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

Options

A. `(R)/((mu_(1)-mu_(2)))`
B. `(2R)/((mu_(2)-mu_(1)))`
C. `(R)/(2(mu_(1)+mu_(2)))`
D. `(R)/(2(mu_(1)-mu_(2)))`

Answer

A

Explanation

The combination of two lenses `1` and `2` is as shown in figure.
`:.(1)/(f)=(1)/(f_(1))+(1)/(f_(2))`
According to lens maker.s formula
`(1)/(f_(1))=(mu_(1)-1)((1)/(oo)-(1)/(R))=((mu_(1)-1))/(R)`
`(1)/(f_(2))=(mu_(2)-1)((1)/(-R)-(1)/(oo))`
`=(mu_(2)-1)(-(1)/(R))=-((mu_(2)-1))/(R)`
`:.(1)/(f)=((mu_(1)-1))/(R)-((mu_(2)-1))/(R)impliesf=(R)/((mu_(1)-mu_(2)))`