Question

The convex lens of a material of refractive index 3/2 has focal length 25 cm in air. If it is submerged in water ($\mu$ of water $\frac{4}{3}$), then its focal will be the length

• A. $50cm$
• B. $75cm$
• C. $1m$
• D. $1.25m$

Answer 1

The correct option is C $1m$

Given,

Refractive index of lens, ${\mu }_2=\frac{3}{2}$

focal length of lens, $f_1=25cm$

Refractive index of water, ${\mu }_1=\frac{4}{3}$

(i) when lens is in air;

$\frac{1}{f_1}=({\mu }_2-1)[\frac{1}{R_1}-\frac{1}{R_2}]$

$\frac{1}{25}=(\frac{3}{2}-1)[\frac{1}{R_1}-\frac{1}{R_2}]$

$\Rightarrow$ $\frac{1}{R_1}-\frac{1}{R_2}=\frac{1}{25}.....\left(1\right)$

(ii) when in water

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

$=(\frac{3/2}{4/3}-1)\times \frac{2}{25}$

$=(\frac{9}{8}-1)\times \frac{2}{25}$

$=\frac{1}{8}\times \frac{2}{25}=\frac{1}{100}$

$f=100cm=1m$