Refractive index: n = c/v and the NCERT table
The absolute refractive index n = c/v tells you how many times slower light travels in a medium than in vacuum. Water is 1.33, crown glass 1.52 and diamond 2.42.
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 = 1.52 at 45° refracts at 27.72°, bending towards the normal.
Show the working
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1 × sin 45° / 1.52 = 0.4652
- r = sin⁻¹(0.4652) = 27.72°
- n₂₁ = n₂/n₁ = 1.52/1 = 1.52. Light travels at c/n: 3 × 10⁸ m/s in medium 1 and 1.97 × 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.
Absolute and relative
- Absolute refractive index of a medium: n = c/v, the speed of light in vacuum divided by its speed in the medium. It has no unit.
- Relative refractive index of medium 2 with respect to medium 1: n₂₁ = v₁/v₂ = n₂/n₁ = sin i / sin r.
- A medium with a larger n is optically denser. Optical density is not the same as mass density: kerosene is lighter than water but optically denser.
- n of glass with respect to water is 1.52/1.33 = 1.14, and n of water with respect to glass is 1.33/1.52 = 0.88.
Air into crown glass at 45°
- Light goes from air (n taken as 1) into crown glass (n = 1.52) at 45°.
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1 × sin 45° / 1.52 = 0.4652
- r = sin⁻¹(0.4652) = 27.72°
- n₂₁ = n₂/n₁ = 1.52/1 = 1.52. Light travels at c/n: 3 × 10⁸ m/s in medium 1 and 1.97 × 10⁸ m/s in medium 2.
Quick answers
What is the refractive index?
The ratio of the speed of light in vacuum to its speed in the medium, n = c/v. It shows how much the medium slows light and bends it.
Which material in the NCERT table has the highest refractive index?
Diamond, with n = 2.42. Light travels in it at only about 1.24 × 10⁸ m/s.
Can the refractive index be less than 1?
The absolute index of a material is at least 1, because light never travels faster than in vacuum. A relative index, such as water with respect to glass, can be less than 1.