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# A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different material of refractive indices μ1 and μ2 and R is the radius of curvature of the curved surface of the lenses, then focal length of the combination is :Rμ1−μ22Rμ2−μ1R2(μ1−μ2)R2−(μ1+μ2)

A
2Rμ2μ1
B
R2(μ1+μ2)
C
Rμ1μ2
D
R2(μ1μ2)
Solution
Verified by Toppr

#### Lens maker formula: 1f=(μ−1)(1R1−1R2) .......(1)For Plano-convex lens: R1=∞R2=−RUsing (1), 1f1=(μ1−1)(1∞−1−R) ⟹1f1=μ1−1RFor Plano-concave lens: R1=−R R2=∞Using (2), 1f2=(μ2−1)(1−R−1∞) ⟹1f2=1−μ2RThus focal length of combination, 1F=1f1+1f2=μ1−1R+1−μ2R⟹ F=Rμ1−μ2

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