The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4/3 for this wavelength, will be :

Solution

Physics sir · 3 steps

Get the refractive index from εᵣ and μᵣ first; the critical angle then follows in one line.

1. Refractive index. Light travels in a medium at speed v = 1/√με. So the refractive index depends on both the relative permittivity and the relative permeability.

   n = c/v = √(μᵣ εᵣ) = √(4/3 × 3) = √4 = 2

2. Critical angle. For light going from this medium into air, sin C = 1/n = 1/2.
3. So. C = sin⁻¹(1/2) = 30°, which is option (c).

The idea to keep. Refractive index is √(μᵣ εᵣ), not εᵣ alone. Once you have n, the critical angle is always sin C = 1/n.

Answer from the NTA final answer key. Solution by PrepWiser.