JEE Main · 2023 · 31 Jan 2023 · Shift 1 · EM Waves

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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 1 0^{8}

m s

^{- 1}

and for the given medium

μ_{r} = 1

)

Answer: 5

Solution

The light slows to

v = 0.2 c

in the medium, so its refractive index is

μ = \frac{c}{v} = \frac{1}{0.2} = 5

. Since

μ = ε_{r} μ_{r}

with

μ_{r} = 1

, the relative permittivity is

ε_{r} = μ^{2} = 25

. The required ratio is

\frac{ε _{r}}{μ} = \frac{25}{5} = 5

, so

x = 5

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Integer answer

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