Question

 An electromagnetic wave of frequency 3 MHz passes from vacuum into a dielectric medium with permittivity c = 4.0. Then
1. Wavelength is doubled and the frequency remains unchanged
2. Wavelength is doubled and the frequency becomes half
3. Wavelength is halved and the frequency remains unchanged 
4. Both the wavelength and frequency remain unchanged 

Answer 1

Correct Answer - Option 3 : Wavelength is halved and the frequency remains unchanged 

Concept:

Phase velocity: Distance traveled by wave in phase point per unit time.

The Phase Velocity of material in free space  is given by:

\({V_p} = \frac{c}{{\sqrt {{u_0}{\epsilon _0}} \;}}\)

Where,

μ₀ = Permeability in free space = 8.85 × 10^-12 Farads/m

ϵ₀ = Permittivity in free space = 4π × 10^-7 Henrys/m

The velocity of a wave in the dielectric medium is given by:

\({V_p} = \frac{c}{{\sqrt {{u_0}{\epsilon_0}{\epsilon_r}} \;}} \) ----(1)

Where,

ϵ_r = Permittivity in a medium  

Calculation:

Given:

f = 3MHz

ϵ_r = 4

From equation (1) we get,

\({V_p} = \frac{c}{{\sqrt {{u_0}{\epsilon_0}4} }} = \frac{c}{2}\)

Now as,

c = fλ

Where,

f = frequency

λ = wavelength

When a wave travels from one medium to another medium,

Frequency remains the same (f₁ = f₂)  but

Wavelength changes

So as c ∝ λ   

\({\lambda _{med}} = \frac{\lambda }{2}\)

So in a given case wavelength will become half but the frequency remains unchanged.