Why a Prism Splits White Light Into a Rainbow

Walk up to a prism and fire a narrow beam of white light into it. What emerges is not white anymore — it is a diagonal ribbon of color, red at one end, violet at the other, with orange and yellow and green and blue filling the space between. This is not magic. It is dispersion, and it is one of the cleanest demonstrations in all of physics that light carries more structure than our eyes immediately reveal.

The effect was documented as early as 1666, when Isaac Newton performed a simple experiment: he passed sunlight through a glass prism and watched a spectrum appear on the far wall. His conclusion was radical for its time — white light is not pure. It is a mixture of distinct colors, each one refrracted at a slightly different angle as it passes through glass.

The Physics: Why Different Colors Bend Differently

When light travels from one medium into another — from air into glass, for instance — it changes direction. This is refraction, and it happens because light travels at different speeds in different materials. The ratio that governs exactly how much bending occurs is called the refractive index.

Here is the counterintuitive part: the refractive index is not constant for a given material. It varies with wavelength. Blue light, with its shorter wavelength, slows down more dramatically when entering glass than red light does. The result is that blue light bends more sharply, while red light passes through with less deviation. White light enters the prism as a unified beam and exits as a fan — each color tracing its own trajectory.

This wavelength-dependent refractive index is what physicists call dispersion. The relationship is encoded in the Cauchy equation (for visible light in transparent media):

n(λ) = A + B/λ²

where n is the refractive index, λ is the wavelength, and A and B are constants determined by the material. The 1/λ² term is why shorter wavelengths (blue, violet) experience a higher refractive index than longer wavelengths (red).

The Visible Spectrum

The rainbow that emerges from a prism is the visible spectrum — the narrow band of electromagnetic radiation that the human eye has evolved to detect. From longest to shortest wavelength:

– Red: ~700 nm – Orange: ~620 nm – Yellow: ~580 nm – Green: ~530 nm – Blue: ~470 nm – Violet: ~410 nm

A prism does not create these colors. It separates wavelengths that were already present in the white light, projecting each onto a different region of space.

Beyond the Lab: Where Dispersion Appears in the Real World

Dispersion is not confined to textbook experiments. It shows up wherever light passes through a curved glass interface at an angle.

Rainbows are formed by dispersion inside water droplets. Sunlight enters a droplet, refracts, reflects off the back surface, and refracts again upon exiting. The second refraction is what splits the light, and the angle at which we see the rainbow (roughly 42° for the primary bow) is a direct consequence of water’s dispersion curve.

Diamond fire — the flashes of color seen when looking at a well-cut diamond — comes from strong dispersion. Diamond has a much larger dispersion than ordinary glass, so the color separation is dramatic even in a tiny stone.

Optical glass design must account for dispersion when building lenses. A simple lens brings different colors to focus at slightly different points, a defect called chromatic aberration. Lens makers solve this by combining lenses made from different types of glass (crown glass and flint glass), using the opposing dispersion of each material to cancel out the effect.

The Interactive Simulation

The prism dispersion simulator lets you control the incoming light directly. Adjust the prism’s index of refraction, its apex angle, and the light’s angle of incidence. Watch how the spectrum fans out — or collapses back together when you reduce the dispersion parameters. Change the refractive index and observe the entire rainbow compress or expand.

What makes this simulation useful is that it shows the full ray path: incident ray, first refraction, internal reflection, second refraction. Each color is computed individually using Snell’s law applied to its specific wavelength, so you see exactly why the angles differ.

The prism is a deceptively simple piece of glass. Push on it with careful observation, and it opens up an entire branch of optics.