Question

An air bubble is contained inside water. It behaves as a

• A. concave lens
• B. convex lens
• C. neither convex nor concave
• D. cannot say

Answer 1

Answer: (A)

The focal length of air lens is
$\frac{1}{f}=\frac{\mu_{2}-\mu_{1}}{\mu_{1}}\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
where $\mu_{2}$ is refractive index of water and $\mu_{1}$ is refractive index of air bubble.
$R_{1}$ and $R_{2}$ are radii of curvatures of air bubble.
Here, $\mu_{2}=1$
$\mu_{1}=\frac{4}{3} $
$R_{1}=R $
$R_{2}=-R $
$\therefore \frac{1}{f}=\frac{1-4 / 3}{4 / 3}\left(\frac{1}{R}-\left(-\frac{1}{R}\right)\right) $
or $\frac{1}{f}=\frac{-\frac{1}{3}}{\frac{4}{3}} \times \frac{2}{R}$
or $ \frac{1}{f}=-\frac{1}{2 R}$
As $f$ is negative, so air bubble behaves as concave lens.