16 Light Waves and Theib Uses
each other the advance is, of course, zero; and here we should have the two wave trains in the same phase, with a consequent maximum of light. Where the thickness of the film is such that the second wave train is half a wave behind, there should be a dark band; at one whole wave retardation, a bright band; and so on.
The alternations of light and dark bands are thus accounted for, but the experiment shows that the first band is dark instead of bright. This discrepancy is due to the assumption that both reflections took place under like conditions, and that the phase of the two trains of waves would be equally affected by the act of reflection. This assumption is wrong, for the first reflection takes place from the inner surface of the first glass, while the second occurs at the outer surface of the second glass. The first reflection is from a rarer medium—the air; while the second is from a denser medium — the glass. A simple experiment with the Kelvin wave apparatus will illustrate the difference between the two kinds of reflection. The upper end of this apparatus is fixed, while the lower end is free; the fixed end, therefore, represents the surface of a denser medium, the free end that of a rarer medium. If now a wave be started at the lower end by twisting the lowest element to the right, the twist travels upward till it reaches the ceiling, whence it returns with a twist to the left — i. e., in the opposite phase. When, however, this left twist reaches the lowest element, it is reflected and returns as a twist to the left—so that the reflection is in the same phase.
There is thus a difference of phase of one-half a period between the two reflections, and, when this is taken into account, experiment and theory fully agree. We may now make use of the experiment to find a rough approximation to the length of the light waves.
If we measure by the microscope the diameter of the fila
Wave Motion and Interference
ment which separates the glasses, it will be found to be, say, two and seven-tenths microns.1 Counting the number of dark bands in red light, we find there are eight; and hence we conclude that at the thickest part of the air film the retardation is eight waves, and hence the distance separating the glasses — that is, the thickness of the filament— is four waves, which gives about sixty-eight hundredths of
a micron for the wave length of red light. If blue light is used, there will be twelve dark bands, whence the wave length of blue light is forty-five hundredths of a micron.
The following table gives the approximate wave lengths of the principal colors:
Red - 0.08 microns
Orange - - - .63 “
Yellow - - - .58 “
Green - .53
Blue - .48
Violet - - - .43
Fig. 17 gives a diagram of the wave lengths of the different colors, magnified about twenty thousand times.
Waves give information concerning direction, distance, magnitude, and character of the source. Light does the same; hence the presumption in favor of the hypothesis that light consists of waves.
i A micron is a thousandth of a millimeter, or about a twenty-five thousandth of an inch.