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Question

An electromagnetic wave of frequency v=3MHz passes from a vacuum into a dielectric medium with permittivity 4. What happens to the wavelength?


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Solution

Step1: Given data

  1. The frequency of the wave is v=3MHz.
  2. the dielectric constant of the medium is k=4.

Step2: Velocity of light

  1. From Maxwell's electromagnetic theory we know that the velocity of light in a medium, c=1μoεo, where, μo is the magnetic permeability and εo permittivity of the medium.
  2. Also, velocity, c=νλ, where, ν is the frequency of light and λ is the wavelength of light.

Step3: Finding the wavelength

As we know, the velocity of light in a medium is vmed=1μoε.

So,

vmed=1μokεo=1μo×4×εoorvmed=12×1μoεoSince,ε=kεoorvmed=c2since,c=1μoεo

Again, we know the velocity, c=νλ

We know that frequency of light is constant in the medium.

Now,

λmedλair=c2c=12orλmedλair=12.

Therefore, the wavelength of the wave will be halved.


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