Wave Motion and Interference
15
generally are among the most beautiful in nature, and while no artist could do justice to such a subject, much less a lithographic plate, such a plate (Plate II) may be used to recall the more striking characteristics.
For the scientific investigation of the interference of light waves, however, the soap film is rather unsatisfactory on account of the excessive mobility of its parts and the resulting changes in thickness. A much more satisfactory arrangement for this purpose is the following: Two pieces of glass with optically plane surfaces are carefully cleaned and freed from dust particles. A single fiber of silk is placed on one of the surfaces near the edge, and the other is pressed against it, thus forming an extremely thin wedge of aii; between the two plates, as shown in Fig. 16.
It will be found that in this case the succession of colored bands will resemble in every respect those in the soap film, except that they are now permanent. The light is reflected from all four surfaces, and hence the purity of the colors is somewhat dimmed by the first and the fourth reflections. These may be obviated by using wedges of glass instead of plates.
To account for the colored fringes it will be best to begin with the simpler case of monochromatic light. If a piece of red glass is interposed anywhere in the path of the light, the bands are no longer colored, but are alternately red and black. They are rather more numerous than before, and a trifle wider. If a blue glass is interposed, the bands consist of alternations of blue and black, and are somewhat narrower (cf. Plate II).
Let us suppose now that red light consists of waves of very small length. The train of waves reflected by the first surface of the film will be in advance of that reflected by the second surface. At the point where the two surfaces touch
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