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

Answer

B

Explanation

`(1)/(F)=(1)/(f_(1))+(1)/(f_(2))`
`=(mu_(1)-1)[(1)/(oo)+(1)/(r)]+(mu_(1)-1)[(1)/((-R ))-(1)/(oo)]`
`=((mu_(1)-1))/(R )-((mu_(2)-1))/(R )`
`=(mu_(1)-1+1-mu_(2))/(R )`
`F=(R )/((mu_(1)-mu_(2)))`