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 . The value of is _______. (Given speed of light in free space and for the given medium )

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Solution

Q.
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 $= 3 \times 10^{8} {ms}^{- 1}$ and for the given medium $μ_{r} = 1$ ) [2023]

Ans.
(5)

$v = \frac{C}{μ} \Rightarrow μ = \frac{C}{v} = \frac{C}{0.2 C} = 5$

$μ = \sqrt{ε_{r} μ_{r}} \Rightarrow ε_{r} = \frac{μ^{2}}{μ_{r}}$

$\frac{ε_{r}}{μ} = \frac{μ}{μ_{r}} = 5$

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