A thin plano-convex lens fits exactly into a thin plano-concave lens. Their plane surfaces are parallel to each other. 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 surfaces of the lenses, if rays are incident parallel to principal axis on lens of refractive index.

Options

A. `mu_(1)` then the focal length of the combination is `(R)/(mu_(1)-mu_(2))`
B. `mu_(2)` then the focal length of combination is `(2R)/(mu_(2)mu_(1))`
C. `mu_(1)` then the focal length of the combination is `(R)/(2(mu_(1)-mu_(2)))`
D. `mu_(2)` then the focal length of the combination is `(R)/((mu_(2)-mu_(1)))`

Answer

A, D

Explanation

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