Question

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $14\text{cm}$ below the surface, the area of this circle in ${\text{cm}}^2$ is

• A. $369$
• B. $728$
• C. $492$
• D. $792$

Answer 1

The correct option is D $792$

Area of the circular horizon, $A=\pi r^2$
$A=\pi [\frac{h}{\sqrt{{\mu }^2-1}}{]}^2=\frac{\pi h^2}{{\mu }^2-1}$

$A=\frac{22}{7}\times \frac{14\times 14}{(\frac{16}{9}-1)}$

$A=\frac{22\times 14\times 14\times 9}{7\times 7}$

$A=22\times 36$

$A=792{\text{cm}}^2$