In a medium the speed of light wave decreases to 0.2 times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is x: 1. The value of x is _________.
(Given speed of light in free space =3 × 10⁸ m s⁻¹ and for the given medium μᵣ=1)

Solution

Physics sir · 3 steps

Get the refractive index from the speed ratio, then square it to get the permittivity.

1. Refractive index. The refractive index is how many times slower light travels in the medium: n = c/v = c/(0.2 c) = 5.

   n = √(εᵣ μᵣ)

2. Relative permittivity. This follows from v = 1/√(μ ε) in a medium. With μᵣ = 1, n² = εᵣ, so εᵣ = 5² = 25.
3. So. εᵣ/n = 25/5 = 5, so the ratio is 5 : 1 and x = 5.

The common slip: 25. Stopping at the permittivity gives 25, which is εᵣ itself. The question asks for εᵣ divided by n, which is 5.

The idea to keep. In a non-magnetic medium, n = √εᵣ. Find n from the speed ratio first, then square it for εᵣ. The given value of c is not needed.

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