A layer of oil 3 cm thick is floating on a layer of coloured water 5 cm thick. The refractive index of the coloured water is 5/3 and the apparent depth of the two liquids is 36/7cm. Then the refractive index of the oil is,

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$\frac{7}{4}$

$\frac{5}{3}$

$\frac{7}{5}$

$\frac{5}{4}$

answer is C.

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Detailed Solution

$\begin{array}{l} μ = \frac{real depth}{apparent depth} \\ apparent depth = \frac{real depth}{μ} \\ \frac{36}{7} = \frac{3}{μ_{oil}} + \frac{5}{(5 / 3)} \Rightarrow μ_{oil} = \frac{7}{5} \end{array}$

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