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`
C. `R//(mu-1)`
D. `(mu+1)//(mu-1)R`

Answer

c

Explanation

when an object is placed in fron of such a lens the rays frst of all refracted from the convex surface, then refract from the polished plane surface and again refracts from conved surface.If `F_(1) and F_(m)` be the focal lengths of lens (conved surface) and mirror (plane poplished surface) respectively then effective focal length f is given by
`(1)/(f)=(1)/(F_(1))+(1)/(f_(m))+(1)/(F_(1))=(2)/(F_(m))=(2)/(f_(1)) (therefore F_(m))=R/2=oo)`
`(1)/(f_(1))=(mu-1)((1)/(R))`
`therefore (1)/(f)=(2(mu-1))/(r)or F=(R)/(2(mu-1))orR=2F=(R)(mu-1)`