Refractive index of water: 1.33
The refractive index of water is 1.33. Light travels 1.33 times slower in water than in vacuum, at about 2.26 × 10⁸ m/s.
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 r22.08°sin r = 0.3759
n₂₁ = n₂/n₁1.33light 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 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.
n = 1.33
- Speed of light in water: c/n = 3 × 10⁸ / 1.33 = 2.26 × 10⁸ m/s.
- Light entering water from air bends towards the normal, which is why a pool looks shallower than it is and a pencil in water looks bent.
- Going from water into air, the critical angle is sin⁻¹(1/1.33) = 48.75°. Beyond it the light is totally reflected.
- Ice (1.31) is slightly less dense optically than water.
Snell's law with these numbers
- Light goes from air (n taken as 1) into water at 30°.
- 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 the refractive index of water?
1.33, from NCERT table 10.3. It is often written as 4/3.
What is the speed of light in water?
v = c/n = 3 × 10⁸ / 1.33 = about 2.26 × 10⁸ m/s.
What is the critical angle of water?
About 48.75°, for light going from water into air.