Example: Calculate the Brewster angle for radiation in air (n1 = 1) that impinges on a quartz laser window (n2 = 1

Example: Calculate the Brewster angle for radiation in air (n₁ = 1) that impinges on a quartz laser window (n₂ = 1.45).

Snell's law tells us that the relationship between the incidence wave and the refracted wave is n₁ sinq₁ = n₂ sin q₂.

The Brewster angle condition is q₁+ q₂ = p/2. Thus, q₂ = p/2 - q₁.

n₁ sinq₁ = n₂ sin(p/2 - q₁)

n₁ sinq₁ = n₂ sin(p/2)cosq₁ - cos(p/2) sinq₁

n₁ sinq₁ = n₂ cosq₁

tanq₁ = n₂/n₁

q₁ = arctan(n₂/n₁) = arctan(1.45/1)

q₁ = 55.4^o