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 × 10 8 m s - 1 and for the given medium μ r = 1 )

Step-by-step solution

Speed of light in medium is related to speed of light in vacuum c and refractive index μ by v = c μ . Then, we have μ = c v = c 0 . 2 c ⇒ μ = 5 Refractive index in terms of relative permeability μ r and relative permittivity ε r of the medium is stated as μ = ϵ r   μ r ⇒ ϵ r = μ 2 μ r ∴   ϵ r μ = μ μ r = 5 Hence, the value of x = 5 .