Test: Plane Waves

1. Under the electromagnetic spectrum, visible light has the lowest frequency among the given option.

2. The spectrum ranges from radio waves having low frequency till gamma rays, having the highest one.

Concept:

Loss tangent is given by

tan⁡θ = σ/ω

And angle between E and H is:  
θ_n  = θ/2

For a plane wave propagating in an unbounded medium, the angle between the electric field and magnetic field is always 90°

Concept:

The waves are used for the transportation of energy or information.

Characteristics of a plane wave in good conductors.

In a good conductor σ >> ωϵ 

σ ≈ ∞, ϵ = ϵ₀, μ = μ₀μ_r 

Calculation:

Given ϵr = 1, μr = 20, σ = 3 S/m and 

Hence the given medium is a good conductor.

In a good conductor the values of α and β are:

α = β = 61.39

Concept:

When more than one incident light ray or any EM wave, reflects off a surface, the laws of reflection still holds, but the surface affects the way we see the reflected rays.

Specular Reflection:

It happens when a beam of light ‘or’ EM waves in general, is reflected “perfectly” (in parallel to each other) from a shiny, polished surface. Ex- mirrors, stainless steel, glass, etc.

Diffuse Reflection:

It happens when a Beam of light is Reflected “irregularly” (in different directions) from an irregular surface. Ex- sheet fo paper, tabletop etc.

This is explained with the help of the diagram shown:-

The velocity is the ratio of the frequency to the phase constant.
In conductors, the phase constant is given by √(ωμσ/2).
On substituting for β,ω in v, we get v = √(2ω/μσ) units.

In free space or air medium, the velocity of the wave propagating will be same as that of the light.
Thus the velocity is the speed of light,
V = c. It is given by 3 x 10⁸m/s.

In free space or air medium, the relative permeability is also unity, like relative permittivity.
The absolute permeability is given by 4π x 10^-7 units.

The total permeability is the product of the absolute and the relative permeability.
For metals or conductors, the relative permittivity is not unity.
Thus the permittivity is the product of absolute and relative permeability.

The intrinsic impedance is the square root of ratio of the permeability to the permittivity. In free space, the permeability and the permittivity is same as the absolute permeability and permittivity respectively.
This is due to unity permeability and permittivity in free space.
Thus η = √(μ/ε), where absolute permeability is given by 4π x 10^-7 and absolute permittivity is given by 8.854 x 10^-12.
The intrinsic impedance will be 377 ohms.

The intrinsic impedance in a conductor is given by η = √(ωμ/2σ) x (1 + j).
The phase shift is represented by the 1 + j term.
In polar form it indicates 45 degree phase shift.