What Fresnel Reflectivity Means
When light reaches the boundary between two materials, part of the light is reflected and part is transmitted. The reflected fraction depends on the refractive indices, the incidence angle, and the polarization of the light.
Fresnel Equations Used
For s-polarized light:
For p-polarized light:
The transmitted angle is found from Snell’s law:
Unpolarized Reflectance
For unpolarized light, the calculator averages the s-polarized and p-polarized reflectance values.
Brewster Angle
Brewster angle is the incidence angle where the p-polarized reflectance becomes zero for an ideal interface.
This is why polarized sunglasses and optical polarizers can reduce glare from some reflected surfaces.
Critical Angle and Total Internal Reflection
If light travels from a higher-index medium to a lower-index medium, there is a critical angle. Above this angle, Snell’s law has no real transmitted angle and total internal reflection occurs.
Correct Example: Air to Glass at 45°
For n₁ = 1.0, n₂ = 1.5, and θᵢ = 45°:
θₜ ≈ 28.13° Rₛ ≈ 0.0920 = 9.20% Rₚ ≈ 0.0085 = 0.85% Ravg ≈ 0.0502 = 5.02%
Normal Incidence Shortcut
At θᵢ = 0°, both polarizations have the same reflectance:
For air to glass with n₁ = 1.0 and n₂ = 1.5:
R = [(1.0 − 1.5) / (1.0 + 1.5)]² R = 0.04 = 4%
Common Mistakes
- Using the angle from the surface instead of the angle from the surface normal.
- Forgetting that s and p polarizations give different reflectance at oblique angles.
- Ignoring total internal reflection when n₁ is greater than n₂.
- Assuming Fresnel equations include coatings or thin-film interference.
- Using real refractive indices for metals or absorbing materials without complex-index optics.
Frequently Asked Questions
What is s-polarized light?
s-polarized light has its electric field perpendicular to the plane of incidence.
What is p-polarized light?
p-polarized light has its electric field parallel to the plane of incidence.
What happens at Brewster angle?
For an ideal non-absorbing interface, p-polarized reflectance becomes zero.
When does total internal reflection happen?
It happens when light travels from a higher refractive index medium to a lower refractive index medium and the incidence angle is greater than the critical angle.
Can this calculator be used for metals?
Not accurately. Metals require complex refractive indices and absorbing-material Fresnel equations.