A thin plano convex lens A has material of refractive index `mu_(A) = 1.8` and its curved surface has radius of curvature R. A thin layer of transparent material B is laid over the curved surface of A. The refractive index of B is `mu_(B) = 1.2` and the curved surface of B that is not touching a has radius of curvature `(R)/(2)` . This surface of B is silvered. A point object is kept at a distance of 10 cm on the principal axis of the system (above the plane surface) and its image is formed at a distance of 40 cm above the plane surface. Find R.

Answer

48cm