Light Refraction: What It Is, the Laws Behind It, and Examples

Two fates for the same ray

When a ray of light reaches a surface separating two transparent materials, it does not generally pick just one path. Part of it bounces back into the material it came from: that is reflection. Another part enters the second material, but changes direction on the way in: that is refraction. It happens every time light meets a pane of glass, the water in a pool, or even just the warmer air sitting above a sidewalk.

These two laws, applied to flat or curved surfaces, explain mirrors and lenses. They also explain prisms, and even a mirage over hot asphalt.

The law of reflection

Reflection is the easier half to measure. The angle of incidence, the angle at which the ray reaches the surface measured from the normal (the perpendicular to the surface at that point), always equals the angle of reflection, the angle at which the ray leaves. This holds on any smooth surface: a mirror, the still water of a lake, a polished floor. On a rough surface, by contrast, light bounces off in many directions at once, an effect called scattering: a sheet of white paper reflects plenty of light, yet it does not work as a mirror, because that light leaves in every direction instead of just one.

A flat mirror produces a virtual image that forms at exactly the same distance behind the reflecting surface as the object sits in front of it. It counts as a real image in the sense that it can be photographed and measured, even though it appears at a physical point where the object could never actually be, behind the solid glass of the mirror. Many people believe a mirror swaps left and right: in fact, the only direction a reflecting surface can tell apart geometrically is the one perpendicular to itself, front and back. Looking into a mirror, the image you see is turned around in depth, and the idea of a left-right swap only arises when you picture having to turn around to stand in your reflection’s place.

Snell’s law and the refractive index

Refraction is the change in direction of a wave, here light, when it crosses into a material where it travels at a different speed. Snell’s law links the refractive indices of the two materials to the angles the ray makes with the normal, before and after it crosses over: the index of the first material times the sine of the angle of incidence equals the index of the second material times the sine of the angle of refraction. The refractive index of a material, written n, is simply the ratio between the speed of light in a vacuum and its speed inside that material: n = c/v. The more a material slows light down, the higher its index.

A vacuum has an index of 1.000 by definition, and air sits very close to it, at 1.000277, since it barely slows light at all. Water, around 1.33, slows it down visibly, and crown glass, between 1.50 and 1.62 depending on the type, even more. Diamond reaches 2.417, among the highest values of any common transparent material — a fact that matters again when we come back to its critical angle.

Real-world example: dip a pencil halfway into a glass of water. Right where the pencil enters the water, it suddenly looks broken or shifted, because the rays of light reaching your eye have changed direction crossing from water into air. The pencil, of course, is straight: it is the path of the light that has bent.

Real-world example: the same principle explains why a fish in a tank can seem to be in two different spots depending on where you look from. The rays leaving the fish refract right where they leave the water, and the eye traces those rays back in a straight line, with no way of “knowing” they changed direction along the way.

Checking how a measured angle changes crossing from one material into another is also a small exercise in Thales’ theorem: the triangles formed by the ray, the normal and the surface stay in proportion, and those same proportions show up in the formula behind Snell’s law.

The critical angle and total internal reflection

When light passes from a material with a higher refractive index into one with a lower index, say from water into air, the ray bends away from the normal: it exits more tilted than it was going in. Raising the angle of incidence far enough, a point comes where the refracted ray skims the surface, leaving at 90° from the normal. That angle of incidence is called the critical angle, and it is found by imposing exactly this condition on Snell’s law. Below the critical angle, light never reflects completely: part of it exits refracted, part of it reflects anyway. Only past the critical angle does light stop leaving at all, staying entirely inside the original material: that is total internal reflection, the physical principle behind fiber optics and polarizing prisms (it has its own Recap).

Diamond takes this effect to the extreme. Because of its very high refractive index, the critical angle for light going from diamond into air is only 24.4°, far lower than that of ordinary glass. The facets of a cut diamond are shaped on purpose to make it unlikely for light to exit at an angle below the critical one: the light stays “trapped” for longer, bounces many times inside the stone, and concentrates before it finally leaves. That is the physical effect behind diamond’s characteristic sparkle, not some magical property of the stone.

Dispersion, curved mirrors and lenses

A prism splits white light into the colors of the rainbow for a precise reason: a material’s refractive index changes with the wavelength of light, an effect called chromatic dispersion. The index generally drops as wavelength grows, so red light refracts less than blue light, which also travels a touch slower inside transparent materials. Isaac Newton was among the first to show with a prism that white light is not a single, simple color but a sum of colors that separate once they refract at different angles.

Curved mirrors follow the same law of reflection, applied point by point to a spherical surface rather than a flat one. For a concave or convex mirror, the focal length is always half the radius of curvature of the spherical cap. In a concave mirror, rays arriving parallel to the optical axis converge at a real focus; in a convex mirror, they appear instead to diverge from a virtual focus behind the surface. The equation describing where the image forms, for rays close to the axis, takes the same mathematical shape found in the equation for thin lenses: the same similar triangles come in handy to derive it, the same reasoning used in the triangle similarity theorems studied in geometry.

In lenses the principle stays the same, but the curvature works through refraction instead of reflection. In a converging lens, rays entering parallel to the optical axis are bent until they all meet at a single point, the focus. In a diverging lens, parallel rays spread apart instead, and traced backward they appear to come from a single virtual focus. The focal length of a lens is the distance between its center and that point. A diverging lens, for example, can correct nearsightedness in eyeglasses, bending light before it ever reaches the eye.

An invisible gradient, over the asphalt

Air looks like a uniform material, but it never quite is. At standard temperature and pressure its refractive index is 1.00029, a tiny difference from a vacuum that still starts to matter over long distances. Close to the ground, air at different heights sits at different temperatures, so its refractive index varies slightly from layer to layer: rays of light curve toward the cooler side of this thermal gradient. Over a very hot road or stretch of asphalt, the air right above the surface is warmer, and therefore slightly less refractive, than the air higher up. Light from the sky arriving at a shallow angle gets bent upward before it reaches the eye, and the effect mimics the shiny surface of a puddle: it is a mirage, not an actual reflection off water.

Pinning down these laws with pencil and paper takes the same scientific method used for any measurable phenomenon: a hypothesis about an angle, a measurement with a protractor, a comparison against what Snell’s law predicts. It is from measurements of exactly this kind, repeated across different materials, that the refractive index tables used in optics today come from.