the refractive index

Poke a straw into a glass of water and it looks bent at the surface; a swimming pool looks shallower than it is. Both illusions happen because light travels slower inside water than in air, and slower light bends when it crosses the boundary. The refractive index is the one number that captures how much a material slows light down, and therefore how strongly it bends and reflects it.

It is defined simply as n equals c divided by v, the speed of light in vacuum divided by its speed in the material. Since light never goes faster than c, n is always at least 1: air is about 1.0003, water 1.33, ordinary window glass about 1.5, and diamond a lofty 2.42. The bending itself follows Snell's law, n1 times sin(theta1) equals n2 times sin(theta2), where the thetas are the angles from the surface normal; the bigger the jump in n, the sharper the bend. Physically, the slowdown comes from light's electric field jiggling the electron clouds of the atoms, which re-radiate and delay the wave; denser, more polarizable materials slow light more and so have higher n.

Refractive index is the master parameter of every lens, prism, camera, and pair of glasses, and it is why a high-index glass can make eyeglass lenses thinner. It also usually varies slightly with color, a property called dispersion, which is exactly why a prism splits white light into a rainbow and why cheap lenses show colored fringes. And when light tries to leave a high-index material at a shallow angle, it can be totally reflected back inside, the total internal reflection that makes optical fibers and diamonds work. One honest subtlety: n depends on wavelength, so quoting a single value (usually measured with yellow sodium light) is a convenient simplification, not the whole story.