Question

A convex lens has $20\, cm$ focal length in air. What is its focal length in water? (Refractive index of air-water $=1.33,$ refractive index for air glass $=1.5)$

• A. 64.4 cm
• B. 72.1 cm
• C. 78.2 cm
• D. 82.2 cm

Answer 1

Answer: (C)

$\frac{1}{f}=\left(\frac{\mu_{2}}{\mu_{1}}-1\right)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]...(i)$
For air-glass lens,
$\frac{1}{20}=(1.5-1)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]$
For water-glass lens,
$\frac{1}{f}=\left(\frac{1.5}{1.33}-1\right)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]...(ii)$
(i) divided by (ii) gives,
$\frac{f}{20}=\frac{(1.5-1)}{\left(\frac{1.5}{1.33}-1\right)}$
$\Rightarrow f=\frac{20 \times 0.5 \times 1.33}{(1.5-1.33)}=78.2\, cm$