Question

A convex lens made up of glass $({\mu }_g=1.5)$ When placed in air has a focal length 4cm, if it is immersed in water $({\mu }_w=1.33)$ then what will be its focal length in water:

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

Answer 1

Answer: (C)

16 cm

Focal length of convex lens, $f=4cm.$

${\mu }_g=1.5$

Lens formula for convex lens,$\frac{1}{f}=(\mu -1)[\frac{1}{R_1}-\frac{1}{R_2}]$

$\frac{1}{4}=(1.5-1)[\frac{1}{R_1}-\frac{1}{R_2}]$

$\frac{1}{2}=[\frac{1}{R_1}-\frac{1}{R_2}]$

Now under water focal length is,

$\frac{1}{f_W}=(\frac{{\mu }_g}{{\mu }_W}-1)[\frac{1}{R_1}-\frac{1}{R_2}]$

$=[\frac{1.5}{\left(\frac{4}{3}\right)}-1]\times \frac{1}{2}$

=$[\frac{4.5}{4}-1]\times \frac{1}{2}=\frac{5}{80}$

$\frac{1}{f_W}=\frac{1}{16}$

$f_W=16cm$