Refractive index of diamond: 2.42
Diamond has the highest refractive index in the NCERT table, 2.42. Light slows to about 1.24 × 10⁸ m/s, and its critical angle is only 24.41°.
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 = 2.42 meets n = 1 at 30°, past the critical angle of 24.41°, so it is totally reflected.
Show the working
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 2.42 × sin 30° / 1 = 1.21
- sin r would be more than 1, so there is no refracted ray: total internal reflection. The critical angle is sin C = n₂/n₁ = 0.4132, C = 24.41°.
- n₂₁ = n₂/n₁ = 1/2.42 = 0.4132. Light travels at c/n: 1.24 × 10⁸ m/s in medium 1 and 3 × 10⁸ m/s in medium 2.
n = 2.42
- Speed of light in diamond: c/n = 3 × 10⁸ / 2.42 = 1.24 × 10⁸ m/s.
- The critical angle is sin⁻¹(1/2.42) = 24.41°, the smallest in the table.
- Light that gets into a cut diamond hits the inner faces at more than 24° most of the time, so it is totally reflected again and again before it leaves. That is the sparkle.
- The picture shows light inside diamond striking the surface at 30°: past the critical angle, so none of it gets out.
Snell's law with these numbers
- Light inside diamond meets the surface with air at 30°.
- n₁ sin i = n₂ sin r, so sin r = n₁ sin i / n₂ = 2.42 × sin 30° / 1 = 1.21
- sin r would be more than 1, so there is no refracted ray: total internal reflection. The critical angle is sin C = n₂/n₁ = 0.4132, C = 24.41°.
- n₂₁ = n₂/n₁ = 1/2.42 = 0.4132. Light travels at c/n: 1.24 × 10⁸ m/s in medium 1 and 3 × 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 diamond?
2.42, the highest value in NCERT table 10.3.
Why does a diamond sparkle?
Its critical angle is only 24.41°, so light inside it is totally reflected many times before it escapes, and comes out in bright flashes.
What is the speed of light in diamond?
About 1.24 × 10⁸ m/s, less than half its speed in vacuum.