Question

An electromagnetic wave of frequency $3MHz$ passes from vacuum into a dielectric medium with relative permittivity ${\epsilon }_r=4$ and relative permeability ${\mu }_r=1,$ then

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

Answer 1

The correct option is D the wavelength is halved and the frequency remains unchanged.

Frequency will always be independent of medium.
Here also frequency remains unchanged.

now,
${\mu }_{\left(refractiveindex\right)}=\frac{c}{v}=\frac{1/\sqrt{{\epsilon }_0{\mu }_0}}{1/\sqrt{\epsilon \mu }}=\sqrt{{\epsilon }_r{\mu }_r}$

Since, ${\mu }_r$ is very close to 1, then
${\mu }_{\left(refractiveindex\right)}=\sqrt{{\epsilon }_r}$

and given, ${\epsilon }_r=4$
${\mu }_{\left(refractiveindex\right)}=\sqrt{4}=2$

Variation of wavelength with medium is given by
${\lambda }_{medium}=\frac{{\lambda }_{vaccum}}{{\mu }_{\left(refractiveindex\right)}}=\frac{\lambda }{2}$
Hence, correct answer is option (d).