Dispersion: Splitting White Light

Aim the torch at the prism and watch white light come apart into colors.

Turning the least: the light goes through the prism evenly, level with its base, and turns as little as it can. Move the torch either way and the light turns more.

Angle going in: 50°
Red turns by: 38°
Violet turns by: 40°
The colors spread over: 1.4°

Prism Water Glass Flint glass Diamond

What’s happening

White light, like sunlight or a torch’s light, is really all the colors mixed together. Light slows down inside glass, and that makes it bend as it goes in and out. But the colors don’t all slow down by the same amount: violet slows down a little more than red, so it bends a little more. A prism’s two sides are tilted towards each other, so the bends add up instead of cancelling, and the colors come out going slightly different ways: they fan out into a spectrum, red, orange, yellow, green, blue, indigo and violet. This spreading is called dispersion.

Try this

Which color turns the most? Which turns the least?
Which prism spreads the colors the widest: water, glass or flint glass?
Move the torch slowly. Where does the light turn the least?
Pick flint glass and move the torch up towards the normal. Which color gets trapped first?
At home: stand a glass of water in a sunny window and look for a little rainbow on the floor or wall.

Learn more: Newton’s prisms, why colors bend differently, and how astronomers read starlight

Newton’s experiment. In 1666 Isaac Newton let a thin beam of sunlight into a dark room through a hole in his window shutter and passed it through a glass prism. A long band of colors appeared on the far wall. People thought the glass was coloring the light, so Newton sent just one color through a second prism: it bent again but stayed the same color. Then he used a second prism, turned the other way, to bring all the colors back together, and got white light again. White light, he showed, is a mixture of all the colors. He named seven, maybe to match the seven notes of a musical scale.

Why the colors bend differently. Each color of light is a wave of a different length, its wavelength $\lambda$ : red waves are the longest, violet the shortest (about half as long). How much a material slows light, its refractive index $n$ , is a little bigger for shorter waves. A good rule for glass and water is Cauchy’s formula, where a and b are numbers for each material:

n(\lambda) = a + \frac{b}{\lambda^2}

For ordinary glass that makes n about 1.51 for red and 1.53 for violet. Tiny as that difference is, it’s enough to split the colors. Flint glass, which has lead in it and is used for sparkly crystal glasses and chandeliers, spreads the colors about twice as much as ordinary glass, and diamond more still. Inside the glass, the light’s electrons are shaken by the passing wave; they follow violet’s faster shaking a little more strongly, and that slows violet down more.

How much the light turns. With $\theta_1$ the angle going in, $\theta_2$ the angle coming out (both from the normal) and $A$ the angle at the prism’s point (60° here), the light turns by

\delta = \theta_1 + \theta_2 - A

It turns the least when it goes through evenly, parallel to the prism’s base, going in and coming out at the same angle. Scientists use that smallest turn, $\delta$ _min, to measure a material’s refractive index very exactly:

n = \frac{\sin\big(\frac{A + \delta_{\min}}{2}\big)}{\sin\frac{A}{2}}

Rainbows: every raindrop is a tiny round prism (see Rainbow in a Raindrop).
Diamonds: their “fire”, the flashes of color, comes from dispersion, with total internal reflection bouncing the light round inside before it gets out.
Spectroscopes: spreading light into its colors shows exactly which colors a lamp, a flame or a star gives off. Every element has its own pattern, so astronomers can tell what stars are made of.
Colored fringes: simple lenses bend the colors differently too, so cheap binoculars show colored edges round things. Camera makers cancel this by pairing a lens of ordinary glass with one of flint glass.

Dispersion: Splitting White Light

What’s happening

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