Question

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability \( \frac{4}{3} \) for this wavelength, will be:

• A. 15°
• B. 30°
• C. 45°
• D. 60°

Hint:

The refractive index \( n \) is fundamentally linked to the speed of light in the medium, which is determined by its electromagnetic properties (\( \epsilon \) and \( \mu \)). For most transparent materials, \( \mu_r \approx 1 \), but always check both values if provided!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The critical angle (\( \theta_c \)) is the angle of incidence in a denser medium for which the angle of refraction in the rarer medium (usually vacuum/air) is 90°. It depends on the refractive index of the medium.

Step 2: Key Formula or Approach
1. Refractive index \( n = \sqrt{\epsilon_r \mu_r} \) 2. Critical angle \( \sin \theta_c = \frac{1}{n} \)

Step 3: Detailed Explanation
1. Calculate Refractive Index (\( n \)): Given \( \epsilon_r = 3 \) and \( \mu_r = 4/3 \). \[ n = \sqrt{3 \times \frac{4}{3}} = \sqrt{4} = 2 \] 2. Calculate Critical Angle (\( \theta_c \)): \[ \sin \theta_c = \frac{1}{n} = \frac{1}{2} \] Since \( \sin 30^\circ = 1/2 \), then \( \theta_c = 30^\circ \).

Step 4: Final Answer
The critical angle of the medium is 30°.