Question

If a parallel beam of light is incident on spherical mirrors then after reflection they pass through focal point. If F is the focal length and R is the radius of curvature of mirror then

• A. \(R = F\)
• B. \(R = 2F\)
• C. \(R = F/2\)
• D. \(R = F/4\)

Hint:

For a spherical mirror the focus lies halfway between the pole and the centre of curvature.

Answer 1

The Correct Option is B

Step 1: Use the mirror equation.
A parallel beam has $u = \infty$, so $\dfrac{1}{v} = \dfrac{1}{F}$.

Step 2: Use geometry.
For a small aperture, the image of a distant object forms at $R/2$ from the mirror.

Step 3: Conclude.
So $F = R/2$ and $R = 2F$.

Final Answer:
Option (B). \[ \boxed{R = 2F} \]