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

Options

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

Answer

B

Explanation

`(1)/(f) = (1)/(f_(1)) + (1)/(f_(2))`
`= (mu_(1)-1)((1)/(oo)-(1)/(R))+(mu_(2)-1)((1)/(oo)-(1)/(R))`
`((mu_(1)-1))/(R) - ((mu_(2) - 1))/(R) = (1)/(f) = (mu_(1) - mu_(2))/(R)`