First slide

Nature of electromagnetic wave

Question

An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with relative permittivity $\in$ = 4.0. Then

Easy

A

Wavelength is doubled and frequency becomes half.
B

Wavelength is halved and frequency remains unchanged.
C

Wavelength and frequency both remain unchanged.
D

Wavelength is doubled and frequency unchanged.

Solution

Frequency of electromagnetic wave does not change with change in medium but wavelength and velocity of wave changes with change in medium. Velocity of electromagnetic wave in vacuum
$c = \frac{1}{\sqrt{μ_{0} \in_{0}}} = v λ_{vacuum} . . . . . . (i)$
Velocity of electromagnetic wave in the medium
$v_{medium} = \frac{1}{\sqrt{μ_{0} μ_{r} \in_{0} ϵ_{r}}} = \frac{c}{\sqrt{μ_{r} \in_{r}}}$
where $μ_{r} and ϵ_{r}$ be relative permeability and relative permittivity of the medium. For dielectric medium, $μ_{r} = 1$
$Here, \in_{r} = 4.0 ∴ v_{medium} = \frac{c}{\sqrt{ϵ_{r}}} . . . . . . . . . (i i) Wavelength of the wave in medium λ_{medium} = \frac{v_{medium}}{v} = \frac{c}{2 v} = \frac{λ_{vacuum}}{2} (Using (i) and (ii))$

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