For a transparent medium relative permeability and permittivity, and are 1.0 and 1.44 respectively. The velocity of light in this medium would be [2019]

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Solution

Q.
For a transparent medium relative permeability and permittivity, $μ_{r}$ and $ε_{r}$ are 1.0 and 1.44 respectively. The velocity of light in this medium would be [2019]

1 $2.5 \times 10^{8}$ m/s

2 $3 \times 10^{8}$ m/s

3 $2.08 \times 10^{8}$ m/s

4 $4.32 \times 10^{8}$ m/s

Ans.
(1)

Given: relative permittivity, $ε_{r} = 1.44$ and relative permeability, $μ_{r} = 1$

Now, as we know that, $ε_{r} = \frac{ε}{ε_{0}} \Rightarrow ε = ε_{r} ε_{0}$

and $μ_{r} = \frac{μ}{μ_{0}} \Rightarrow μ = μ_{r} μ_{0}$

where, $ε$ and $μ$ are the permittivity and permeability of the medium.

$∴$ Velocity of light in the medium will be

$v = \frac{1}{\sqrt{μ ε}} = \frac{1}{\sqrt{μ_{r} μ_{0} ε_{r} ε_{0}}} = \frac{c}{\sqrt{μ_{r} ε_{r}}} = \frac{3 \times 10^{8}}{\sqrt{1 \times 1.44}}$

$= 2.5 \times 10^{8} m/s$

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