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

Answer

D

Explanation

The equivalent focal length `(f )` of the given lens as shown in figure is given by

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