Consider a spherical mirror of radius 2 m, and rays which go parallel to the optic axis. What is the position of the point where the reflected rays intersect the optic axis? (i) 0.25 m from the mirror. (ii) 0.5 m from the mirror. (iii) 1 m from the mirror (iv) 2 m from the mirror. (v) Infinity, ie. the rays never intersect the optic axis.

(iii) 1 m from the mirror

Explanation:

In a spherical mirror, rays parallel to the principal or optic axis converge at a point called the focal point if it is a concave mirror. If it is a convex mirror, the parallel rays, after reflection, appear to diverge from the focal point.

It is known that the focal point is at a distance of half the radius of the mirror when measured from the mirror.

Hence, for a mirror of radius 2 m, it's focal point will be at 2/2 = 1 m from the mirror.

We could also use the mirror formula to confirm this:

where f = the focal length or half of the radius of the mirror

u = object distance

v = image distance

For the question, because the rays are parallel to the optic axis. Substituting this in the equation,

Hence, it is seen that the image distance equals the distance of the focal point.

It should be added that by the principle of reversibility of light, a light source placed at the focal point will produce parallel rays upon reflection on a concave spherical mirror.