# A Question About Brewster's Law

In most textbooks I read, they state that when the angle of reflection + angle of refraction = 90, there is maximum polarization. What I don't understand is what maximum polarization means. Does it mean that the polarized light is of the highest intensity? Does it mean that most of the light beam is polarized when reflected at that angle, as compared to any other angle? What does it mean? Please explain this at the level of a high school student.

• How do i cancel the downvote ? – Abhirup Mukherjee Oct 23 '18 at 17:12
• @AbhirupMukherjee: after a 5-minute grace period, downvotes are "locked in" unless and until the question is edited. If someone edits the question, then you'll be able to remove the downvote. – Michael Seifert Oct 24 '18 at 13:56

Any light beam can be viewed as a superposition of two polarized light beams. For example, if a wave is coming towards you, there would be one polarization that's vertical, and the other one would be horizontal. If you pass this beam through a polarizing filter, it will block one of the polarizations but let the other one through. Depending on how much of each polarization was in the original beam, the beam that you would see on the other side of the polarizer might be the same intensity (brightness), a little dimmer, or be totally extinguished. In this way, you can imagine measuring the intensity of each of the two polarizations that make up the original beam.

We can quantify how much a beam is polarized by looking at how much the intensity of the polarizations differs, expressed as a fraction of the total intensity: $$\text{polarization} = \frac{|I_A - I_B|}{I_A + I_B} \times 100\%,$$ where $$I_A$$ and $$I_B$$ are the intensities of the the two possible polarizations. If, for example, all of the light intensity in the original beam is in polarization $$A$$, and none is in $$B$$, then you'll get a polarization of 100%. On the other hand, if the intensities of the two polarizations are equal, you'll get 0% polarization, i.e. the original beam was unpolarized. If one of the polarizations is brighter than the other, but both polarizations have some intensity, then you'll get somewhere in between, i.e., partial polarization.

At Brewster's angle, it turns out that only one of the polarizations of light can reflect from the surface. This means that if you reflect a beam of unpolarized light from a surface, the reflected beam will contain all of its intensity in one polarization, and no intensity in the other polarization. Thus, the reflected beam is 100% polarized, which is as polarized as it can be.

(I've glossed over some details here, but this is still basically correct and doesn't require an explanation of things like incoherent states.)

Assuming as in most cases we start with unpolarized light, the reflected ray at Brewster's angle is almost all polarized (it's about 50% of the light). The other light is absorbed, when you look at water you see the strong reflection only which is a stronger signal than the light going in the water and bouncing off the bottom of the lake and then coming back to your eye for example. If you use polarizing sunglasses to block the glare you can see deeper in the water.

Polarization is a property of light, sunlight has many polarizations (but we call it unpolarized which seems counter intuitive), lasers have strongly polarized light ( but it really has a single direction of polarization). It all has to do with light being a wave like phenomenon in the electromagnetic field. The interaction of light with matter is based on Quantum Mechanics (QM) which means it's very probabilistic (photon meets electron interaction), sometimes a photon that should be reflected actually gets absorbed and vice versa, but on average it is very predictable. A lightwave that's 45 degrees to the normal has a 50/50 chance of being reflected and becoming polarized or being absorbed into the water.