Snell's Law of Refraction
When light travels from one medium to another, it bends — a phenomenon called refraction. The Snell's Law calculator lets you explore this in detail: find the angle of refraction, determine the critical angle for total internal reflection, or calculate an unknown refractive index.
The Snell's Law Formula
Snell's law states that the product of the refractive index and the sine of the angle of incidence is constant across the boundary:
n₁ × sin(θ₁) = n₂ × sin(θ₂)
Where:
- n₁ — refractive index of the first medium (where the ray originates)
- n₂ — refractive index of the second medium (where the ray enters)
- θ₁ — angle of incidence (between the incoming ray and the normal to the surface)
- θ₂ — angle of refraction (between the refracted ray and the normal)
Finding the Angle of Refraction — an Example
Suppose a light ray travels from water (n₁ = 1.333) to air (n₂ = 1.000) at an angle of incidence of 30°:
sin(θ₂) = n₁ / n₂ × sin(θ₁) = 1.333 / 1.000 × sin(30°) = 1.333 × 0.5 = 0.6665
θ₂ = arcsin(0.6665) ≈ 41.76°
Because the ray moves into a less optically dense medium (n₂ < n₁), it bends away from the normal — the refracted angle is larger than the incident angle.
Critical Angle Formula
When light travels from a denser medium (higher n) into a less dense one (lower n), there is a maximum angle of incidence beyond which refraction no longer occurs and all light is reflected back. This is called total internal reflection, and the boundary angle is the critical angle:
θ_c = arcsin(n₂ / n₁)
For water-to-air: θ_c = arcsin(1.000 / 1.333) ≈ 48.75°. Any light hitting the water surface from inside at an angle greater than 48.75° will be totally internally reflected.
Refractive Indices of Common Media
| Medium | Refractive Index (n) | Speed of Light (m/s) |
|---|---|---|
| Vacuum | 1.000 000 | 299,792,458 |
| Air (20°C) | 1.000 293 | 299,704,644 |
| Ice | 1.309 | 228,947,640 |
| Water (20°C) | 1.333 | 224,901,318 |
| Ethanol | 1.361 | 220,274,399 |
| Olive Oil | 1.467 | 204,357,849 |
| Glycerin | 1.473 | 203,524,411 |
| Glass (crown) | 1.523 | 196,845,672 |
| Glass (flint) | 1.620 | 185,056,455 |
| Diamond | 2.419 | 123,930,738 |
FAQs
What does the refractive index mean?
The refractive index (n) of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium: n = c / v. A higher refractive index means light travels more slowly through that medium.
When does total internal reflection occur?
Total internal reflection occurs only when light travels from a denser medium (higher n) to a less dense one (lower n), and the angle of incidence exceeds the critical angle. This principle is used in optical fiber cables to transmit light over long distances.
Is Snell's Law valid for all types of waves?
Snell's law applies to all waves crossing boundaries between media — including sound waves, seismic waves, and water waves — not just light. However, for anisotropic media like crystals, the law must be modified as the ray may split into two components (birefringence).
What is the difference between the metric and US unit systems here?
The refractive index and angles are dimensionless, so the calculation is the same in both systems. The difference appears in the speed of light in each medium: metric shows it in meters per second (m/s) while US customary shows feet per second (ft/s). 1 m/s = 3.28084 ft/s.
What does "bending toward/away from the normal" mean?
The normal is an imaginary line perpendicular to the surface at the point of incidence. When light slows down (enters a denser medium, n₂ > n₁), it bends toward the normal — the refracted angle is smaller. When it speeds up (n₂ < n₁), it bends away from the normal — the refracted angle is larger.