Question

A thin oil layer floats on water. A ray of light making an angle of incidence \( 45^\circ \) shines on the oil layer. The angle of refraction of light ray in water is:

• A. \( \sin^{-1} \left( \frac{3}{\sqrt{32}} \right) \)
• B. \( \sin^{-1} \left( \frac{3}{32} \right) \)
• C. \( \sin^{-1} \left( \frac{9}{\sqrt{32}} \right) \)
• D. \( \sin^{-1} \left( \frac{9}{32} \right) \)

Hint:

Snell's law is used to calculate the angle of refraction when light passes from one medium to another with different refractive indices. \( \mu_1 \sin i = \mu_2 \sin r \).

Answer 1

The Correct Option is D

Using Snell's law: \[ \mu_{\text{oil}} \sin i = \mu_{\text{water}} \sin r \] Substitute the values: \[ 1.54 \sin 45^\circ = 1.33 \sin r \] \[ \sin r = \frac{1.54 \times \frac{1}{\sqrt{2}}}{1.33} \] After calculating: \[ \sin r = \frac{9}{\sqrt{32}} \Rightarrow \sin^{-1} \left( \frac{9}{\sqrt{32}} \right) \]