What refraction is
When light passes from one transparent material to another, such as from air into water, it changes speed and bends. This is refraction. It makes a straw look broken in a glass of water, a pool look shallower than it is, and it lets lenses focus light in glasses, cameras and the human eye.
Snell’s law
n₁ × sin θ₁ = n₂ × sin θ₂
- n₁ and n₂ are the refractive indices of the two media,
- θ₁ is the angle of incidence and θ₂ the angle of refraction, both measured from the normal, the line perpendicular to the surface.
The refractive index is the ratio of the speed of light in a vacuum to its speed in the material: in water, with n = 1.333, light travels at about 225,000 km/s.
Worked example
A ray of light goes from air into water at 30° from the normal.
- sin θ₂ = 1.0003 × sin 30° ÷ 1.333 = 0.375.
- θ₂ = arcsin 0.375 = 22.04°: the ray bends toward the normal.
- It is deviated by 7.96° from its original path.
- In water, light travels at 224,901 km/s.
Common refractive indices
| Material | Index |
|---|---|
| Air | 1.0003 |
| Ice | 1.31 |
| Water | 1.333 |
| Acrylic (Plexiglas) | 1.49 |
| Crown glass | 1.52 |
| Diamond | 2.417 |
Indices vary slightly with the color of light, which is why prisms and raindrops split white light into a rainbow. The values above are for yellow light.
Critical angle and total internal reflection
When light goes from a denser medium to a lighter one, such as from water to air, it bends away from the normal. Beyond a certain angle of incidence, the critical angle, it cannot leave at all and is entirely reflected. This total internal reflection keeps light trapped inside optical fibers over thousands of miles and makes diamonds sparkle, since their critical angle is only 24.4°.
- Critical angle = arcsin(n₂ ÷ n₁), only when n₁ > n₂.
- Water to air: arcsin(1 ÷ 1.333) = 48.6°.
- Glass to air: about 41°.
Set the first medium to water and the second to air, then try angles above 48.6° to see the calculator flag total internal reflection.
Everyday consequences
A fish seen from the bank is not where it appears to be: spear fishers learn to aim below the image. A swimming pool looks about a quarter shallower than its real depth when seen from straight above, because of the 1.333 ratio between the two indices.