Light lab

Dispersion of light through a prism

Shine white light into a glass prism and watch it split into a rainbow of colours. Change the angle and the material and see how far each colour turns.

Prism diagram: a white beam enters a triangular prism and leaves as a fan of coloursSeen from above. Red turns the least and violet the most. Drag sideways on the diagram to change the entry angle.60°White lightRedVioletnormal

Colours are drawn 5× wider than real life so you can see them. Real spread right now: –. Dashed lines are normals: lines at right angles to the glass face, which angles are measured from.

55.0°

How slanted the white beam is when it hits the prism, measured from the dashed line.

60°
Prism made of

Drag the sliders or use the arrow keys (hold Shift for 5° steps). You can also drag sideways on the diagram.

Red bend (700 nm)
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Violet bend (400 nm)
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Real colour spread
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Minimum bend (589 nm)
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Refractive index, 400 nm
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Refractive index, 589 nm
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Refractive index, 700 nm
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"Bend" (deviation) is how far a colour ends up turned from the direction it came in. Refractive index tells you how much the material slows light: 1.5 means light goes 1.5 times slower than in empty space.

Bend vs. entry angle
Line chart of how much yellow light bends at each entry angle, for the chosen material and top angleminimum bend (minimum deviation)Entry angleBend

Yellow light (589 nm) for the chosen material. The bright dot is your entry angle. The beam bends least when it passes through the prism evenly, with the same slant going in and coming out. Where the line stops, the light can't get out.

What's real and what isn't. All the bending happens in one flat plane, so the 3D view is for looking around, not extra physics. Screens can't show pure rainbow colours; each ray is an approximate screen colour. The glass numbers come from a simple formula fitted to published values, good to about the third decimal place.

What is happening?

White light, like sunlight, is a mix of many colours. When light passes from air into glass it slows down, and it changes direction at the surface. This bending is called refraction.

Each colour slows down by a slightly different amount, so each one bends by a slightly different amount. That splitting into colours is called dispersion. In a prism the two faces are tilted towards each other, so the bend at the second face adds to the first and the colours fan out.

In the NCERT Class 10 science book (CBSE), this is the "dispersion of white light by a glass prism" in the chapter The Human Eye and the Colourful World.

Why red bends least

Glass slows violet light a little more than red light. A bigger slow-down means a bigger bend, so violet turns the most and red the least, with orange, yellow, green and blue in between. The difference is small: for ordinary crown glass it is about one and a half degrees between red and violet in a 60° prism.

Newton's experiment

Isaac Newton began experimenting with prisms in 1666 and published his results in 1672. He let a thin beam of sunlight into a dark room and through a prism, and saw a long band of colours on the far wall. When he passed just one colour through a second prism, it bent again but did not change colour. And a second prism turned the other way could mix the colours back into white. So the colours were in the white light all along; the prism only separates them.

Why flint glass spreads colours more

Flint glass, traditionally made with lead, slows light more than ordinary crown glass, and it slows the colours by more different amounts. So it bends light further and fans the colours out much more; switch the material above and compare the real spread. Lens makers pair crown and flint glass so the colour spreading of one cancels the other's.

Rainbows are the same idea

A raindrop acts like a tiny prism with a mirror at the back. Sunlight bends going into the drop, reflects off the back and bends again coming out. Water slows the colours by different amounts too, so they fan out, and you see red on the outside of the bow and violet on the inside.

Show the maths

Refractive index for each colour, using Cauchy's formula: n(λ) = A + B / λ², with λ (wavelength) in micrometres. Values used here, fitted to each material's published index at 587.6 nm and its Abbe number (a measure of how much it spreads colour):

  • Crown glass (Schott BK7): A = 1.5046, B = 0.00420
  • Dense flint glass (Schott SF10): A = 1.6894, B = 0.01342
  • Water at about 20 °C: A = 1.3239, B = 0.00313

Snell's law at each face, with angles measured from the normal and A the top angle: sin i = n sin r₁, r₂ = A − r₁, n sin r₂ = sin e. Deviation δ = i + e − A. If n sin r₂ > 1 there is no way out: total internal reflection.

Minimum deviation happens when r₁ = r₂ = A/2, giving n = sin((A + δmin)/2) / sin(A/2). For BK7 at 589 nm in a 60° prism that is about 38.6°.

Questions and answers

What is dispersion of light?

Dispersion is white light splitting into its colours. It happens because each colour bends by a slightly different amount when it passes into glass or water. A prism makes this easy to see.

Why does violet bend more than red?

Light slows down inside glass, and violet light slows down a little more than red light. The more a colour slows down, the more it bends at the glass surface. So violet turns the most and red the least.

Did the prism create the colours, or were they already in the white light?

They were already there. Isaac Newton showed this in the 1660s: a second prism could not split a single colour any further, and a second, upside-down prism could mix the colours back into white. The prism only sorts the colours; it does not add them.

Why does a prism make colours but a window pane does not?

A window's two faces are parallel. The second face bends each colour back by exactly as much as the first face bent it, so all the colours leave in the same direction and stay mixed as white. A prism's faces are tilted towards each other, so the two bends add up instead of cancelling.

What is minimum deviation and why does it matter?

Deviation means how far the beam turns away from its original direction. As you change the entry angle, the turn first gets smaller and then larger again; the smallest turn is the minimum deviation. It happens when light passes through the prism evenly, the same slant in and out. Scientists use it to measure a material's refractive index accurately.

Why does the light sometimes not come out of the prism?

If light inside the glass meets the far face at too steep a slant, it cannot pass out and bounces back inside instead. This is called total internal reflection. A larger entry angle, a smaller top angle or a material like water lets the light out again.

Is a rainbow the same thing?

It is the same idea. Each raindrop bends sunlight as it enters, reflects it off the back of the drop and bends it again as it leaves, and each colour bends by a slightly different amount. You see each colour coming from drops at a slightly different angle, roughly 40 to 42 degrees from the point directly opposite the sun.

Why do the colours look so spread out on this page?

In real life the fan of colours is narrow, only about one or two degrees for ordinary glass. That would be a few pixels on a screen, so the diagram draws the colours 5 times wider after they leave the prism. The real spread is shown in the numbers beside the diagram.

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