Optics of Prisms

Introduction

Many people suppose that the main optical action of a prism is to disperse white light into its component parts, because that's what Isaac Newton used prisms for. But because dispersion is really a very small effect, it isn't the main optical action of a prism; more correctly, it should be looked at a a minor side effect.

The main effect of a prism is to deviate a beam of light. But, because of the dispersion in the refractivity of transparent materials, the deviation is slightly different for light of different colors. This slight difference in the deviation — only one or two percent, typically — is where the dispersive power of a prism comes from.

The aim of this page is to show the deviation of light by a prism, and to indicate how small the dispersive effect really is.

Prisms

It may be helpful to remind you what a prism really is: a geometric figure bounded by planes, whose bases are equal polygons, similarly oriented in parallel planes. The planes defined by corresponding (and hence parallel) sides of these polygons intersect in lines that are all parallel, so that the side faces of the prism are all parallelograms.

Prisms are usually classified by the shapes of the bases; so we have triangular, rectangular, hexagonal and other types of prism. The kind Newton experimented with were triangular; usually these are made with rather short side faces.

In optics, prisms made for the purpose of dispersing light are usually made with bases that are equilateral triangles, so that the angles between adjacent sides of the prism are 60°. However, prisms are also often used to re-direct light by using internal reflection; these often have bases that are isosceles right triangles, with angles of 45°-90°-45°. As optical technology developed, opticians found uses for more complicated pieces of glass with plane entrance, exit, and reflecting or refracting faces; but these are often not “prisms” in the geometric sense, but more complicated polyhedra, or even more complex shapes, with unused corners cut or rounded off to reduce weight.

However, for our present purpose, the interesting prisms are those that deviate light by refraction, not reflection, and these are triangular. The ones used for dispersing light sometimes have only two adjacent faces polished; the third side and the bases are often left in a rough-ground state, and may be painted black to absorb unwanted reflections. The angle between the two polished faces is called the refracting angle. If the prism is to be used for its dispersion, the refracting angle is usually about 60°.

On the other hand, refracting prisms are sometimes used to produce a very small angular deviation. These have a small refracting angle, and are often called wedges (although they do not have a sharp edge, which would be fragile and easily broken). If we are to compare the effects of atmospheric refraction — which typically produces an angular deviation (even at the horizon) of only half a degree, and never more than a few degrees — with a glass prism, one of these wedges would be the appropriate form. Sometimes a very thick wedge is used (e.g., the “Dove prism” used as an image rotator) to produce a small angular deviation by refraction, and the dispersion is merely a nuisance. For small angles, the deviation of a glass prism is about 1/3 of the prism angle, so a wedge angle of only a degree and a half would suffice to mimic the horizontal refraction of the standard atmosphere.

An example

Refraction at 38 deg. incidence Here's a beam of white light, coming vertically upward through a prism (shown in gray here) with a refracting angle of 38°. The bases of the prism are parallel to your screen. One side of the prism is horizontal, so the beam is not deviated when it enters the prism (at the bottom of the picture). When the light leaves the glass at the inclined face and enters the air, it is refracted, and the beam is deflected to the right; the deflection is larger at shorter (bluer) wavelengths.

The figure was constructed using the actual dispersion curve of BK 7 crown glass, similar in its optical properties to ordinary window glass. Although the angle was chosen to give a large deflection, the dispersion is barely visible on your screen.

You can see that ordinary glass produces very little dispersion. When dispersion is really wanted, a different type of glass (called “flint” glass, from one of the ingredients originally used in making it) is used. Yet even the highest-dispersion flint glasses have only 2 or 3 times as much dispersion at the same angular deflection as crown glass.

When you consider that air is more like crown glass than flint glass, and that the deflection produced by the whole atmosphere is (usually) only about half a degree, you can see why the dispersion of atmospheric refraction is only perceptible under unusual circumstances.

© 2002, 2004 – 2008, 2012 Andrew T. Young


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