Question

A converging beam of solar rays is incident on a concave spherical mirror whose radius of curvature is $0.8$ m. Determine the position of the point on the principal axis of the mirror, where the reflected rays intersect, if the extensions of the incident rays intersect the principal axis $40$ cm from the mirror's pole?

• A. $10$ cm from the pole
• B. $30$ cm from the pole
• C. $50$ cm from the pole
• D. $20$ cm from the pole

Answer 1

The correct option is D

$20$ cm from the pole

Step 1: Given data

Given Data:

Radius of curvature is $R=80$ cm

Distance between the mirror and the lens is $u=40$ cm

Step 2: Finding the focal length of a mirror

Formula : $f=\frac{-R}{2}$

Substitute the value, we get

$f=\frac{-80}{2}=-40$ cm

Step 3: Finding the value of image distance

Use Lens Makers formula

Formula : $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$

$\frac{1}{v}=\frac{1}{-40}-\frac{1}{40}$

$\frac{1}{v}=\frac{1}{-20}$

$\Rightarrow$ $v=-20$ cm

Thus, reflected rays intersect at distance $20$ in front of the mirror's pole.

Hence, option D) is correct.