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A luminous ob...

Question

A luminous object is placed 20 cm from surface of a convex mirror and a plane mirror is set so that virtual images formed in two mirrors coincide. If plane mirror is at a distance of 12 cm from object, then focal length of convex mirror is:

A

- 5 c m

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B

- 10 c m

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C

- 20 c m

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D

- 40 c m

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Solution

The correct option is A $- 5 c m$
Mirror Equation: $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$
For plane mirror, $f = \infty$ , hence $v = - u = - 12 c m$
Thus, there is a distance of $12 - (- 12) = 24 c m$ between object and image
For convex mirror, $u^{'} = 20 c m$ (given)
Since the images coincide, $v^{'} = - (24 - 20) = - 4 c m$
So $f^{'} = {(\frac{1}{20} + \frac{1}{- 4})}^{- 1} = {(- \frac{1}{5})}^{- 1} = - 5 c m$

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