A layer of oil 3cm thick is floating on a layer of coloured water 5cm thick. Refractive index of coloured water is 5/3 and the apparent depth of the two liquids appears to be 36/7 cm. Find the refractive index of oil.
Answer & explanation
Correct answer: option 3
Apparent depth (AI) = $\frac{t_1}{μ_1}+\frac{t_2}{μ_2}$
$∴\frac{36}{7}=\frac{5}{5/3}+\frac{3}{μ_2}$
$∴\frac{3}{μ_2}=\frac{36}{7}-3=\frac{15}{7}$
$∴μ_2=\frac{7}{5}=1.4$