Question

Show that  Brewster angle does not exist for TE  polarized light.

. WHERE is TE transverse electric

Answer 1

Solution:

For a plane electromagnetic wave incident on the plane boundary between medium 1 and medium 2, the amplitude reflectivities of TE(transverse electric) and TM(transverse magnetic) waves are given by the Fresnel formulae:

where,

θi and θt are the angles of incidence and transmission, respectively. The numerators in above equations cannot vanish because θi is not equal to θt. However, rTM can vanish because tan (θi + θt) diverges to infinity when (θi+θt) is equal to π/2.

Physically, Brewster’s phenomena can be understood as follows:

The direction of the induced electric dipole in medium 2 is perpendicular to the wave vector therein. With regard to TM waves, the dipole lies in the plane of incidence. A linearly vibrating dipole radiates transversally and cannot emit radiation in the direction of the vibration. This direction coincides with the wave vector of the reflected wave when the Brewster condition is satisfied. The oscillating dipoles in the medium 2 do not send any waves in the direction of the reflection. On the other hand, with regard to TE waves, each dipole is perpendicular to the plane of incidence and emits waves isotropically in the plane. Therefore, no special angles exist for TE waves. Hence, Brewster’s effect in dielectric media exists only for TM waves, and not for TE waves.