An object is placed at a distance of 25 cm from the pole of a convex mirror and a plane mirror is set at a distance 5 cm from convex mirror so that the virtual images formed by the two mirrors do not have any parallax. The focal length of the convex mirror is

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-37.5 cm

-7.5 cm

+7.5 cm

37.5 cm

answer is A.

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Detailed Solution

Clearly, the distance of IMAGE I from P is 15 cm. WITH RESPECT TO THE MIRROR IMAGE WILL BE FORMED AT 20 cm on the other side of it.

Now, $u = - 25 cm, v = 15 cm, f = ?$

$\frac{1}{u} + \frac{1}{v} = \frac{1}{f} or \frac{1}{f} = \frac{1}{- 25} + \frac{1}{15}$

or $\frac{1}{f} = \frac{- 3 + 5}{75} f = \frac{75}{2} cm = 37.5 cm$

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