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

Options

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

Answer

B

Explanation

When an object is placed in front of such a lens, the rays are first of all refracted from the convex surface, then reflected from the polished plane surface and again refracted from convex surface. If `f_(l)` and `f_(m)` be the local lengts of lens (convex surface) and mirror (plane polished surface) respectively, then effective focal length is
`(1)/(F)=(1)/(f_(l))+(1)/(f_(m))+(1)/(f_(l))=(2)/(f_(l))+(1)/(f_(m))=(2)/(f_(l)) ( :.f_(m)=(R)/(2)=oo)`
Now, `(1)/(f_(l))=(mu-1)((1)/(R)):.(1)/(F)=(2(mu-1))/(R)` or `F=(R)/(2(mu-1))`