Question

The plane surface of a plano-convex lens is silvered
and it then acts like a concave mirror of focal length
30 cm. If μ for lens is 1.5, the radius of curvature
of the convex surface is
(1) 15 cm (2) 30 cm
(3) 60 cm (4) 90 cm

Answer 1

$$\begin{gathered} \mathrm{If}\mathrm{a}\mathrm{planoconvex}\mathrm{lens}\mathrm{of}\mathrm{radius}\mathrm{of}\mathrm{curvature}\mathrm{R}\mathrm{and}\mathrm{of}\mathrm{focal}\mathrm{length}\mathrm{f}\mathrm{is}\mathrm{silvered}\mathrm{on}\mathrm{the}\mathrm{curved}\mathrm{surface},\mathrm{it}\mathrm{acts}\mathrm{like}\mathrm{a}\mathrm{concave}\mathrm{mirror}\mathrm{of}\mathrm{focal}\mathrm{length} \\ f=\frac{R}{2\mu } \\ f=30cm \\ \mu =1.5 \\ R=f\times 2\mu \\ R=30\times 2\times 1.5 \\ R=90cm \end{gathered}$$