An object 'O' is placed in front of a small plane mirror M₁ and a large convex mirror M₂ of focal length 'f'. The distance between 'O' and M₁ is x and the distance between M₁ and M₂ is y. The images of 'O' formed by M₁ and M₂ coincide. The magnitude of 'f' is

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x-y

$\frac{x^{2} - y^{2}}{2 y}$

$\frac{x^{2} + y^{2}}{2 y}$

$\frac{x^{2} + y^{2}}{x + y}$

answer is B.

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Detailed Solution

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}; u = x + y; v = x - y;$

$u-negative, v-positive, f-positive$

$\Rightarrow \frac{1}{f} = \frac{1}{x - y} - \frac{1}{x + y} = \frac{2 y}{x^{2} - y^{2}};$

$\Rightarrow f = \frac{x^{2} - y^{2}}{2 y}$

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