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Q.

Using a system of concentric mirrors (Fig.), an image of the Sun was obtained consider only two successive reflections. Mirror radii are $R_{1}$ = 12 cm, $R_{2}$ = 30 cm. What must be the focal length of a thin lens to produce an image of the Sun of the same size as this system?

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a

8 cm

b

10 cm

c

16 cm

d

20 cm

answer is B.

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Detailed Solution

Let the angle subtended by sun at earth be $α .$ The diameter of image formed by mirror 1 is $\frac{R_{1}}{2} α .$ Then the size of image made by mirror 2 is $\frac{R_{2}}{R_{2} - R_{1}} \frac{R_{1}}{2} α .$ So the focal length of lens required is $F_{} = \frac{R_{2} R_{1}}{2 (R_{2} - R_{1})} = 10 c m$

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