Question

A ray of light in a transparent material of refractive index 2.5 is approaching a material with a refractive index of 1.25. At the boundary, the critical angle is

• A. 60°
• B. 90°
• C. 30°
• D. 45°

Answer 1

Answer: (C)

30°

Answer 2

• Concept: Total Internal Reflection (TIR) occurs when light travels from a denser medium to a rarer medium. The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.

• Formula: The critical angle ($\theta_c$) is given by Snell's Law: $\mu_1 \sin \theta_c = \mu_2 \sin 90^\circ$ Since $\sin 90^\circ = 1$, the formula simplifies to: $\sin \theta_c = \frac{\mu_2}{\mu_1}$ where $\mu_1$ is the refractive index of the denser medium (from which light is coming) and $\mu_2$ is the refractive index of the rarer medium (to which light is going).

• Given values: Refractive index of the first material (denser medium), $\mu_1 = 2.5$ Refractive index of the second material (rarer medium), $\mu_2 = 1.25$

• Calculation: Substitute the values into the formula: $\sin \theta_c = \frac{1.25}{2.5}$ $\sin \theta_c = \frac{1}{2}$ To find $\theta_c$, take the inverse sine of (1/2): $\theta_c = \arcsin\left(\frac{1}{2}\right)$ $\theta_c = 30^\circ$

The critical angle at the boundary is 30°.