and to know their directions after reflection.

The intersection of at least two reflected rays gives the position of image of the point object. Any two of the following rays can be considered to locate the image.

a)    A ray parallel to the principal axis. After reflection, it passes through the principal focus in a concave mirror or appear to diverge from principal focus in a convex mirror.

b)   A ray through the principal focus of a concave mirror or directed towards the principal focus of a convex mirror. After reflection, it emerges parallel to the principal axis.

c)  A ray through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror. Then it is reflected back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.

d) A ray incident obliquely to the principal axis, towards pole (P), on the concave mirror or a convex mirror. It is reflected obliquely.

In all these cases, the laws of reflection are followed. i.e., angle of reflection equals angle of incidence.

(a) Image formation by a Concave Mirror

Ray diagrams:

 Position of the object Position of the image Size of the image Nature of the image At infinity At focus F Highly diminished, point-sized Real & inverted Beyond C b/w F & C Diminished Real & inverted At C At C Same size Real & inverted b/w C & F Beyond C Enlarged Real & inverted At F At infinity Highly enlarged Real & inverted b/w P & F Behind the mirror Enlarged Virtual & erect

When the object is between F & P, image is not obtained on the screen. Here, virtual image can be seen in mirror.

Uses of concave mirrors

·   Used in torches, search-lights and vehicles headlights to get powerful parallel beams of light.

·   Used as shaving mirrors to see a larger image of the face.

·   Used by dentists to see large images of teeth of patients.

·   Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

(b) Image formation by a Convex Mirror

Show a pencil in the upright position in front of a convex mirror. Its image in the mirror is erect and diminished.

As the pencil is moved away from the mirror, the image becomes smaller and moves closer to the focus.

Two positions of the object to study the image formed by a convex mirror are shown below.

(a) Formation of image when the object is at infinity

(b) Formation of image when the object is at a finite distance from the mirror

 Position of the object Position of the image Size of the image Nature of the image At infinity At the focus F, behind the mirror Highly diminished, point-sized Virtual & erect Between infinity and the pole P b/w P & F, behind the mirror Diminished Virtual & erect

In plane mirrors and concave mirrors of any sizes, we cannot see a full-length image of a distant object. But it is possible in a convex mirror with wider field of view.

A convex mirror is fitted in a wall of Agra Fort facing Taj Mahal to observe the full image of Taj Mahal.

Uses of convex mirrors

Convex mirrors give an erect, diminished, virtual image. Also, they have a wider field of view as they are curved outwards. So, they are used as rear-view (wing) mirrors in vehicles. It enables the driver to see traffic behind him.