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# A layer of oil 3 cm thick is floating on a layer of colored water 5 cm thick refractive index of colored water is $\large\frac{5}{3}$ and apparent depth of two liquids appears to be $\large\frac{36}{7}$cm. Then refractive index of oil:

$(a)\;1.2 \\ (b)\;1.6 \\ (c)\;1.4 \\ (d)\;1.8$

Apparent depth $=\large\frac{t_1}{\mu_1}+\frac{t_2}{\mu_2}$
$\therefore \large\frac{36}{7}=\frac{5}{\Large\frac{5}{3}}+\frac{3}{\mu_2}$
$\large \frac{3}{\mu_2}=\frac{36}{7}$$-3 =\large \frac{15}{7} \therefore \mu_2=\large\frac{7}{5}$$=1.4$
Hence c is the correct answer.