Refraction and Snell's Law

Refractive index (n) — a measure of how much a material slows light down, and therefore how strongly it refracts.

Snell's law relates the angles either side of a boundary:

n = sin i / sin r

where i is the angle of incidence and r the angle of refraction, both measured from the normal. For light passing from air into a material, n is the refractive index of that material.

Typical values: air is almost exactly 1, water is 1.33, and glass is about 1.5. A larger refractive index means a greater bend.

Refractive index can also be written in terms of speed:

n = speed of light in a vacuum / speed of light in the material

so a refractive index of 1.5 means light travels 1.5 times more slowly in that glass than in a vacuum. Because nothing travels faster than light in a vacuum, n is never less than 1.

Which way does it bend? Air into glass slows the light, so it bends towards the normal and r < i. Glass into air speeds it up, so it bends away and r > i.

Measuring the refractive index of glass — place a rectangular glass block on paper and draw round it. Shine a ray at the block and mark the incoming ray with two pins, then mark where it emerges with two more. Remove the block, join the marks to find the path through the glass, and measure i and r from the normal. Repeat for several angles and calculate n for each, or plot sin i against sin r — the gradient is the refractive index, and using a graph averages out the errors of individual readings.

Dispersion — different colours have slightly different refractive indices, so they bend by different amounts. Violet is refracted most and red least, which is why a prism spreads white light into a spectrum and why rainbows exist.

Example: light strikes a glass block at 40° to the normal and refracts to 25°. n = sin 40 ÷ sin 25 = 0.643 ÷ 0.423 = 1.5. Using the angles from the surface instead of the normal would give sin 50 ÷ sin 65 = 0.85, which is less than 1 and therefore impossible — a useful check.