Question

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.

Answer 1

Answer:

(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:

$\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}$

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

u = object distance

v = image distance

For the question, $u = \infty$ because the rays are parallel to the optic axis. Substituting this in the equation,

$\dfrac{1}{f}=\dfrac{1}{\infty}+\dfrac{1}{v}$

$\dfrac{1}{f}=0+\dfrac{1}{v}$

$\dfrac{1}{f}=\dfrac{1}{v}$

$f = v$

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.