Activity . CAUTION: Do not look at the Sun directly or even into a mirror reflecting sunlight. It may damage your eyes. Hold a concave mirror in your hand and direct its reflecting surface towards the Sun.
Direct the light reflected by the mirror on to a sheet of paper held close to the mirror. Move the sheet of paper back and forth gradually until you find on the paper sheet a bright, sharp spot of light. Hold the mirror and the paper in the same position for a few minutes. What do you observe?
Why? The paper at first begins to burn producing smoke. Eventually it may even catch fire. Why does it burn?
The light from the Sun is converged at a point, as a sharp, bright spot by the mirror. In fact, this spot of light is the image of the Sun on the sheet of paper. This point is the focus of the concave mirror. The heat produced due to the concentration of sunlight ignites the paper.
The distance of this image from the position of the mirror gives the approximate value of focal length of the mirror. Let us try to understand this observation with the help of a ray diagram. Observe Fig. .
(a) closely. A number of rays parallel to the principal axis are falling on a concave mirror. Observe the reflected rays. They are all meeting/intersecting at a point on the principal axis of the mirror.
This point is called the principal focus of the concave mirror. Similarly, observe Fig. . (b).
How are the rays parallel to the principal axis, reflected by a convex mirror? The reflected rays appear to come from a point on the principal axis. This point is called the principal focus of the convex mirror. The principal focus is represented by the letter F.
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 . Figure . Figure .
Figure . Figure . Figure . (a) Concave mirror (b) Convex mirror The reflecting surface of a spherical mirror is by-and-large spherical.
The surface, then, has a circular outline. The diameter of the reflecting surface of spherical mirror is called its aperture. In Fig. .
, distance MN represents the aperture. We shall consider in our discussion only such spherical mirrors whose aperture is much smaller than its radius of curvature. Is there a relationship between the radius of curvature R, and focal length f, of a spherical mirror? For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length.
We put this as R = 2f . This implies that the principal focus of a spherical mirror lies midway between the pole and centre of curvature.