120
Light Waves and Their Uses
From eaeh of these sources it is spread out in circular waves. If the incident wave is plane and falls normally upon the grating, all these waves start from the separate openings in the same phase of vibration. Hence, in a plane parallel to the grating we should have, as the resultant of all these waves, a plane wave traveling in the direction of the normal to the grating. When this wave is concentrated in the focus of a lens, it produces a single bright line, which is the image of the slit and is just as though the grating were not present.
Suppose we consider another direction, say AC (Fig. 87). We have a spherical wave, starting from the point B, another in the same phase from the point a, etc. Now, if the direction AC is such that the distance ab from the opening a to the line through B perpendicular to AC is just one wave, then along the line BC the light from the openings B and a differ in phase by one whole wave. When ab is equal to one wave, cd will be equal to two waves; hence, along BC the light from the opening c will be one wave behind the light from a,.etc.; and if these waves are brought to a focus, they will produce a bright image of the source. Since the wave lengths are different for different colors, the direction AC in which this condition is fulfilled will be different for different colors. A grating will there
Action of Magnetism on Light Waves 121
for© sort out the colors from a source of light •uid bend them at different angles, forming a spectrum. Since th© blue waves are shorter than the red, th© blue will be bent least and the red most, the intervening colors coming in their proper order between. Again, we may also have an image formed when the direction AC is such that this difference in phase of the light from successive openings, instead of one wave, is two. The spectrum thus formed is said to be of the second order. When this difference in phase is three waves, the spectrum is said to be of the third order, etc.
Plate I, Fig. 2, represents the spectrum produced by a coarse grating. The source of light was a narrow slit illuminated by sunlight. The central image appears just as though no grating were present, and on either side are diffuse spectral images colored as 011 Plate I. Three such images, which are the spectra of th© first, second, and third orders, may be counted 011 the right, and the same on the left. The grating used in producing this picture had about six hundred openings to the inch. Now, a finer grating produces a much greater separation of the colors. The large concave gratings used for the best grade of spectroscopic work produce spectra of the first order which are four feet long. Those of higher order are correspondingly longer.
The efficiency of such gratings depends on the total difference of path in wave lengths between the first wave and the last. Thus in the grating shown in Fig. 87 there will be, in the case of the first spectrum, as many waves along AC as there are openings between A and B. If we call the total number of openings in the grating n, then there will be n waves along AC, In the second spectrum, then, since each one of the intervals corresponds to two waves, the total difference in the path is twice as great, so that the number of waves in AC will be 2 n. For the third spectrum the number would be IS ii, and for the mth spectrum run.