First slide

Ray optics

Question

A concave mirror of focal length f is kept at a distance of 27 cm from a plane mirror. A point object is placed mid way between the mirrors at point O. Rays of light emerging from the object first get reflected by the concave mirror and then by the plane mirror and the final image is formed at the location of the object. Then the value of f is

Moderate

A

9 cm
B

12 cm
C

18 cm
D

15 cm

Solution

A ray of light emerging from the object O gets reflected from the surface of concave mirror, then it strikes the plane mirror at B, gets reflected from the surface of plane mirror, then this reflected ray strikes the surface of the concave mirror and after reflection converges at the location O of the object.
using $\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{(- d)} + \frac{1}{(- \frac{d}{2})} = \frac{1}{(- f)}$
$\Rightarrow f = \frac{d}{3} = \frac{27}{3} cm = 9 cm$

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