Snell's law describes how light bends crossing a boundary: n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the normal. This calculator solves for the refraction angle, tells you which way the ray bends, and flags total internal reflection with the critical angle when it applies.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Snell's law & critical-angle relations, recomputed in code.
The law
A higher refractive index means light travels slower in that medium. Entering a slower (denser) medium, the ray bends toward the normal; entering a faster (rarer) medium, it bends away. If n₁ sin θ₁ exceeds n₂, the sine would be greater than 1 — impossible — so the light reflects entirely. The angle at which this starts is the critical angle.
Worked examples
Air (1.00) → glass (1.50) at 30°:
Glass (1.50) → air (1.00) at 30°:
Glass → air at 50° (beyond critical):
Total internal reflection is what keeps light trapped inside optical fibres and makes a diamond sparkle: its high index (≈2.42) gives a small critical angle of about 24.4°, so most rays bounce internally before escaping.
Frequently Asked Questions
n₁ sin θ₁ = n₂ sin θ₂ — index × sine of the angle is conserved across a boundary.
θ₂ = arcsin(n₁ sin θ₁ / n₂). Air→glass at 30° ≈ 19.47°.
Toward the normal into a denser medium; away from it into a rarer one.
Beyond the critical angle (denser→rarer), all light reflects — no refraction.
θc = arcsin(n₂/n₁) when n₁ > n₂. Glass→air ≈ 41.81°.