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 $\frac{1}{f}=-\frac{1}{2R}$
As $f$ is negative, so air bubble behaves as concave lens.