Question

A plano-convex lens acts like a concave mirror of $28$ cm focal length when it's plane surface is silvered and like a concave mirror of 10 cm focal length when its curved surface is silvered. What is the refractive index of the material of the lens ?

• A. $1.50$
• B. $1.55$
• C. $1.60$
• D. $1.65$

Answer 1

The correct option is B $1.55$

Let $f_1$ and $f_2$ be the focal length in the 2 cases.

Then, $f_1=\frac{R}{2(\mu -1)}$ = -28

$f_2=\frac{R}{2\mu }=-10$

Eliminating $R$ from the $2$ equations,

The refractive index comes out to be, $\mu =1.55$