The refractive index
- The refractive index (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material:
n = (speed of light in a vacuum) / (speed of light in the medium)
- A few key facts about n:
- Light always travels slower in matter than in a vacuum, so n is always greater than 1
- The higher the refractive index, the slower light moves through the material and the more the ray bends when it enters
- Refractive index is a ratio of two speeds, so it has no units
- Typical values for common materials:
- air ≈ 1.00 (effectively the same as vacuum)
- water ≈ 1.33
- perspex / acrylic ≈ 1.49
- crown glass ≈ 1.50
- diamond ≈ 2.42 (one of the largest of any everyday material, which is why cut diamonds sparkle so brightly)
Snell's law
n = sin i / sin r
- where:
- n = refractive index of the second medium (taking the first medium as air, where n ≈ 1)
- i = angle of incidence in air (measured from the normal)
- r = angle of refraction in the denser medium (measured from the normal)
- Important details:
- sin i / sin r is not the same as i / r; never just cancel the "sin"
- When solving for r, find sin r first, then take sin⁻¹ to get the angle
Example A — a ray of light hits a glass block (n = 1.50) at an angle of 30° to the normal. Calculate the angle of refraction inside the glass.
- Rearrange Snell's law: sin r = sin i / n
- sin r = sin 30° / 1.50 = 0.500 / 1.50 = 0.333
- r = sin⁻¹(0.333) = 19.5°
Example B — a light ray enters a water tank from air. The angle of refraction inside the water is 22°. The refractive index of the water is 1.33. Calculate the angle of incidence.
- Rearrange Snell's law: sin i = n × sin r
- sin i = 1.33 × sin 22° = 1.33 × 0.3746 = 0.4982
- i = sin⁻¹(0.4982) = 29.9°