Question

A planoconvex lens becomes an optical system of $28cm$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.
If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length $10cm$. The refractive index of the material of lens if:

• A. $1.50$
• B. $1.55$
• C. $1.75$
• D. $1.51$

Answer 1

The correct option is B $1.55$

Effective focal length of the combination, $\frac{1}{F}=\frac{2}{f}+\frac{1}{f_m}$

$f_m⟹\infty$

This gives, $f=56$

$f_m=\frac{R}{2}$

Hence,

$\frac{1}{F}=\frac{2}{f}+\frac{2}{R}$

This gives, $R=31.11$

$\frac{1}{f}=(\mu -1)\left(\frac{1}{R}\right)$

$\mu =1.55$