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One plano -convex and one plano-concave ...

One plano -convex and one plano-concave lens of same radius of curvature R but of different materials are joined side by side as shown in the figure. If the refractive index of the meterial of 1 is `mu_(1)` and that of 2 is `mu_(2)`, then the focal length of the combination is:

A

`R/(2(mu_(1)-mu_(2))`

B

`R/(2-(mu_(1)-mu_(2))`

C

`(2R)/(mu_(1)-mu_(2))`

D

`R/(mu_(1)-mu_(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`1/f_(1) =(mu_(1)-1)(1/infty -1/(-R)) =(mu_(1)-1)/R`
`1/f_(2) =(mu_(2)-1)(1/(-R) -1/infty) =(-mu_(2)-1)/R therefore 1/F =1/f_(1) + 1/f_(2) =((mu_(1)-1)-(mu_(2)-1))/R =(mu_(1)-mu_(2))/R`
`therefore F=R/(mu_(1)-mu_(2))`
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