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 $12cm$ below the water surface, the radius of this circle in $cm$ is

• A. $36\sqrt{7}$
• B. $\frac{36}{\sqrt{7}}$
• C. $36\sqrt{7}$
• D. $4\sqrt{5}$

Answer 1

Answer: (B)

The situation is shown in figure.

$\sin {\theta }_C=\frac{1}{\mu }$
$\tan {\theta }_C=\frac{AB}{AO}$
$\therefore AB=OA\tan {\theta }_C$
or $AB=\frac{OA}{\sqrt{{\mu }^2-1}}$
$=\frac{12}{\sqrt{{\left(\frac{4}{3}\right)}^2-1}}$
$=\frac{36}{\sqrt{7}}$