A diver looking up through water in a lake sees the outside world contained in a circular horizon. I

Question

A diver looking up through water in a lake sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and if the diver is situated 12 cm below the surface what is the radius of the horizontal circle\

Professor PC Thomas Classes · Answer

Critical angle for water is $49^{\circ}$. So the fish under water sees the rising sun and setting sun at $49^{\circ}$ with the vertical and $41^{\circ}$ with the horizontal. The fish under water sees the outside world within a cone of semivertical angle $49^{\circ}$. If d is the depth of the fish under water, the radius of the circular horizon is $\mathrm{r}=\frac{\mathrm{d}}{\sqrt{\mathrm{n}^{2}-1}}$ where n is the refractive index of water. As the fish goes down the radius of the circular horizon goes on increasing, but the semivertical angle of the cone in which the fish sees the outside world remains constant. The area of the circular horizon will be $\pi \frac{d^{2}}{n^{2}-1}$\