Question

An electromagnetic wave of frequency $\upsilon$ = 3.0 MHz passes from vacuum into a dielectric medium with relative permittivity $\varepsilon$ = 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)

Wavelength is halved and frequency remains unchanged

Answer 2

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