Ray optics

Question

A bird in air looks at a fish directly below it inside in a transparent liquid in a tank. If the distance of the fish as estimated by the bird is h1 and that of the bird as estimated by the fish is h2, then the refractive index of liquid is

Moderate

Solution

Let h be the height the bird from the water before and d be the depth of the fish from the water surface

${\mathrm{h}}_{1}=\mathrm{h}+\frac{\mathrm{d}}{\mathrm{\mu}},{\mathrm{h}}_{2}=\mathrm{d}+\mathrm{\mu h}$

$\Rightarrow \frac{{\mathrm{h}}_{2}}{{\mathrm{h}}_{1}}=\frac{\mathrm{d}+\mathrm{\mu h}}{(\mathrm{d}+\mathrm{\mu h})/\mathrm{\mu}}=\mathrm{\mu}$

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