Question

An electromagnetic wave of frequency $\upsilon = 3.0MHz$ passes from vacuum into a dielectric medium with permittivity $\varepsilon = 4.0$ then
A) Wavelength is halved and frequency remains unchanged.
B) Wavelength is doubled and frequency becomes half.
C) Wavelength is doubled and frequency remains unchanged.
D) Wavelength and frequency both remain unchanged.

Answer 1

Hint:When an electromagnetic wave travels from one medium to another medium the frequency of the wave does not change but the wavelength and velocity change with the medium.

Step by step solution:
In this question it is given that a electromagnetic wave pass from vacuum into a dielectric medium when electromagnetic wave pass through any medium its frequency never will be change
But its velocity will change as well as wavelength
The velocity of electromagnetic wave directly proportional to the wavelength of wave
$ \Rightarrow v \propto \lambda $
And we know in vacuum, electromagnetic wave travel with a definite and constant speed given by
$ \Rightarrow c = \dfrac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }}$ ........... (1)
Where ${\mu _0} \Rightarrow $permeability of free space
${\varepsilon _0} \Rightarrow $ Permittivity of free space
And speed of electromagnetic wave in any other medium is given by
$ \Rightarrow {v_{medium}} = \dfrac{1}{{\sqrt {{\mu _0}{\varepsilon _0}\varepsilon } }}$
$ \Rightarrow {v_{medium}} = \dfrac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} \sqrt \varepsilon }}$ ........... (2)
Where $\varepsilon \Rightarrow $ permittivity of medium
From equation (1)
$ \Rightarrow {v_{medium}} = \dfrac{c}{{\sqrt \varepsilon }}$
$\varepsilon = 4$ Given in question
$ \Rightarrow {v_{medium}} = \dfrac{c}{{\sqrt 4 }} = \dfrac{c}{2}$
Means velocity become half of velocity in vacuum
As we know
$ \Rightarrow v \propto \lambda $
So
$ \Rightarrow {\lambda _{medium}} = \dfrac{{{\lambda _{space}}}}{2}$
Hence we see that the wavelength and velocity become half and frequency does not change
Hence option A is correct

Note:We use in this question velocity of wave directly proportional to its wavelength in that medium this can be understand by formula which given below
We know the relation between velocity and wavelength of electromagnetic wave is given as
$ \Rightarrow v = \upsilon \lambda $
Where $v $ is the velocity of the wave, $\upsilon $ is the frequency of the electromagnetic wave, and $\lambda $ is the wavelength of electromagnetic wave.