Refractive index of air: 1.0003
The refractive index of air is 1.0003, so close to 1 that light travels in air at almost its speed in vacuum. Sums usually take air as 1.
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 = 1.0003 into n = 1.33 at 30° refracts at 22.09°, bending towards the normal.
Show the working
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1.0003 × sin 30° / 1.33 = 0.3761
- r = sin⁻¹(0.3761) = 22.09°
- n₂₁ = n₂/n₁ = 1.33/1.0003 = 1.3296. Light travels at c/n: 3 × 10⁸ m/s in medium 1 and 2.26 × 10⁸ m/s in medium 2.
n = 1.0003
- n = c/v = 1.0003 means light in air is only 0.03 percent slower than in vacuum.
- The vacuum has n = 1 exactly, by definition.
- Hot air is slightly rarer than cool air. The small change in n is what bends light into a mirage on a hot road.
- The picture uses 1.0003 for air; switch to "Air (taken as 1)" and the angle barely moves.
Snell's law with these numbers
- Light goes from air (n = 1.0003) into water (n = 1.33) at 30°.
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1.0003 × sin 30° / 1.33 = 0.3761
- r = sin⁻¹(0.3761) = 22.09°
- n₂₁ = n₂/n₁ = 1.33/1.0003 = 1.3296. 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 the refractive index of air?
1.0003, from NCERT table 10.3. For most sums it is taken as 1.
What is the refractive index of vacuum?
Exactly 1, because n = c/v and light in vacuum travels at c.
Why do stars twinkle?
The refractive index of air changes a little with temperature and density, so starlight is bent by slightly different amounts from moment to moment.