Question 8: EM waves

Question

An electromagnetic wave of frequency $$3 \mathrm{~MHz}$$ passes from vacuum into a dielectric medium $$(\mu_r=1)$$ of relative permittivity 4.0. Then,

Accepted Answer

When an electromagnetic wave passes from one medium to another, the frequency remains unchanged. Here's why:
In vacuum, the speed of light is $$c$$ and the wavelength is given by the formula:
$$\lambda_0 = \frac{c}{f}$$
When the wave enters the dielectric medium, its speed becomes:
$$v = \frac{c}{\sqrt{\epsilon_r \mu_r}}$$
Given that $$\mu_r = 1$$ and $$\epsilon_r = 4.0$$, we have:
$$v = \frac{c}{\sqrt{4.0}} = \frac{c}{2}$$
The frequency $$f$$ remains the same as in vacuum, so the new wavelength $$\lambda'$$ in the medium is:
$$\lambda' = \frac{v}{f} = \frac{c/2}{f} = \frac{1}{2}\left(\frac{c}{f}\right) = \frac{\lambda_0}{2}$$
Thus, the wavelength is halved, and the frequency remains unchanged.
The correct option is:
Option D
Wavelength is halved and frequency remains unchanged.

Answer

Wavelength is halved and frequency is doubled

Answer

Wavelength doubled and frequency remains unchanged

Answer

Wavelength and frequency are unchanged

Answer

Wavelength is halved and frequency remains unchanged

EM waves

An electromagnetic wave of frequency $3 \mathrm{~MHz} passes from vacuum into a dielectric medium (\mu_r=1)$ of relative permittivity 4.0. Then,

Choose the correct answer: