Question

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

• 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

Answer 1

Answer: (B)

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
$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}=v{\lambda }_{\text{vacuum }}\dots \dots \dots \dots .(i)$
Velocity of electromagnetic wave in the medium
$v_{\text{medium }}=\frac{1}{\sqrt{{\mu }_0{\mu }_r{ϵ}_0{ϵ}_r}}=\frac{c}{\sqrt{{\mu }_r{ϵ}_r}}$
where ${\mu }_r$ and ${\in }_r$ be relative permeability and relative
permittivity of the medium.
For dielectric medium, ${\mu }_r=1$
$\therefore v_{\text{medium }}=\frac{c}{\sqrt{{ϵ}_r}}$
Here , ${\in }_r=4.0$
$\therefore v_{\text{medium }}=\frac{c}{\sqrt{4}}=\frac{c}{2}\dots \dots \dots \dots ...(ii)$
Wavelength of the wave in medium
${\lambda }_{\text{medium }}=\frac{v_{\text{medium }}}{v}=\frac{c}{2v}=\frac{{\lambda }_{\text{vacuum }}}{2}($ Using (i) and (ii))