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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

AIIMSAIIMS 2008

Solution:

The situation is shown in figure.
image
$ \sin \theta_{C} =\frac{1}{\mu}$
$\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}} $
$=\frac{12}{\sqrt{\left(\frac{4}{3}\right)^{2}-1}}$
$=\frac{36}{\sqrt{7}}$