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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

Ray Optics and Optical Instruments

Solution:

The situation is shown in figure.
image
$sin\theta_{c} =\frac{1}{\mu}$
$ \tan \theta_C=\frac{AB}{AO} $
$\therefore AB=OA \tan \theta_C $
or $ AB=\frac{OA}{\sqrt{\mu^2-1}} $
$ =\frac{12}{\sqrt{\bigg(\frac{4}{3}\bigg)^2-1}}=\frac{36}{\sqrt 7} $