Question

A plano convex lens when silvered in the plane side behaves like a concave mirror of focal length 30 cm. However, when silvered on the convex side it behaves like a concave mirror of focal length 10 cm. Then the refractive index of the material will be

• A. 3
• B. 2.0
  
• C. 2.5
• D. 1.5

Answer 1

The correct option is D 1.5

Here, $\frac{1}{F}=\frac{2}{f}+\frac{1}{f_m}$
Plano-convex lens silvered on plane side will have focal length $f_m=\infty$.

$\frac{1}{F}=\frac{2}{f}+\frac{1}{\infty }$
$\Rightarrow f=60cm$
Plano convex silvered on the plane side will have a focal length of $\frac{R}{2}$.
So, $\frac{1}{F}=\frac{2}{f}+\frac{2}{R}\Rightarrow R=30cm$

Now, from $\frac{1}{f}=(\mu -1)\frac{1}{R}$, we get $\mu =1.5$