A converging mirror $M_{1}$ , a point source S and a diverging mirror $M_{2}$ are arranged as shown in figure. The source is placed at a distance of 30 cm from $M_{1}$ . The focal length of each of the mirrors is 20 cm. Consider only the images formed by a maximum of two reflections. It is found that one image is formed on the source itself, then

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The distance between the mirrors is 50 cm

The location of the image formed by the single reflection from $M_{2}$ is 10 cm

The location of the image formed by the single reflection from $M_{2}$ is 5 cm

The distance between the mirrors is 25 cm

answer is A, B.

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Detailed Solution

For mirror $M_{1} :$
$\begin{array}{l} u = - 30 c m \\ f = - 20 c m \end{array}$
By mirror formula, $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$ , we have
$\frac{1}{- 30} + \frac{1}{v} = \frac{1}{- 30}$
Which on solving gives v = -60 cm.
For mirror $M_{2} :$ The image formed by mirror $M_{1}$ behaves like virtual object for mirror $M_{2}$ . Let it is at a distance x from the pole of mirror $M_{2}$ . Thus
$\begin{array}{l} u_{2} = + x \\ v_{2} = - (30 - x) \end{array}$
Again by mirror formula, we have
$\frac{1}{x} + \frac{1}{- (30 - x)} = \frac{1}{20}$
Which on solving gives x = 10 cm or 60 cm ,
X = 60 cm is not possible. $∴ x = 10 c m$
(a) Thus the separation between the mirrors = 60-10 = 50 cm
(b) The image formed by mirror $M_{2}$ is at a distance 10 cm.