Dispersion of Light Simulator

What Is the Dispersion of Light Simulator?

Four Sliders, One Spectrum: What to Try First

The four controls map onto the four things that really decide what a prism does. The apex angle A sets how sharply the two refracting faces meet; the angle of incidence i sets how the white beam strikes the first face; the mean index n_d says how strongly the glass bends the middle of the spectrum; and the Abbe number V_d says how differently it treats red and violet. Under the canvas, the sim is simply solving Snell's law, sin i = n sin r, at both faces — the same two-boundary refraction you can work through one interface at a time in the Snell's law calculator — with each colour's index set by Cauchy's relation n(λ) = A + B/λ².

The readouts are there to prove the core rule rather than ask you to trust it. At every setting you can reach, n (violet) is larger than n (red), and the violet deviation sits above the red one — the fan on screen always puts violet at the bigger angle. That corrects the classic exam mistake of expecting red, the “stronger” colour, to bend most: bending is set by the index, and the index rises as the wavelength shortens. Since a medium slows light to v = c/n (the idea explored in our speed of light guide), violet is also the colour the glass slows the most.

Two experiments are worth running deliberately. First, drag V_d up and watch the angular-dispersion readout shrink while the whole fan stays put: a high Abbe number means the indices for red and violet crowd together, and the spectrum narrows. Then drag n_d up instead and watch every deviation grow at once — the fan swings as a whole. Colour itself is fixed by frequency rather than by the wavelength that changes inside the glass, a distinction unpacked in the frequency formula guide.

Finally, push the geometry until it breaks. Raise A or n_d and the status line will announce the moment violet stops emerging: it has hit the second face beyond the critical angle and is totally internally reflected, shown as a dashed ray bouncing back inside the prism. Sweep i slowly from 20° to 80° and each deviation dips through a minimum — the symmetric passage a prism spectrometer exploits to measure the index of a glass sample.

Where the ideal prism breaks down

Cauchy's relation is a curve fit, not a law of nature. It describes glass well only in the transparent window between the material's absorption bands, and this simulator fits it from three visible reference lines at 656.3, 587.6 and 486.1 nm, then evaluates it out at 680 nm and 410 nm — a little beyond the data it was anchored on. Walk towards an absorption band, in the ultraviolet or the infrared, and the index does the opposite of everything the readouts suggest: it falls as the wavelength shortens. That is anomalous dispersion, and Cauchy's two terms cannot represent it at all. Real lens design uses Sellmeier's equation instead, with a resonance term for each absorption band.

The canvas traces a single ray; a real spectrometer never has one. A beam has width, so each colour emerges as a band rather than a line, and two nearby wavelengths blur together unless the prism is physically large. A prism's resolving power is its base length multiplied by the rate at which the index changes with wavelength, so doubling the dispersion of the glass while halving the prism buys you nothing. That is why laboratory prisms are chunky blocks and not the slim wedge drawn here.

Nothing is lost at the surfaces here, and in a real prism a good deal is. Every face reflects part of the beam — about 4% at each surface for an index of 1.52 near normal incidence, and considerably more at the steep angles this simulator works at. Worse, the reflected fraction depends on polarisation, so a prism partly polarises the light passing through it and the spectrum is not uniformly bright across the fan. Anti-reflection coatings exist precisely to claw that back.

Two honest caveats about the picture itself. The fan between red and violet is drawn four times wider than life so that it is visible at all: at the default settings the true angular dispersion is only 1.57°, with red and violet deviating 38.63° and 40.20°. And the index is treated as a fixed number, which it is not. Optical glass shifts its index with temperature, so a precision spectrometer has to be temperature-stabilised before its readings mean anything.

Where this is actually used

The achromatic lens in every camera. A simple lens focuses violet closer than red, which is this same fan happening at a curved surface. The fix is to cement a low-dispersion crown element to a high-dispersion flint one so their colour spreads cancel while their focusing powers do not. The simulator shows why that pairing works: hold n_d at 1.52 and drop the Abbe number from 58 to 25, and the dispersion readout jumps from 1.57° to 3.68° while the red deviation shifts only from 38.63° to 38.24°. More than double the colour spread for almost the same bending is exactly the trade an achromat is built on.

Measuring the index of a glass sample. Set A = 60°, n_d = 1.52 and V_d = 58, then sweep the angle of incidence: the red deviation falls to 38.63° around i = 49° and climbs again either side. Put that minimum into the spectrometer formula, n = sin((A + D)/2) divided by sin(A/2), and it returns 1.5166 — the exact figure the sim prints for n (red). That is the standard undergraduate index measurement, and it needs nothing but a prism and a protractor.

The width of a rainbow. Set the mean index to 1.33 and the Abbe number to 56, roughly water, and the readouts give 1.3277 for red against 1.3394 for violet. That gap of about 0.012 is the whole cause of the rainbow. Sunlight refracting into a raindrop and reflecting once inside comes back at close to 42° for red and 40° for violet, which is why the bow is a couple of degrees of colour and no wider.