The plane face of a planoconvex lens is silvered. If `mu` be the refractive index and R, the radius of curvature of curved surface, then the system will behave like a concave mirror of radius of curvature

Options

A. `muR`
B. `R^2//mu`
C. `R//(mu-1)`
D. `[(mu+1)//(mu-1)]R`

Answer

C

Explanation

When an object is placed in front of such a lens, the rays first of all refracted from the convex surface, then reflect from the polished plane surface and again refracts from convex surface. If `f_l and f_m` be the focal lengths of lens (convex surface) and mirror (plane polished surface) respectively, then effective focal length F is given by
`1/F =1/(f_1)+1/(f_(m))+1/(f_(1))`
`=2/(f_1)+1/(f_m)=2/(f_1) ( :. f_m=R/2=oo)`
Now, `1/(f_1)=(mu-1)(1/R)`
`:. 1/F=(2(mu-1))/R`
or `F=R/(2(mu-1))`
As, `R = 2F =(R)/((mu-1))`