Brewster's Angle

Brewster's angle: The Fresnel's equations eqs 1-4 tell us the variation of amplitude coefficient fro reflected and the transmitted ray for the given interface. The amplitude reflection Coefficient for the air –glass interface as a function of angle of incidence is shown in fig 1(a) for both the s polarized (perpendicular component) as well as p polarized (parallel component) wave. The corresponding reflectivity is shown in fig 1(b). Here air is taken as the first medium with refractive index n 1 =1 and the glass as the second medium having refractive index n = 1.5 .

Fig 1. (a) Variation of amplitude coefficient of reflection as a function of fig. 2(b) Reflectivity vs. a function of angle of incidence plotted.

The variation of amplitude coefficient of transmission as a function of angle of incidence is shown in fig. 2(a). Corresponding transmittance of both the waves shown in fig 2(b).

Fig.2 (a) Variation of amplitude coefficient of transmission as a function of angle of incidence.(b) Variation of transmittance of both the waves is shown.

Equation 1 shows that in the present case where n₁ < n₂ (air glass interface), the amplitude coefficient of reflection for the s wave (perpendicular component) is negative, indicating that the reflected and the incident wave are out of phase. The magnitude of reflection coefficient for this particular components increases with the increasing angle of incidence going to the value of 1 at (fig 1) .

Using the snall's law, equation 3 can be re-written as

..........................(1)

This will be positive and decrease with the angle of incidence for

or equivalently

......................................(2)

For the present case of air-glass interface, where n₁ < n₂ , the above inequality will hold for

..........................................(3)

For ...........................................(4)

For , indicating that the reflected light will only be only s polarized. Beyond this