Question

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be ______ × 10^-2 cm. 

Options

• 167

• 367

• 667

• 967

Answer 1

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be 667 × 10^-2 cm. 

Explanation:

Wavelength of EM wave λ_v in vacuum

= `"c"/"f"=(3xx10^8)/(3xx10^9)` = 0.1 m

∴ Wavelength of EM wave λ_m in medium = `0.1/mu`

 Where µ is refractive index given by,

µ = `sqrt(mu_"r"epsilon_"r")`

Assuming material to be non-magnetic,

µ_r = 1

∴ µ = `sqrt(1xx2.25)` = 1.5

λ_m = `0.1/1.5 = 1/15`m

= 6.67 cm 

= 667 × 10^-2 cm.