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A plano convex lens fits exactly into a ...

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 materials refractive indices `mu_(1)` and `mu_(2)` and R is the radius curvature of the curved surface of the lenses, the focal length of the combination is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C

Focal length of first lens `(1)/(f_(1))=(mu_(1)-1)((1)/(oo)-(1)/(-R))=(mu_(1)-1)/(R)`
Focal length of second lens `(1)/(f_(2))=(mu_(2)-1)((1)/(-R)-(1)/(oo))=((mu_(2)-1))/(R)`
So focal length of the combination
`(1)/(f)=(1)/(f_(1))+(1)/(f_(2))=(mu_(1)-1)/(R)=((mu_(2)-1))/(R)`
`(1)/(f)=(mu_(1)-mu_(2))/(R)`
`f=(R)/(mu_(1)-mu_(2))`
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