Numford
Refraction

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.

Angle of refraction r22.09°sin r = 0.3761
n₂₁ = n₂/n₁1.3296light in 2 at 2.26 × 10⁸ m/s
Critical angle Cnoneonly from denser to rarer
The ray bendsTowards normalinto a denser medium

Light from n = 1.0003 into n = 1.33 at 30° refracts at 22.09°, bending towards the normal.

°
Show the working
  1. n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1.0003 × sin 30° / 1.33 = 0.3761
  2. r = sin⁻¹(0.3761) = 22.09°
  3. 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.
What it means

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.
Worked example

Snell's law with these numbers

  1. Light goes from air (n = 1.0003) into water (n = 1.33) at 30°.
  2. n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 1.0003 × sin 30° / 1.33 = 0.3761
  3. r = sin⁻¹(0.3761) = 22.09°
  4. 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.
NCERT table 10.3

Refractive index of common media

MediumnSpeed of light
Air1.00033 × 10⁸ m/s
Ice1.312.29 × 10⁸ m/s
Water1.332.26 × 10⁸ m/s
Alcohol1.362.21 × 10⁸ m/s
Kerosene1.442.08 × 10⁸ m/s
Fused quartz1.462.05 × 10⁸ m/s
Turpentine oil1.472.04 × 10⁸ m/s
Benzene1.52 × 10⁸ m/s
Crown glass1.521.97 × 10⁸ m/s
Canada balsam1.531.96 × 10⁸ m/s
Rock salt1.541.95 × 10⁸ m/s
Carbon disulphide1.631.84 × 10⁸ m/s
Dense flint glass1.651.82 × 10⁸ m/s
Ruby1.711.75 × 10⁸ m/s
Sapphire1.771.69 × 10⁸ m/s
Diamond2.421.24 × 10⁸ m/s

Speed of light = c/n, with c = 3 × 10⁸ m/s. Air is taken as 1 in most sums.

Questions

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.

Try your own mirror or lens