Each quarter of a vessel of depth H is filled with liquids of the refractive indices μ1,μ2,μ3 and µ4 from the bottom respectively. The apparent depth of the vessel when looked normally is

H 2 1 μ 1 + 1 μ 2 + 1 μ 3 + 1 μ 4

H 4 1 μ 1 + 1 μ 2 + 1 μ 3 + 1 μ 4

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Each quarter of a vessel of depth H is filled with liquids of the refractive indices $μ_{1}, μ_{2}, μ_{3}$ and µ₄ from the bottom respectively. The apparent depth of the vessel when looked normally is

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$\frac{H}{2} (\frac{1}{μ_{1}} + \frac{1}{μ_{2}} + \frac{1}{μ_{3}} + \frac{1}{μ_{4}})$

$\frac{μ_{1} + μ_{2} + μ_{3} + μ_{4}}{4 H}$

$\frac{H}{4} (μ_{1} + μ_{2} + μ_{3} + μ_{4})$

$\frac{H}{4} (\frac{1}{μ_{1}} + \frac{1}{μ_{2}} + \frac{1}{μ_{3}} + \frac{1}{μ_{4}})$

answer is B.

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Detailed Solution

Apparent depth of bottom
$\begin{array}{l} = \frac{H / 4}{μ_{1}} + \frac{H / 4}{μ_{2}} + \frac{H / 4}{μ_{3}} + \frac{H / 4}{μ_{4}} \\ = \frac{H}{4} [\frac{1}{μ_{1}} + \frac{1}{μ_{2}} + \frac{1}{μ_{3}} + \frac{1}{μ_{4}}] \end{array}$

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