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 is :

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

Answer 1

Answer: (B)

For case 1: When plane surface is silvered, focal length is
$f=\frac{R}{2(\mu -1)}$
where $\mu$ is refractive index, $R$ is radius of curvature, $f$ is focal length.

For case 2: When curved surface is silvered, focal length is
$f^{\prime }=\frac{R}{2\mu }$

Taking ratio of Eq. (1) and Eq. (2), we get
$\frac{f}{f^{\prime }}=\frac{R}{2(\mu -1)}\times \frac{2\mu }{R}=\frac{\mu }{\mu -1}$
Now as $f=28cm$ and $f^{\prime }=10cm$ (given). Therefore,
$\frac{28}{10}=\frac{\mu }{\mu -1}$
$\Rightarrow (2.8)\mu -1=\mu$
$2.8\mu -2.8=\mu$
$\Rightarrow 2.8\mu -\mu =2.8$
$1.8\mu =2.8\Rightarrow \mu =\frac{2.8}{1.8}$
$\Rightarrow \mu =1.55$
Therefore, refractive index of material of lens $=1.55$.