A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices `mu_1`, and `mu_2`, and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is ......

Options

A. `(R)/(2(mu_1+mu_2))`
B. `(R)/(2(mu_1-mu_2))`
C. `(R)/((mu_1-mu_2))`
D. `(2R)/((mu_1-mu_2))`

Answer

A, B, C

Explanation

`1/f=(1)/(f_1)+(1)/(f_2)`
but `f_1=(R)/(mu_1-1)` and
`f_2=-(R)/(mu_2-1)`
`therefore 1/f=((mu_1-1))/(R)-((mu_2-1))/(R)`
`therefore 1/f=([mu_1-1-mu_2+1])/(R)=((mu_1-mu_2))/(R)`
`therefore f=(R)/((mu_1-mu_2))`