Refraction and Prisms

Refraction is the bending of light as it passes from one transparent material into another, because its speed changes. Light bends towards the normal when it slows down (air to glass) and away from the normal when it speeds up (glass to air). It explains why a pencil looks bent in water.

Snell's law says n₁ sin i = n₂ sin r, where i is the angle of incidence, r the angle of refraction, and n₁ and n₂ the refractive indices of the two materials. Equivalently, sin i ÷ sin r is constant for a given pair of materials.

Total internal reflection happens when light travelling in a denser material hits the boundary with a rarer material at an angle greater than the critical angle. No light is refracted out; all of it reflects back. It is used in optical fibres, periscope prisms and binoculars, and causes mirages and the sparkle of diamonds.

The critical angle is the angle of incidence (in the denser material) for which the refracted ray grazes along the surface at 90°. It is given by sin C = 1/n for a material against air. It is about 48.8° for water, 41.8° for glass and 24.4° for diamond.

Dispersion is the splitting of white light into its colours. A glass prism bends each colour by a different amount because the refractive index depends on wavelength: violet bends most and red least. The band of colours is called a spectrum, VIBGYOR. Isaac Newton showed that a second prism can recombine them into white light.

Sunlight enters raindrops, refracts and disperses into colours, reflects off the back of each drop, and refracts again as it comes out. Each colour leaves at a slightly different angle, about 40° to 42° from the direction opposite the Sun, so we see a circular band of colours with red on the outside.