The stratification of a photographic plate by these nodes and loops in front of a mirror is the basis of the color photographs of Lippmann, as the strata are closer together with short waves than with long.

References.

A. A. Michelson. Light Waves and Their Uses.

Edwin Edser. Light for Students.

S. P. Thompson. Light, Visible and Invisible.

DIFFRACTION.

928. Diffraction Bands Around Shadows.-The observation of shadows suggests that light is propagated in straight lines. The form which the shadow of an obstacle would have if this were the case is called the geometrical shadow; it is the projection

of the obstacle upon the screen by straight lines radiating from the luminous source as a center.

Ordinary shadows are blurred at the edges because the angular magnitude of the source causes a penumbra. Hence to make an accurate comparison of a real shadow with the geometrical shadow the source of light should be a mere point. But when the experiment is tried, as, for example, when we examine closely the shadows cast by a moderately distant arc lamp, instead of finding a clear-cut boundary, the entire edge of the shadow is observed FIG. 572.-Diffraction bands at to be surrounded by a series of alternate cle line is edge of the geometrical dark and bright bands, parallel to the edge, very distinct next the shadow and gradually fading out into the fully illuminated region.

shadow.

These bands were known at the time of Newton and were called diffraction bands or fringes, because to explain them on the emission theory it was supposed that the luminous corpuscles were bent aside from their straight course as they shot by the edge of the obstacle.

In the year 1816 a young French artillery officer, Joseph

Fresnel, then less than thirty years of age, presented to the French Academy a memoir which marked an epoch in the science of optics, for in it he showed that the varied phenomena of diffraction are readily explained in every detail by the interference of light waves taken in connection with Huygens' principle, and without recourse to any additional hypothesis.

929. Huygens' Principle.-Let there be a train of waves. advancing in the direction OP whose crests are represented by the parallel lines on the left of

figure 573, and let AB be a row of particles parallel to the wave front; then as the waves sweep by AB the particles are all set vibrating simultaneously and in the same phase. Now, each of these vibrating particles may be considered as a center of disturbance from which spherical waves spread out into the region beyond. Thus, if we choose, we may consider the vibration that is produced at the point P as due to the combined effect of all these little elementary waves or wavelets whose centers lie in the line AB, just as though the line of particles AB was the actual source from which waves spread out. This is known as Huygens'

principle.

930. Diffraction by a Narrow Slit.-If sunlight shining through a narrow slit falls on a second narrow slit parallel with the first, there will be seen on a white screen held back of it, a central bright band and on each side alternate bright and dark bands, which widen out when the second slit is made narrower. The wave theory affords a simple explanation; for let S be the slit (looked down upon endwise) which is very narrow compared with its distance from the screen at b, (Fig. 574), and let AB represent the greatly magnified cross-section of the slit in the plane of the paper. Then the ether particles lying in ACB are kept in vibration by the successive waves passing through the slit, and by Huygens' principle these particles may be considered

as the centers of wavelets which spread out in all directions and produce the effects which are observed. Now, on account of the extreme narrowness of the slit, b, is practically equally distant from all points along the line AB, and therefore the wavelets starting simultaneously at all points along AB reach b, in the same phase and so reenforce each other and make it a bright spot.

Just below b, there will be a point d, which is a whole wave length farther from A than from B. Then d, is a half wave length farther from C than from B, and for every point between B and C there is another between C and A which is just a half wave length farther from d1. Therefore the wavelets going to d1 from one-half of the slit will be exactly neutralized by

FIG. 574.-Diffraction through narrow slit perpendicular to the plane of the paper.

wavelets from the other half, and d, will therefore be a dark spot in consequence of this interference. In the same way the dark spot d, above b, is explained.

But a little beyond d, there will be a point b2 which is 14 wave lengths farther from A than from B. In that case the wave front in the slit may be conceived as divided into three equal parts AD, DE, and EB, such that wavelets coming to b from AD have a half wave length farther to travel than from the corresponding point in DE. Therefore waves from these segments interfere at b, while waves from the third segment will be effective and make b, a bright spot, though much less bright than b1, since only one-third of the width of the slit is effective. Of course DE might be regarded as opposing EB, and in that case AD is effective.

The same reasoning shows that there will be a dark spot where the difference in path from A and B amounts to 2 wave

lengths and again a bright spot where the difference amounts to 2 wave lengths. There will therefore be a series of alternate dark and bright spots on each side of b, as experiment shows.

If the slit is made narrower the line AB is shorter, and consequently the point d,, which is one wave length farther from A than from B is farther away from b, than before. Therefore the bands spread out as the slit is made narrower, and if it had a width of only one wave length or less, light would go out from it in every direction, though the intensity would be less in oblique directions in consequence of partial interference.

931. Shadow of a Circular Obstacle.-When Fresnel's memoir was presented to the French Academy it was objected by Poisson that if his views were correct there should be a bright spot in the center of the shadow cast by a circular disc. Fresnel at once acknowledged the justness of the criticism and, making the experiment, found the bright spot, thus obtaining a triumph for the new theory.

The experiment may be made by fastening to a piece of plate glass a bicycle ball about inch in diameter and observing its shadow as cast by a distant arc light at a distance of 8 or 10 ft. back of the obstacle; the central bright spot may be readily seen either by receiving the shadow on a card or by looking toward the object and viewing the shadow directly with a small pocket magnifier. Or the shadow may be received upon a sensitive film and photographed.

The central spot is bright because it is equally distant from every part of the edge of the obstacle, and therefore wavelets coming from points just outside the edge around its whole circumference come together in the same phase at that point.

Similarly a bright line is found in the center of the shadow of a wire, since the central line is equidistant from the two edges

and waves coming around the wire on both sides reach the central line in the same phase and therefore reenforce each other. (See figure 575.)

The student should observe through a pocket magnifier the diffraction bands formed by the wires of a mosquito netting or screen of thin silk, standing a few feet from the screen and looking through it toward a distant arc light.

932. Miscellaneous Diffraction Phenomena.-In figure 576 are shown at A the diffraction bands in the shadow of the pointed end of a needle. It will be observed that there is a central bright band, broadest near the very point, while where the needle is thicker many fine interference bands are seen in the shadow.

This is shown in B which is the shadow of a somewhat thicker wire showing the many fine bands due to the interference of the waves coming around the two sides of the wire. At C is shown the diffraction pattern which may be seen by looking through the cloth of a silk umbrella toward an electric arc lamp.

A small round obstacle gives rise to a series of diffraction rings, and where the rings due to a great number of fine particles are all of the same size and are superposed the effect may be very intense. This is the explanation of the coronas seen so often around the moon. They are brightest when the light from the moon comes through a region full of minute water particles nearly uniform in size. These coronal rings are larger the smaller the particles that cause them, and the average diameter of the water drops can be immediately calculated from the angular radius of the rings.

Beautiful coronas may be seen on looking at an electric light or gas flame through a piece of glass coated with lycopodium powder, which is