First slide

Electromagnetic waves and its nature

Question

An electromagnetic wave of frequency $3.0 M H z$ passes from Vacuum into a non-magnetic medium with permittivity $\in = 25 \in_{0}$ , where $\in_{0}$ is the free space permittivity. The change in wavelength is

Moderate

A

20 m
B

-20 m
C

-80 m
D

80 m

Solution

when an electro magnetic wave is travelled from one medium to another medium its frequency remains constant but its velocity and wavelength will be changed. Speed of electromagnetic wave in vacuum is $C = \frac{1}{\sqrt{μ_{0} \in_{0}}} = f λ$
Where $' f'$ is frequency and $' λ'$ is wavelength of electromagnetic wave
Speed of electromagnetic wave in a medium is $C' = \frac{1}{\sqrt{k μ_{0} \in_{0}}}$ where $' K'$ is dielectric constant
$C' = \frac{1}{\sqrt{k μ_{0} \in_{0}}} = f λ'$ where $λ'$ is wavelength of wave in a medium
Therefore, $\frac{f λ'}{f λ} = \frac{1}{\sqrt{k}} \Rightarrow λ' = \frac{λ}{\sqrt{k}} \Rightarrow λ' = \frac{λ}{\sqrt{\frac{\in}{\in_{0}}}}$
$λ' = \frac{λ}{\sqrt{25}} \Rightarrow λ' = \frac{λ}{5}$
Change in wavelength is $λ' - λ = \frac{λ}{5} - λ \Rightarrow λ' - λ = - \frac{4}{5} λ = - \frac{4}{5} \times \frac{C}{f}$
$\Rightarrow λ' - λ = \frac{- 4}{5} \times \frac{3 \times 10^{8}}{3 \times 10^{6}} = \frac{- 400}{5} ∴ λ' - λ = - 80 m$

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