Snell's Law Calculator — Light Refraction and Angles
Calculate refraction angles using Snell's Law n₁sin(θ₁) = n₂sin(θ₂). Find critical angle for total internal reflection with glass, water, and optical fiber examples.
Light bends when it crosses from one transparent medium to another. This is refraction, and Snell's Law describes exactly how much it bends based on the refractive indices of the two materials. It's why a straw in a glass of water looks broken, why swimming pools look shallower than they are, and why fiber optic cables can guide light around corners.
The CalcHub Snell's Law calculator solves for refraction angles and refractive indices in any two-medium interface.
Snell's Law
n₁ × sin(θ₁) = n₂ × sin(θ₂)- n₁, n₂ = refractive indices of medium 1 and 2
- θ₁ = angle of incidence (measured from normal)
- θ₂ = angle of refraction (measured from normal)
Refractive Indices
| Medium | n |
|---|---|
| Vacuum | 1.000 |
| Air | 1.0003 |
| Water | 1.333 |
| Crown glass | 1.52 |
| Flint glass | 1.62 |
| Diamond | 2.42 |
| Optical fiber core | 1.46–1.50 |
Total Internal Reflection
When light travels from a denser to a less dense medium, at angles beyond the critical angle, it reflects completely — no light passes through. This is total internal reflection (TIR).
Critical angle: sin(θ_c) = n₂/n₁ (for n₁ > n₂)For glass (n = 1.5) to air: sin(θ_c) = 1/1.5, so θ_c = 41.8°
Fiber optic cables exploit TIR to guide light across vast distances with almost no loss.
Worked Example
A ray of light travels from air into water at 30° from the normal. Find the refraction angle.
n₁ sin(θ₁) = n₂ sin(θ₂)
1.0 × sin(30°) = 1.333 × sin(θ₂)
0.5 = 1.333 × sin(θ₂)
sin(θ₂) = 0.375
θ₂ = 22.0°
The ray bends toward the normal as it enters the denser water — as expected.
Why does a diamond sparkle so much?
Diamond has an extremely high refractive index (n = 2.42), giving a critical angle of only 24.4°. Most light entering a diamond hits internal surfaces at angles greater than this, creating total internal reflection multiple times before exiting. This creates the characteristic brilliance and fire.
Does Snell's Law work for all waves?
Yes — Snell's Law applies to any wave crossing a medium boundary, including sound. It's derived from Fermat's principle (light takes the path of least time) which applies to waves generally. Seismic waves refract as they pass through layers of different density in Earth's interior.
What is the refractive index physically?
n = c/v_medium. It describes how much slower light travels in that medium compared to vacuum. In glass with n = 1.5, light travels at 2/3 of its vacuum speed. Higher n means slower propagation and greater bending.