---
title: "Brewster’s Law | College Physics I"
description: "Brewster’s law gives the angle where reflected light is fully polarized and the reflected and refracted rays are perpendicular in College Physics I."
canonical: "https://fiveable.me/intro-college-physics/key-terms/brewsters-law"
type: "key-term"
subject: "College Physics I – Introduction"
unit: "Unit 27"
---

# Brewster’s Law | College Physics I

## Definition

Brewster’s law gives the Brewster angle, the incidence angle where reflected light is fully polarized and the reflected and refracted rays are at 90° in College Physics I.

## What It Is

Brewster’s law is the rule in College Physics I that tells you the angle of incidence where reflected light from a transparent surface becomes completely polarized. At this special angle, the reflected ray and the refracted ray are perpendicular to each other, so the geometry of reflection and refraction lines up in a very specific way.

The law is usually written as tan(θB) = n2 / n1, where θB is the Brewster angle, n1 is the refractive index of the medium the light is coming from, and n2 is the refractive index of the second medium. For air to glass, that angle is often around 56°. If the light hits the surface at that angle, the reflected beam does not contain the polarization component in the plane of incidence.

The setup matters because Brewster’s law is about unpolarized or partially polarized light. Unpolarized light has electric field vibrations in many directions, but at the Brewster angle, the component parallel to the plane of incidence is not reflected. What comes back is reflected light polarized perpendicular to the plane of incidence, which is why glare can be reduced with polarizing sunglasses and camera filters.

A useful way to picture it is to trace the incident ray, the reflected ray, and the refracted ray at the boundary. As you change the incoming angle, the polarization of the reflected beam changes too. At the Brewster angle, the reflected and refracted rays make a right angle, and that geometry is the clue that you have found the special angle.

This is not the same thing as saying no light is reflected at all. Instead, one polarization component is missing from the reflected beam, so the reflected light that remains is strongly polarized. That distinction shows up in optics problems, lab observations with a rotating polarizer, and any situation where you compare how light behaves at a dielectric boundary.

## Why It Matters

Brewster’s law shows up whenever College Physics I turns from basic ray diagrams to polarization at surfaces. It connects refraction, reflection, and the direction of the electric field, so it gives you a clean example of how wave behavior and geometry work together.

It also explains real devices and observations. Glare off water, pavement, or glass is often partially polarized, which is why polarizing sunglasses reduce that bright reflected sheen. In a lab, you may shine light at a plastic or glass surface, rotate a polarizer, and look for the angle where the reflected light is strongest in one polarization direction.

The law is also a nice check on your physics reasoning. If a problem gives you refractive indices, you can find the Brewster angle with a quick tangent calculation. If a diagram shows reflected and refracted rays at 90°, you can recognize that the surface is being hit at the Brewster angle and infer which polarization is reflected.

It matters because it tells you what is happening to the light field, not just where the beam goes. That makes it a bridge topic between geometric optics and wave optics, which is a pattern that comes up again and again in introductory physics.

## Connections

### Polarization

Brewster’s law is one of the easiest ways to see polarization in action. The reflected light at the Brewster angle is polarized perpendicular to the plane of incidence, so this term connects the ray picture to the electric-field direction of the wave. If you already know polarization, Brewster’s law gives you a concrete boundary example.

### Refractive Index

The Brewster angle depends on the refractive indices of the two media, so you cannot use the law without them. A larger index contrast usually changes the angle, which is why air-glass and air-water interfaces give different results. This makes refractive index the quantity you plug into the tangent relationship.

### Snell's Law

Snell’s law tells you how the refracted ray bends, and Brewster’s law describes a special angle where that refracted ray is perpendicular to the reflected ray. In practice, the two laws often appear in the same diagram. One predicts the refraction angle, and the other identifies the polarization-specific angle.

### [Brewster’s angle](/intro-college-physics/key-terms/brewsters-angle)

This is the angle named directly in the law. If you see either term, the idea is the same: the incidence angle where reflected light is fully polarized and the reflected and refracted rays are at 90°. The spelling and punctuation vary across notes, but the physics does not.

## On the AP Exam

A quiz problem might give you two refractive indices and ask for the angle where reflected light becomes fully polarized. You use tan(θB) = n2 / n1, solve for the angle, and then interpret what the result means for the reflected beam. Other questions may show a diagram of light hitting glass and ask you to identify the Brewster angle from the right-angle relationship between reflected and refracted rays.

In a lab write-up or short answer, you may also explain why a rotated polarizer makes glare dim or disappear at certain angles. The move is not just memorizing the formula, but linking the surface geometry to the polarization state of the reflected light. If you can say which ray is perpendicular to which, and which polarization is reflected, you are using the term correctly.

## Brewster’s law vs Brewster’s angle

These are often treated as the same idea, but there is a small wording difference. Brewster’s law is the rule or relationship, while Brewster’s angle is the actual angle you calculate from that relationship. If a problem asks for the law, it wants the formula or principle, and if it asks for the angle, it wants the numerical result.

## Key Takeaways

- Brewster’s law gives the angle where reflected light from a transparent surface becomes completely polarized.
- At the Brewster angle, the reflected ray and refracted ray are perpendicular to each other.
- You find it with tan(θB) = n2 / n1, using the refractive indices of the two media.
- The law applies to unpolarized or partially polarized light, not to a beam that is already fully polarized in the same way.
- In College Physics I, it shows up in polarization diagrams, glare problems, and labs with reflecting surfaces.

## FAQs

### What is Brewster’s law in College Physics I?

Brewster’s law is the relationship that gives the angle of incidence where reflected light becomes completely polarized. At that angle, the reflected and refracted rays are perpendicular, and the reflected beam lacks the polarization component in the plane of incidence.

### How do you calculate the Brewster angle?

Use tan(θB) = n2 / n1, where n1 is the refractive index of the medium the light starts in and n2 is the refractive index of the second medium. After you plug in the values, take the inverse tangent to get the angle in degrees.

### What happens to light at the Brewster angle?

The reflected light becomes fully polarized perpendicular to the plane of incidence. The refracted ray still exists, but it is at a right angle to the reflected ray, which is the geometric clue that you are at the Brewster angle.

### Is Brewster’s law the same as Brewster’s angle?

Not exactly. Brewster’s law is the formula and rule, while Brewster’s angle is the specific angle you calculate from it. In many class notes, people use the terms loosely, but the distinction can matter on a short-answer question.

## Related Study Guides

- [27.8 Polarization](/intro-college-physics/unit-27/8-polarization/study-guide/xUtC3QW26Y64CcHr)

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