White Light Colours through Crossed Polarisers

Supporting pages are an introduction to birefringence and a statement of the problem (.doc file).

This applet was written to show how colours are created when white light passes through crossed polarisers with a birefringent plate in between. The birefringent plate has its optic axis perpendicular to its thickness.

• The incident light is represented by 6 colours across the spectrum. The amplitude of the light for each colour can be set as a number from 0 to 10, in arbitrary units. The default amplitude is 10.
• The applet shows the spectral colour for specimens of different thickness, increasing thickness from left to right. The thickness of current interest is marked by a white vertical line. Where it cuts a particular wave shows how much of that wave gets through the analyser. The phase of this variation is half the phase difference between waves polarised along the fast and slow axes, commonly known as the 'retradation' of the plate.
• The birefringence just affects the thickness scale over which the changes take place. If you enter a birefringence value (between 0.0001 and 1.0), then the specimen thickness to achieve the retardation shown at the white line is specified at the bottom of the line.
• When you move the line, the colour appropriate to the retardation chosen is shown in the lowest panel, with the rgb colour coefficients labelled (maximum = 255).
• To account for the loss of light through the polarisers, the colour spectrum is globally scaled so that the most intense colour is completely saturated. This, however, still leaves a good number of colours rather dark. If a real specimen were fairly uniformly thick, the observer's eye would adapt to this darker light and show the colour better. A hidden feature of the applet is revealed by clicking on our logo. The spectrum will brighten, saturating the brighter colours but still leaving the weaker colours unsaturated.

Try altering the spectral content of the light. You can choose just 3 wavelengths for red, green and blue, setting the others to be zero. You can progressively reduce the amplitudes of colours towards the blue, representing a filament lamp source. However, in reality, your eye can partly adapt to changing white light sources, re-defining what it interprests as white. You can alter the birefringence and see what thicknesses are need to produce a given effect. You can see very simply how a plate that is quarter-wave or half-wave is only so at one particular wavelength and what colour it will let through if other wavelengths are present.

The applet and web pages were designed and coded by Gary Skinner, from an intital idea by Sylvanus P Thompson, as part of his undergraduate physics project.