Question

An electromagnetic wave of frequency $v=3.0 \,MHz$ 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
$c=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}=v \lambda_{\text {vacuum }} \ldots \ldots \ldots \ldots .( i )$
Velocity of electromagnetic wave in the medium
$v_{\text {medium }}=\frac{1}{\sqrt{\mu_{0} \mu_{r} \epsilon_{0} \epsilon_{r}}}=\frac{c}{\sqrt{\mu_{r} \epsilon_{r}}}$
where $\mu_{r}$ and $\in_{r}$ be relative permeability and relative
permittivity of the medium.
For dielectric medium, $\mu_{r}=1$
$\therefore v_{\text {medium }}=\frac{c}{\sqrt{\epsilon_{r}}}$
Here , $\in_{r}=4.0$
$\therefore v_{\text {medium }}=\frac{c}{\sqrt{4}}=\frac{c}{2} \ldots \ldots \ldots \ldots . . .(i i)$
Wavelength of the wave in medium
$\lambda_{\text {medium }}=\frac{v_{\text {medium }}}{v}=\frac{c}{2 v}=\frac{\lambda_{\text {vacuum }}}{2}($ Using (i) and (ii))