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

Answer

C

Explanation

Focal length of the combination `(1)/(f)=(1)/(f_(1))+(1)/(f_(2)) ...(i)`
We have, `(1)/(f_(1))=(mu_(1-1))((1)/(oo)-(1)/(-R))=(mu_(1)-1)/(R)`
`and (1)/(f_(2))=(mu_(1)-1)((1)/(-R)-(1)/(oo))=-(mu_(2)-1)/(R)`
Putting these values of `(1)/(f_(1)) and (1)/(f_(2))` in Eq. (i)
`(1)/(f)=((mu_(1)-1)/(R))-((mu_(2)-1))/(R)=([mu_(1)-1-mu_(2)-1])/(R)=(mu_(1)-mu_(2))/(2)`
`f=(R)/(mu_(1)-mu_(2))`