Reckoning / Light / Prisms and colour
Light · dispersion
Prisms and colour
A prism bends light twice, both times towards its thick base. White light comes out as a fan of colours, because each colour has its own refractive index. Turn the incoming ray and watch the deviation fall to a least value, then rise again.
The prism and the ray
Measured
Deviation
The ray meets the first face at angle i and leaves the second at angle e. Its total turn, the deviation, is
Turn the incoming ray and δ passes through a least value, the minimum deviation. It happens when the ray crosses the prism symmetrically, parallel to the base, entering and leaving at the same angle. There the index follows from two angles alone. Measuring them on a prism of the glass is how glass makers measure indices to five decimal places:
For a 60° prism of crown glass in yellow light, δmin = 38.65°, reached at i = 49.3°. Make the incidence too small, or the prism too steep, and the ray meets the second face beyond the critical angle and is totally reflected inside.
Dispersion
In blue F light the same crown prism deviates by 39.14° and in red C light by 38.43°, which opens a fan of 0.71°. A flint glass prism opens it to 1.67°. Flint glasses, with lead or titanium oxide in them, spread colours more for the same amount of bending, which is what a spectroscope needs and an achromatic lens exploits.
A prism with a 90° corner is also used without any colour at all: light enters the long face square on, is totally reflected by the two short faces, and goes back the way it came (try the right-angle prism on the free bench). Binoculars use such prisms (Ignazio Porro, 1854) to fold the light path and turn the image the right way up.
Prisms making colours were well known, but people thought the glass coloured the light. From 1666 Isaac Newton experimented with prisms. Passing a single colour from one prism through a second, he found that it did not change. White light is a mixture, and the prism only sorts it. He reported this in 1672 and set it out in Opticks (1704) (Newton, Opticks). Newton counted seven colours, choosing the number to match the notes of the musical scale; the spectrum itself is continuous. In 1814 Joseph von Fraunhofer saw dark lines crossing the solar spectrum and used them to measure the dispersion of his glasses. The F and C lines in the table on the refraction page still carry his letters (his D is the yellow sodium line). The d line beside them is a line of helium, an element found only in 1868.
These are rays, the geometrical-optics picture: light is treated as lines that bend and split at surfaces. Diffraction and interference, which need the wave picture, are not shown. The bench is a flat cross-section, so a lens here is really a cylinder of glass seen end-on. That is exact for rays in the plane of the drawing. Air is taken as n = 1, and the glass and water indices are given relative to air, so the angles are right. Colours on screen are an approximation of the spectrum.