Question

A glass convex lens has got a focal length $40$cm. The focal length of the same lens if it is immersed in water will be.[Given, ${}^a{\mu }_g=\frac{3}{2}$ and ${}^a{\mu }_w=\frac{4}{3}$]

• A. $1.6$m
• B. $0.8$m
• C. $2.4$m
• D. $0.2$m

Answer 1

The correct option is A $1.6$m

From lens-maker's formula
$\frac{1}{f}=(\mu -1)\left[\frac{1}{R_1}-\frac{1}{R_2}\right]$
For glass lens in air medium
$\frac{1}{f_e}=({\mu }_g-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
When, the same lens is immersed in water, then
$\frac{1}{f_w}={(}^g{\mu }_w-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
$=\left(\frac{{}^a{\mu }_g-}{{}^a{\mu }_w}-1\right)$ $\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
So, $\frac{f_w}{f_a}=\frac{{(}^a{\mu }_g-1)}{\left(\frac{{}^a{\mu }_g}{{}^a{\mu }_w}-1\right)}$ $=\frac{\left(\frac{3}{2}-1\right)}{\left(\frac{3}{2}\times \frac{3}{4}-1\right)}=\frac{1/2}{\frac{9-8}{8}}$
$\Rightarrow f_w=\frac{1}{2}\times \frac{8}{1}{f}_a=4f_a$
$=4\times 0.4=1.6$m.