Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

When light propagates through a material medium of relative permittivity, $\varepsilon_r$ and relative permeability, $\mu_r$ , the velocity of light, $v$ is given by: ( $c$ = velocity of light in vacuum)

$v = \frac{c}{\sqrt{\varepsilon_r \mu_r}}$

$v = c$

$v = \sqrt{\frac{\mu_r}{\varepsilon_r}}$

$v = \sqrt{\varepsilon_r \mu_r}$

Step-by-Step Solution

Speed in Vacuum: The speed of light in a vacuum ( $c$ ) is related to the permeability ( $\mu_0$ ) and permittivity ( $\varepsilon_0$ ) of free space by the equation: $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ .
Speed in Medium: In a material medium, the speed of light ( $v$ ) is determined by the absolute permeability ( $\mu$ ) and permittivity ( $\varepsilon$ ) of that medium: $v = \frac{1}{\sqrt{\mu \varepsilon}}$ .
Relative Properties: The absolute values are related to the relative values by $\mu = \mu_0 \mu_r$ and $\varepsilon = \varepsilon_0 \varepsilon_r$ .
Substitution: Substituting these into the velocity equation: $v = \frac{1}{\sqrt{(\mu_0 \mu_r) (\varepsilon_0 \varepsilon_r)}} = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \cdot \frac{1}{\sqrt{\mu_r \varepsilon_r}}$ Since $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ , we get: $v = \frac{c}{\sqrt{\mu_r \varepsilon_r}}$

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