Question

All lights are switched off, except for a bright point-light source kept at the bottom of a swimming pool filled with clear water of refractive index $4/3$. As a result, only a circular patch of $6\, m$ diameter of the water surface is visible to spectators standing around the swimming pool. Which of the following gives the nearest value of the depth of the pool?

• A. 1.6 m
• B. 2.0 m
• C. 2.6 m
• D. 3.0 m

Answer 1

Answer: (C)

2.6 m

Answer 2

Given situation is shown in the figure.
$\mu_W = \frac{4}{3} ; r = \frac{D}{2} = \frac{6}{2} = 3 \, m$
$h = ?$
This situation is seen if there is phenomena of total internal reflection of light.
$\therefore \:\:\: \sin \, C = \frac{1}{ \mu_W} = \frac{3}{4}$
Again from figure,
$\sin C = \frac{r}{\sqrt{r^{2}+h^{2}}} ; \frac{3}{4} =\frac{3}{\sqrt{3^{2} +h^{2}}}$
or $16 = 9 + h^2 ; h^2 = 7 , h = \sqrt{7} \, m = 2.6 \, m$