Enter interface values
Use real refractive indices for transparent, nonmagnetic media. The calculator compares Brewster behavior, critical behavior, and Fresnel reflectance.
Formula used
1) Brewster angle
θB = arctan(n₂ / n₁)
This angle makes the p-polarized reflected component vanish for ideal lossless dielectric boundaries. It is measured from the normal in Medium 1.
2) Critical angle
θc = arcsin(n₂ / n₁), only when n₁ > n₂
If light travels from a higher index medium to a lower index medium, incidence above this angle causes total internal reflection.
3) Snell’s law
n₁ sin(θi) = n₂ sin(θt)
This relation gives the transmitted angle whenever refraction is physically possible.
4) Fresnel reflectance
The graph uses the standard Fresnel equations for s and p polarization. Reflectance is plotted as a percentage against the incident angle.
How to use this calculator
- Select presets or type custom refractive indices for both media.
- Choose degrees or radians for all angle fields.
- Enter a snapshot incident angle for the detailed Fresnel comparison.
- Set the graph maximum angle and sample points.
- Press Calculate now to view results above the form.
- Download the results as CSV or PDF when needed.
Example data table
| Medium 1 | n₁ | Medium 2 | n₂ | Brewster Angle | Critical Angle | Comment |
|---|---|---|---|---|---|---|
| Air | 1.0003 | Crown Glass | 1.5200 | 56.66° | Not available | No total internal reflection in this direction. |
| Crown Glass | 1.5200 | Air | 1.0003 | 33.34° | 41.15° | Brewster occurs before the critical angle. |
| Water | 1.3330 | Air | 1.0003 | 36.89° | 48.63° | Total internal reflection is possible. |
| Acrylic | 1.4900 | Water | 1.3330 | 41.82° | 63.41° | Large gap between Brewster and critical values. |
FAQs
1. What is the Brewster angle?
It is the incident angle where p-polarized reflected light ideally becomes zero at a dielectric boundary. It depends on the refractive-index ratio between the two media.
2. What is the critical angle?
It is the largest incident angle that still allows refraction when light travels from a higher index medium to a lower index medium. Beyond it, total internal reflection begins.
3. Does every interface have a critical angle?
No. A critical angle exists only when the first medium has a higher refractive index than the second medium. Otherwise, light can still refract for all incident angles below 90°.
4. Does every interface have a Brewster angle?
For ideal transparent, nonmagnetic dielectric media, yes. The calculator uses that standard assumption. Conductive or absorbing materials need more advanced complex-index models.
5. Why are s and p reflectance different?
The electric field orientation changes how boundary conditions apply. That difference creates separate Fresnel equations for perpendicular and parallel polarization states.
6. Can Brewster angle be larger than critical angle?
In the common lossless dielectric case with total internal reflection present, Brewster angle usually appears before the critical angle. The calculator reports the actual ordering for your values.
7. What refractive-index values should I enter?
Use real refractive indices measured at the wavelength and temperature that match your design. Optical constants can change with material grade and wavelength.
8. Why does the transmitted angle disappear sometimes?
When the selected incident angle exceeds the critical angle, refraction no longer occurs. The calculator then reports total internal reflection instead of a real transmitted angle.