Question

A convex lens of focal length $16$cm is completely immersed in water.If the refractive indices of material of lens and water are $1.5$ and $1.33$ respectively, then its focal length be :

• A. $16cm$
• B. $62.59cm$
• C. $18cm$
• D. $24.24cm$

Answer 1

The correct option is B $62.59cm$

Given,

Focal length, $f=16cm$

Refractive index of lens, ${\mu }_2=1.5$

Refractive index of water, ${\mu }_1=1.33$

From lens maker's formula

$\frac{1}{f}=\left(\frac{{\mu }_2-{\mu }_1}{{\mu }_1}\right)[\frac{1}{R_1}-\frac{1}{R_2}]$

when lens is in air,

$\frac{1}{16}=\left(\frac{1.5-1}{1}\right)[\frac{1}{R_1}-\frac{1}{R_2}]$

$\Rightarrow$ $[\frac{1}{R_1}-\frac{1}{R_2}]=\frac{1}{8}......\left(1\right)$

when lens is in water

$\frac{1}{f}=\left(\frac{1.5-1.33}{1.33}\right)[\frac{1}{R_1}-\frac{1}{R_2}]$

$=\frac{0.17}{1.33}\times \frac{1}{8}$ (from (1))

On solving

$f=62.59cm$