One equation for how light bends
When light crosses from one transparent material into another — air to water, water to glass — it changes direction. Snell's law is the exact rule for by how much, and it depends only on the angle it arrives at and how much each material slows light down.
The refractive index n is just how much slower light goes in a material than in a vacuum: 1.000 for vacuum, about 1.333 for water, 1.52 for glass, 2.417 for diamond. A higher index bends light more.
Which way does it bend?
Entering a denser medium, light bends toward the normal; leaving one, it bends away. Air into water at 30° refracts to 22.0° — closer to the normal. The bigger the jump in index, the sharper the bend, which is why a straw looks broken at the water line and why a diamond throws light around so dramatically.
| Medium | Index | Critical angle |
|---|---|---|
| Water | 1.333 | 48.6° |
| Glass | 1.52 | 41.1° |
| Diamond | 2.417 | 24.4° |
The limit that becomes a mirror
Going from dense to sparse, the refracted ray tips further from the normal as the incident angle grows, until at the critical angle it would lie flat along the surface. Past that there is nowhere left to refract to, so the boundary reflects everything — total internal reflection. It is the principle behind optical fibre and the reason a diamond's low critical angle keeps light bouncing inside until it leaves through the top.
Frequently asked questions
What is Snell's law?
It relates the angles a ray makes on each side of a boundary to the refractive indices of the two materials: n₁ sinθ₁ = n₂ sinθ₂. Rearranged, the refracted angle is θ₂ = arcsin(n₁ sinθ₁ / n₂). Angles are measured from the normal, the line at right angles to the surface, not from the surface itself.
Worked example: air to water
Light hitting water at 30° from air (n₁ = 1.000, n₂ = 1.333): sinθ₂ = 1.000 × sin30° / 1.333 = 0.375, so θ₂ = 22.0°. The ray bends toward the normal because it is entering a denser medium where light travels more slowly.
What is the critical angle?
When light goes from a denser to a less dense medium, there is an incident angle beyond which it cannot refract out at all. That is the critical angle, θc = arcsin(n₂ / n₁). For water to air it is 48.6°; for glass to air about 41.1°; for diamond to air just 24.4°, which is part of why diamonds sparkle.
What is total internal reflection?
Past the critical angle, all the light reflects back into the denser medium instead of refracting out — total internal reflection. It is how optical fibres trap light along their length and how a prism can act as a perfect mirror. The calculator flags it instead of returning an impossible angle.
Why does light bend at a boundary at all?
Because it changes speed. Light travels slower in a denser medium (a higher refractive index), and a wavefront crossing the boundary at an angle changes direction as one edge slows before the other — the same way a marching band wheels when one side takes shorter steps. No speed change, at 0° incidence, means no bend.