If an optical medium possesses a relative permeability of and relative permittivity of , then the velocity of light is greater in vacuum than that in this medium by _______ times. () [2025]

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Solution

Q.
If an optical medium possesses a relative permeability of $\frac{10}{π}$ and relative permittivity of $\frac{1}{0.0885}$ , then the velocity of light is greater in vacuum than that in this medium by _______ times. ( $μ_{0} = 4 π \times 10^{- 7} H / m, \in_{0} = 8.85 \times 10^{- 12} F / m, c = 3 \times 10^{8} m / s$ ) [2025]

Ans.
(6)

Since velocity of light in terms of $μ$ and E is

$v = \frac{1}{\sqrt{μ ε}} = \frac{1}{\sqrt{μ_{0} μ_{r}}} \times \frac{1}{\sqrt{ε_{0} ε_{r}}} = \frac{1}{\sqrt{μ_{r} ε_{r}}} \times \frac{1}{\sqrt{μ_{0} ε_{0}}}$

$v = \frac{c}{\sqrt{μ_{r} ε_{r}}} = \frac{c}{\sqrt{\frac{10}{π} \times \frac{1}{0.0885}}} = \frac{c}{\sqrt{36}} = \frac{c}{6}$

$\Rightarrow c = 6 v$

Velocity of light in vacuum is greater by 6 times the velocity of light in medium.

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