Question

A plano-convex lens (f=20 cm) is silvered at plane surface. The focal length will be

• A. 20 cm
• B. 40 cm
• C. 30 cm
• D. 10 cm

Answer 1

Answer: (D)

10 cm

For the given plano-convex lens,
focal length, $f=20cm$
refractive index, $\mu$
radius of curvatures, $R_1=?,R_2=\infty$
$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
$\Rightarrow \frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{\infty })$
$\Rightarrow \frac{1}{f}=(\mu -1)(\frac{1}{R_1}-0)$
$\Rightarrow \frac{1}{f}=\frac{(\mu -1)}{R_1}$---------(1)
When plane surface is silvered the focal length $f_1$ is given by
$\frac{1}{f_1}=\frac{2(\mu -1)}{R}$-------------(2)
from equation (1) and (2):
$\frac{1}{f_1}=\frac{2}{f}=\frac{2}{20}$
$\Rightarrow f_1=\frac{20}{2}cm$
$\Rightarrow f_1=10cm$
Hence, the correct option is $\left(D\right)$