Question

A double convex lens of focal length $20cm$ is made of glass $\mu =\frac{3}{2}$. What will be lts focal length when lmmersed in a liquid of $\mu =\frac{4}{3}$?

• A. $80cm$
• B. $15cm$
• C. $17.7cm$
• D. $22.5cm$

Answer 1

The correct option is A $80cm$

We use the lens makers formula for calculating the focal length of the lens,

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}+\frac{1}{R_2})$

$\frac{1}{20}=\frac{1}{2}(\frac{1}{R_1}+\frac{1}{R_2}$)

So,
$(\frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{10}$)

When immersed in the liquid,

$\frac{1}{f}=({\mu }^{{}^{\prime }}-1)(\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{f}=(\frac{9}{8}-1)\left(\frac{1}{10}\right)$

$f=80$