Brewster's Angle Formula and Reflected-Refracted Perpendicularity

It is tan. The formula is tan(iB) = mu (refractive index). Students confuse it with the critical angle for total internal reflection, which uses sin: sin(C) = 1/mu. Brewster = tan, critical angle = sin. Also note Brewster's angle is measured going from rarer to denser (air to glass), while critical angle is denser to rarer.

Start from Snell's law: mu = sin(i)/sin(r). At Brewster's angle mu = tan(iB) = sin(iB)/cos(iB). Setting the two right sides equal gives sin(r) = cos(iB) = sin(90 - iB), so r = 90 - iB. This means iB + r = 90. Since the reflected ray leaves at angle iB and the refracted ray at r from the same normal, the angle between them is 180 - (iB + r) = 90 degrees. So the perpendicularity is a direct result of the formula, not a separate rule.

The REFLECTED light is completely (plane) polarised, with its electric vector perpendicular to the plane of incidence. The refracted (transmitted) light is only PARTIALLY polarised because it still carries both vibration components. This is a very common NEET trap: many students wrongly pick the refracted ray.

No. The ordinary law of reflection still holds, so the angle of reflection equals the angle of incidence, both equal to iB. Brewster's angle only makes the reflected light polarised; it does not break the reflection law. For mu = 1.73 (root 3), iB = 60 degrees, so the reflected ray also comes off at 60 degrees.

For glass with mu = 1.5, tan(iB) = 1.5, so iB = tan-inverse(1.5) which is about 56.3 degrees. For water mu = 1.33, iB is about 53 degrees. Because mu is greater than 1 for any denser medium, tan(iB) is greater than 1, so iB always lies between 45 and 90 degrees.

Brewster's law states tan(iB) = mu, where iB is the polarising angle (Brewster's angle) and mu is the refractive index of the reflecting medium relative to the medium of incidence.

Exactly 90 degrees. The two rays are perpendicular to each other, which follows directly from iB + r = 90 combined with the geometry of reflection and refraction.

Yes, the reflected light is completely plane polarised with its electric vector perpendicular to the plane of incidence. The refracted light remains only partially polarised.

tan(iB) = 1.5 gives iB = tan-inverse(1.5), which is about 56.3 degrees.

Brewster's angle uses tan: tan(iB) = mu and gives polarised reflected light (rarer to denser). The critical angle uses sin: sin(C) = 1/mu and gives total internal reflection (denser to rarer). Different formulas, different phenomena.