Question

An electromagnetic wave of frequency $v$ = $3.0$ $MHz$ passes from vacuum into a dielectric medium with relative permittivity $\epsilon$ = $4$. Then,

• A. Wavelength is doubled and frequency becomes half.
• B. Wavelength is halved and frequency remains unchanged.
• C. Wavelength and frequency both remains unchanged.
• D. Wavelength is doubled and frequency remains unchanged.

Answer 1

The correct option is B Wavelength is halved and frequency remains unchanged.

Frequency of electromagnetic waves does not change with change in medium but wavelength and velocity of wave change with medium.
Velocity of electromagnetic wave in vacuum
$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}=v{\lambda }_{vacuum}$
Velocity of electromagnetic wave in medium
$v_{medium}=\frac{1}{\sqrt{{\mu }_0{\mu }_r{\epsilon }_0{\epsilon }_r}}=\frac{c}{\sqrt{{\mu }_r{\epsilon }_r}}$
For a dielectric medium, ${\mu }_r=1$
$\frac{{\lambda }_{medium}}{{\lambda }_{vacuum}}=\frac{v_{medium}}{v_{vacuum}}=\frac{1}{2}\therefore {\lambda }_{medium}=\frac{{\lambda }_{vacuum}}{2}$