Question

A planoconvex lens becomes an optical system of $28\, cm$ 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 $10 \,cm$ . 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
$f'=\frac{R}{2 \mu}$

Taking ratio of Eq. (1) and Eq. (2), we get
$\frac{f}{f'}=\frac{R}{2(\mu-1)} \times \frac{2 \mu}{R}=\frac{\mu}{\mu-1}$
Now as $f=28\, cm$ and $f'=10\, cm$ (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 $=1.55$.