Optics
Brewster's angle
At Brewster’s angle (θ_B = arctan(n₂/n₁)), only the p-polarized reflected component is zero; the reflected beam is therefore s-polarized.
Brewster's angle — interactive physics simulation. At Brewster’s angle (θ_B = arctan(n₂/n₁)), only the p-polarized reflected component is zero; the reflected beam is therefore s-polarized.
Brewster's angle
At θ_B, reflected p-polarization vanishes, leaving s-polarization.
At Brewster’s angle (θ_B = arctan(n₂/n₁)), only the p-polarized reflected component is zero; the reflected beam is therefore s-polarized.
- θ_B = arctan(n₂/n₁)
- Polarized reflection
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
At one special angle of incidence (Brewster's angle), light reflecting off a surface becomes perfectly polarized — the reflected beam contains only one polarization direction. Does a higher-index surface have a larger or smaller Brewster angle?
Predictions to weigh
- A higher index gives a smaller Brewster angle.
- Larger — a higher refractive index requires a steeper incidence angle to satisfy the Brewster condition.
- Brewster's angle doesn't depend on the surface's index.
Variable roles
What you set:
- Glass index n₂
What you measure:
- Brewster angle θ_B (°)
How the investigation runs
- Open the brewster preset and press Reset. Light travels from air (n₁ = 1.0) toward glass.
- Enable the Brewster-angle readout.
- Set the glass's refractive index for each trial and record the Brewster angle.
Governing equation
Brewster's Angle — θ_B = arctan(n₂/n₁)
At the specific incidence angle θ_B = atan(n₂/n₁), reflected light becomes perfectly polarized (purely s-polarized, with the reflected and refracted rays at exactly 90° to each other). This is the physical basis for polarized anti-glare sunglasses and camera filters.
What the printable worksheet asks students to work out
- For one trial, compute θ_B = atan(n₂/n₁) using n₁ = 1.0. Compare to the table.
- Explain why a higher-index surface (n₂ larger) requires a LARGER Brewster angle — steeper incidence — to achieve perfectly polarized reflection.
Where this shows up beyond the lab
- At Brewster's angle, reflected glare (like off a lake or wet road) is almost entirely horizontally polarized. This is exactly why polarized sunglasses (blocking horizontal polarization) are so effective at cutting glare — they're tuned to block precisely the light that's most strongly reflected at typical viewing angles.
- At Brewster's angle, the reflected beam contains ZERO p-polarized light (polarized in the plane of incidence) — only s-polarized light reflects. Explain why this means a camera with a polarizing filter, rotated to block s-polarized light, can nearly eliminate reflections off glass or water at this specific angle.
- AP Physics 2 — Unit 14: Waves, Sound, and Physical Optics
- IB Physics — C.3 Wave phenomena
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Brewster
- Select the interface
- Press Play
- Polarized reflection
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.