A plano-convex lens P and a concavo-convex lens Q are in contact as shown in figure. The refractive index o fthe material of the lens P and Q is `1.8 and 1.2` respectively. The radius of curvature of the concave surface of the lens Q is double the radius of curvature of the convex surface. The convex surface of Q is silvered.

The radius of curvature of common surface is

Options

A. `48 cm`
B. `24 cm`
C. `12 cm`
D. `8 cm`

Answer

A

Explanation

Focal length of lenses is
`1/F=(1.8-1)(1/oo-1/(-2R))+(1.2-1)(1/(-2R)-1/(-R))`
`F=2R`

Now combined power of system,
`P=2P_L+P_m`
or `-1/f=2P_L+P_m`
or `1/8=2(1/(2R))+2/R`
`or R=24 cm`
`:.` Radius of curvature of common surface
`=2R=48 cm`