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>> $A plano convex lens fits exactly into a$

Question

A plano convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lens are made of different materials of refractive indices $μ_{1}$ and $μ_{2}$ $R$ is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

A

$\frac{2 R}{M _{2} - M _{1}}$

B

$\frac{R}{2 ( M _{2} + M _{2} )}$

C

$\frac{R}{2 ( M _{1} - M _{2} )}$

D

$\frac{R}{( M _{1} - M _{2} ) _{1}}$

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Solution

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Correct option is D)

$\frac{1}{F} \frac{1}{F} \frac{1}{r _{e}} \frac{1}{F _{C}} F = (μ_{1}, - 1) (\frac{- 1}{R}) - (μ_{2} - 1) (\frac{1}{R}) = \frac{- μ _{1}}{R} + \frac{1}{R} + \frac{μ _{2}}{R} - \frac{1}{R} = \frac{μ _{2} - μ _{1}}{R} = \frac{R}{μ _{2} - μ _{1}}$
Hence option (D) is correct

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