Snell’s Law
How much does light bend when it passes from one material into another? Solve for either angle or either refractive index, and see the critical angle, total internal reflection and how much light is reflected.
What is Refraction?
Light travels more slowly in water or glass than in air. The refractive index n says how much slower: n = c / v. When light crosses a boundary at an angle, the change in speed makes it change direction — that is refraction.
Going into a slower medium, light bends towards the normal; going into a faster one, it bends away. Beyond the critical angle it cannot leave at all and is reflected completely: total internal reflection, which keeps light trapped inside optical fibres.
Ray Diagram
refractionRefractive Indices
yellow light, 589 nm| Material | n | Critical angle to air |
|---|---|---|
| Vacuum / air | 1.000 | — |
| Ice | 1.31 | 49.8° |
| Water | 1.333 | 48.6° |
| Acrylic (PMMA) | 1.49 | 42.2° |
| Crown glass | 1.52 | 41.1° |
| Optical fibre core | ~1.46 | 43.2° |
| Diamond | 2.417 | 24.4° |
Key Relations
At this angle the refracted ray skims along the surface. A diamond’s small critical angle traps light inside, which is why it sparkles.
Looking straight down into water, refraction makes the bottom seem closer. A 2 m deep pool looks only 1.5 m deep.
Some light is always reflected at a boundary. Straight on, glass reflects about 4%; at grazing angles almost everything is reflected.
Sources & Verification
- E. Hecht, Optics, 5th ed., Pearson, 2017 — Ch. 4 (The Propagation of Light).