Question

A plane wave of angular frequency ω is incident on a plasma medium with permeability µ₀ and permittivity ε = ε0 (1 − ω_p² /ω²) where ω_p is the plasma frequency and ω = 2ω_p.

a) Calculate the critical angle θc such that the incident wave is totally reflected

b) Calculate the Brewster angle θ_B such that TM waves are totally transmitted

c) In general for any two isotropic media, can you find an incident angle θ such that θ = θ_B > θ_c ? If you can give an example. If you cannot, explain why not.

A plane wave of angular frequency w 1s incident on a plasma medium with permeability Ho and permittivity W) where up is the plasma frequency and w 2wp a) Calculate the critical angle θ such that the incident wave is totally reflected b) Calculate the Brewster angle θΒ such that TM waves are totally transmitted c) In general for any two isotropic media, can you find an incident angle θ such that θ = θΒ > ? If you can give an example. If you cannot, explain why not.

Answer 1

Plasma is found in upper side of atmosphere. Ionosphere contains plasma. It is used in communication it can reflected only few frequency. EM - waves (i) Case - 1 w_p > w All the wave having frequency w < w_p can not travel through plasma. It will reflect and go back into original medium. Ii) Case - 2 If w > w_p k rightarrow real, n - real so wave will propagate rightarrow propagation Reflective index of plasma medium n < C/V epsilon = epsilon_0(1 - w_p^2/w^2) therefore w = 2wp epsilon = epsilon_0(1 - 1/4) = epsilon/epsilon_0 = 3/4 epsilon_r = 3/4 \r\n (a) mu_1 = mu_0 epsilon_0 mu_1 = mu_0 epsilon_2 = epsilon_0 n_1 sin theta i = n_2 sin theta T sin theta i/sin theta T = n_2/n_1 = V_1/V_2 = squareroot epsilon_2 mu_2/squareroot epsilon_1 mu_1 so n_2/n_1 = squareroot epsilon_6 n_2/n_1 = squareroot 3/2 if epsilon_1 > epsilon_2 or n_1 > n_2