A convex mirror and a concave mirror of radius 10 cm each are placed 15 cm apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in convex mirror, the position of the final image is

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at the pole of the concave mirror

at the pole of the convex mirror

coincident with the object itself

5 cm behind the convex mirror

answer is B.

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Detailed Solution

For a concave mirror, $u = - \frac{15}{2} cm, v = ?$

$f = - \frac{10}{2} cm = - 5 cm$

From the mirror formula,

$\begin{array}{rcl} \frac{1}{f} & = & \frac{1}{u} + \frac{1}{v} \\ \Rightarrow & \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \\ \Rightarrow & \frac{1}{v} = \frac{1}{- 5} - \frac{1}{- 15 / 2} \\ \Rightarrow & \frac{1}{v} = - \frac{1}{5} + \frac{2}{15} = \frac{- 1}{15} \end{array}$

or $v = - 15 cm$

Clearly, the position of the final image is on the pole of the convex mirror.

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