Each quarter of a vessel of depth H is filled | vedclass

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(B) The apparent depth $d'$ of an object in a medium of refractive index $n$ and real depth $d$ is given by $d' = \frac{d}{n}$.Since the vessel of tot

Vedclass · Accepted Answer

$\frac{H}{4} \left( \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3} + \frac{1}{n_4} \right)$

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(B) The apparent depth $d'$ of an object in a medium of refractive index $n$ and real depth $d$ is given by $d' = \frac{d}{n}$.Since the vessel of total depth $H$ is divided into four equal quarters,each layer has a real depth of $d = \frac{H}{4}$.The apparent depth of each layer is $\frac{H/4}{n_1}, \frac{H/4}{n_2}, \frac{H/4}{n_3}$,and $\frac{H/4}{n_4}$ respectively.The total apparent depth is the sum of the apparent depths of all four layers:$d'_{total} = \frac{H/4}{n_1} + \frac{H/4}{n_2} + \frac{H/4}{n_3} + \frac{H/4}{n_4}$$d'_{total} = \frac{H}{4} \left( \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3} + \frac{1}{n_4} \right)$.

Each quarter of a vessel of depth $H$ is filled with liquids of the refractive indices $n_1, n_2, n_3$ and $n_4$ from the bottom respectively. The apparent depth of the vessel when looked normally is

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