Question

A layer of oil of thickness 5.8 cm is floating on a water layer of thickness 8 cm. If the total apparent depth is 10 cm and the refractive index of water is 3/4, then the refractive index of oil is

• A. 1.55
• B. 1.50
• C. 1.45
• D. 1.40

Hint:

- Refractive index: $\mu = \text{real depth}/\text{apparent depth}$. - For layered liquids, add contributions: $h_\text{app} = \sum h_i/\mu_i$. - Carefully check units (cm vs m) and $\mu$ values (should be $>1$ for liquids).

Answer 1

The Correct Option is B

1. Apparent depth formula: $h_\text{app} = \frac{h_1}{\mu_1} + \frac{h_2}{\mu_2}$, $\mu_1$ = oil, $\mu_2$ = water.
2. Given: $h_\text{oil} = 5.8~\text{cm}, h_\text{water} = 8~\text{cm}, h_\text{app} = 10~\text{cm}, \mu_\text{water} = 3/4$? Check: refractive index normally $>1$, likely $\mu_\text{water} = 4/3$.
3. Using $10 = 5.8/\mu_\text{oil} + 8/(4/3) = 5.8/\mu_\text{oil} + 6 \implies 5.8/\mu_\text{oil} = 4 \implies \mu_\text{oil} = 5.8/4 \approx 1.45-1.5$