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Q.

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. Then find the magnitude of f if an object O is placed in front of a small plane mirror M₁ and a large convex mirror M₂ of focal length f.

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a

$x - y$

b

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

c

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

d

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

answer is B.

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Detailed Solution

For plane mirror image forms at distance ‘x’ For convex mirror object distance u = x + y Image distance $v = x - y$

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

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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. Then find the magnitude of f if an object O is placed in front of a small plane mirror M1 and a large convex mirror M2 of focal length f.