The convex surface of a plano-convex lens is silvered and the radius of curvature of this surface is R. Find the focal length of the system:

Explanation

`P_("final mirror") = P_("lens") + P_("concave mirror") + P_("lens")`
As the ray of light first goes through lens then mirror then again lens.
`P_("final mirror") = 1/f_(l) - 1/f_(m) + 1/f_(l) = 2/f_(l) = 2/f_(l) - 1/f_(m),-` where `f_(l)` is given as
`1/f_(l) =(mu-1)(1/oo - 1/(-R) ) = + ((mu-1))/R`
`implies f_(l) = (+R)/(mu-1) = 2R` for `mu=1.5`
`f_(m) = R/2 , P_("final mirror") = 2/(2R) + 2/R = 3/R`
`F_("final mirror")= - 1/P_("final mirror") = - R/3`
and hence the final mirror will be concave.