Question

A plano convex lens when silvered in the plane side behaves like a concave mirror of focal length $60cm$. However, when silvered on the convex side it behaves like a concave mirror of focal length $20cm$. Then the refractive index of the material will be

• A. $3$
• B. $2$
• C. $2.5$
• D. $1.5$

Answer 1

The correct option is D $1.5$

Given that. a plano-convex lens when silvered on the plane side behaves like a concave mirror of focal length $F=60cm$.
To find the refractive index of the lens
We know that,
$\frac{1}{F}=\frac{2}{f}+\frac{1}{f_m}$
As it is silvered on plane side initially$f_m=\infty$.

$\frac{1}{F}=\frac{2}{f}+\frac{1}{\infty }$
$\Rightarrow f=120cm$
However, when silvered on the convex side, it behaves like a concave mirror of focal length $F=20cm$.
As silvering is done on curved face $f_m=\frac{R}{2}$.
So, $\frac{1}{F}=\frac{2}{f}+\frac{2}{R}$
$\frac{1}{20}=\frac{2}{120}+\frac{2}{R}\Rightarrow R=60cm$
Now,
from $\frac{1}{f}=(\mu -1)\frac{1}{R}$,
$\frac{1}{120}=(\mu -1)\frac{1}{60}$
we get $\mu =1.5$