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  4. A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is (4/3) and the fish is 12 cm below the water surface, the radius of this circle, in cm, is

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

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Solution:

The situation is shown in figure.
image
$\sin \theta_C=\frac{1}{\mu}$, hence, $\tan \theta_C=\frac{A B}{A O}$
$\therefore A B=O A \tan \theta_C$
or $A B=\frac{O A}{\sqrt{\mu^2-1}}=\frac{12}{\sqrt{\left(\frac{4}{3}\right)^2-1}}=\frac{36}{\sqrt{7}}$