Snell's law: n₁ sin i = n₂ sin r
sin i / sin r is a constant, n₂₁ = n₂/n₁. Light from air into water (n = 1.33) at i = 30° bends towards the normal to r = 22.08°.
Refraction
Snell's law: n₁ sin i = n₂ sin r, so sin i / sin r = n₂₁ = n₂/n₁. Angles are measured from the normal. Going from a denser to a rarer medium beyond the critical angle C (sin C = n₂/n₁), there is no refracted ray. Drag the incoming ray or type an angle.
Light from n = 1 into n = 1.33 at 30° refracts at 22.08°, bending towards the normal.
Show the working
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1 × sin 30° / 1.33 = 0.3759
- r = sin⁻¹(0.3759) = 22.08°
- n₂₁ = n₂/n₁ = 1.33/1 = 1.33. Light travels at c/n: 3 × 10⁸ m/s in medium 1 and 2.26 × 10⁸ m/s in medium 2.
Laws of refraction
- The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
- For light of a given colour and a given pair of media, sin i / sin r is a constant. This is Snell's law, and the constant is the refractive index of the second medium with respect to the first, n₂₁.
- In terms of the absolute indices, n₂₁ = n₂/n₁, so n₁ sin i = n₂ sin r.
- Going into an optically denser medium (larger n), light slows down and bends towards the normal. Going into a rarer one it speeds up and bends away from the normal.
Air into water at 30°
- A ray of light goes from air (n taken as 1) into water (n = 1.33) at an angle of incidence of 30°. Find the angle of refraction.
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1 × sin 30° / 1.33 = 0.3759
- r = sin⁻¹(0.3759) = 22.08°
- n₂₁ = n₂/n₁ = 1.33/1 = 1.33. Light travels at c/n: 3 × 10⁸ m/s in medium 1 and 2.26 × 10⁸ m/s in medium 2.
Refractive index of common media
| Medium | n | Speed of light |
|---|---|---|
| Air | 1.0003 | 3 × 10⁸ m/s |
| Ice | 1.31 | 2.29 × 10⁸ m/s |
| Water | 1.33 | 2.26 × 10⁸ m/s |
| Alcohol | 1.36 | 2.21 × 10⁸ m/s |
| Kerosene | 1.44 | 2.08 × 10⁸ m/s |
| Fused quartz | 1.46 | 2.05 × 10⁸ m/s |
| Turpentine oil | 1.47 | 2.04 × 10⁸ m/s |
| Benzene | 1.5 | 2 × 10⁸ m/s |
| Crown glass | 1.52 | 1.97 × 10⁸ m/s |
| Canada balsam | 1.53 | 1.96 × 10⁸ m/s |
| Rock salt | 1.54 | 1.95 × 10⁸ m/s |
| Carbon disulphide | 1.63 | 1.84 × 10⁸ m/s |
| Dense flint glass | 1.65 | 1.82 × 10⁸ m/s |
| Ruby | 1.71 | 1.75 × 10⁸ m/s |
| Sapphire | 1.77 | 1.69 × 10⁸ m/s |
| Diamond | 2.42 | 1.24 × 10⁸ m/s |
Speed of light = c/n, with c = 3 × 10⁸ m/s. Air is taken as 1 in most sums.
Quick answers
What is Snell's law?
For a given pair of media, sin i / sin r is a constant, the refractive index of the second medium with respect to the first: sin i / sin r = n₂₁ = n₂/n₁, or n₁ sin i = n₂ sin r.
Does light bend towards or away from the normal?
Towards the normal when it enters an optically denser medium (larger n), and away from it when it enters a rarer one.
What happens at an angle of incidence of 0°?
sin 0° = 0, so r = 0°. Light falling along the normal passes straight through without bending, though it still slows down.