Question

A convex lens of glass $(\mu=1.5)$ has a focal length of $8\, cm$ when placed in air. What is the focal length of lens when it is immersed in water $\left(\mu=\frac{4}{3}\right) ?$

• A. 4 cm
• B. 8 cm
• C. 16 cm
• D. 32 cm

Answer 1

Answer: (D)

Given,
focal length $f =8 cm$
$ \mu_{ g }=1.5 $
$ \therefore \frac{1}{ f }=(\mu-1)\left[\frac{1}{ R _{1}}-\frac{1}{ R _{2}}\right] $
$ \frac{1}{8}=(1.5-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right] $
$ \frac{1}{8}=(0.5)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right] $
$ \left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]=\frac{1}{4} $
Lens when immersed in water,
Lens when immersed in water,
$ \frac{1}{ f _{ w }}=\left(\frac{\mu_{ g }}{\mu_{ w }}-1\right)\left[\frac{1}{ R _{1}}-\frac{1}{ R _{2}}\right] $
$=\left[\frac{1.5}{1.33}-1\right] \frac{1}{4} $
$=\frac{1}{8} \times \frac{1}{4} $
$=\frac{1}{ f _{ W }}=\frac{1}{32} $
$\therefore f _{ w }=32 $