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radiation of longer wave-lengths, one that we can see. The reason why fluorescent screens are so useful in X-ray work is obvious: they convert an invisible radiation into a visible one. Many substances show fluorescence; nearly all petroleum products, such as kerosene, vaseline, and lubricating oils, fluoresce with a bluish glow.

Fluorescence is something different from reflection. When light is reflected, there is no change in the frequency or the color. When a body fluoresces, it absorbs light of one frequency and emits a different kind, usually one having a lower frequency or a longer wave-length.

In some cases fluorescence persists after the exciting source of light has been removed. In this case it is called phosphorescence. Sometimes it persists for only a fraction of a second, while with other substances the phosphorescent light may be given out for hours afterwards. Phosphorescent paints can be purchased which will absorb light during the daytime and reëmit it at night. This must not be confused with the luminous products containing radium which are now coming into such common use, nor with the slow oxidation of phosphorus, as in the glowing trail left by a damp match.

Fluorescence and phosphorescence are special cases of the more general subject of luminescence.

CHAPTER XLVI

INTERFERENCE AND DIFFRACTION

Introduction, 646. The interference of waves, 647. The interference of light-waves, 648. The Fresnel mirrors, 649. The Fresnel biprism, 650. The colors of thin films, 651. Newton's rings, 652. Interference and the wave theory, 653. Diffraction, 654. Some experiments showing diffraction of light, 655. The diffraction grating, 656. The theory of the diffraction grating, 657. An alternative explanation of the grating, 658. X-ray spectra, 659.

646. Introduction. The subjects of interference and diffraction of light may be looked at from two different standpoints, both of them important.

1. A study of these subjects furnishes definite evidence that light is propagated by wave-motion. Recently the same method of reasoning has been used to prove that X-rays also are propagated by a wave-motion. The study of interference and diffraction gives us methods by which it can be determined whether any radiation is a wave-motion or not.

2. There are numerous applications of the principles which are stated in this chapter. The measurements of the wave-lengths of light and X-rays, and the measurements of other extremely short distances, are based on interference. The most refined measurements which have ever been made in many different fields are based on the interference of light.

647. The interference of waves. Attention has been called to the fact that when the paths of two or more wave-trains cross, the disturbance at any instant is the sum of the disturbances of the different waves. Sometimes (see section 329) these disturbances add in such a way that the resultant at certain points is always zero. For example, suppose that two pieces of wire are attached to one prong of an electrically driven tuning-fork, and that these wires dip down into water or mercury. When the fork

C

is vibrating, two different sets of circular ripples travel out from the wires, one set having one wire as center, and the other set having the other wire as center. Fig. 437 represents diagrammatically a portion of the disturbed region. The full lines show the position of the crests of the waves at one instant, and the broken lines the position of the troughs at the same instant. The wave-lengths of the two sets of waves are equal, because the two sources have the same frequency of vibration. Along the line A the crests and the troughs from the two sources meet in phase. They do this because each point on this line is equally distant from the sources S1 and S2. Along this line the disturbances add so as to reënforce each other. S. But all points on the line B are half a wave-length nearer S1 than S2; hence the disturbances from S1 reaching any point on this line are half a wave-length ahead of those from S2, and the two groups

meet with opposite phases:

-B'

S

-A

FIG. 437

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B

crests are meeting troughs. Along this line at all times there is destructive interference. If the amplitudes of the waves given off by S1 and S2 are equal, there will be no disturbance along this line. All points on the line B' are half a wave-length nearer S2 than S1, and there is interference along this line. However, all points on the lines C and C' are one wave-length nearer one source than the other. Hence the waves meet in phase, as shown in the figure, thus reënforcing each other.

In determining whether the waves reënforce or destructively interfere at any one point, the path difference of the two wavetrains must be considered. In the explanation of such cases as that given in Fig. 437, there is reënforcement when the path difference is zero, or one wave-length, or some whole multiple of a wavelength; but there is interference when the path difference is half a wave-length, or one and one-half wave-lengths, or two and onehalf wave-lengths, or any odd number of half-wave-lengths. This statement may be regarded as a general rule.

The principles involved in this experiment are true for all types of waves, but the apparatus required and the details of the necessary adjustments are very different for different kinds of waves.

648. The interference of light-waves. There are two reasons why the experimental methods for showing interference of light are difficult:

1. Light-waves have extremely short wave-lengths; therefore a difference of path of half a wave-length is a very small distance.

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2. In the case of the waves of Fig. 437 the two sources were made to vibrate together by attaching the two wires to the same prong of a tuning-fork. But it is impossible to get two different sources of light which will vibrate in phase. This difficulty in the case of light-waves restricts the experimenter to a single source. In 1816 and 1826 Fresnel designed two different experiments which successfully meet these difficulties and which show clearly the interference of light-waves.

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649. The Fresnel mirrors. Fresnel used two mirrors, M1 and M2 (Fig. 438), to reflect light from a narrow source S to a screen AB. The light that is reflected to the screen by M1 appears to come from S1 (the image of S in the mirror M1), and the light reflected from the mirror M2 appears to come from the image S2. When some suitable screen (not shown in the figure) is so placed that no light reaches the screen AB directly from S, AB is illuminated only by light from two virtual sources, S1 and S2. The two sources S1

2

2

and S2 vibrate in phase, for they are both images of the same source; thus the second difficulty mentioned in the last section is overcome. By adjusting the mirrors M1 and M2 until they are nearly parallel, the images S1 and S2 are moved until they are very close together. When all the necessary adjustments are properly made, a series of narrow parallel bright and dark bands appear on the screen. These bands are perpendicular to the plane of the figure and parallel to the narrow source S. The central bright band is equally distant from the sources S1 and S2. The first dark band on either side is half a wave-length nearer to one source than to the other, the second dark band is 3 half-wave-lengths nearer, the third is 5 half-wave-lengths nearer, and so on. The path differences for the bright bands on each side is 1 wave-length, 2 wavelengths, 3 wave-lengths, and so on.

Fresnel's apparatus can be used to measure wave-lengths of light. The details will be found in more advanced treatises, but the general principles can be understood from the following procedure: The angle between the two mirrors is measured, usually by some optical method based on reflecting light from the two mirrors. When this angle and the position of S with respect to the mirrors are known, the position of the two images, and their distance apart, can be computed. Then the following data are known or can be determined: (1) the positions of S1 and S2 with respect to the screen and (2) the distance between the bands on the screen. It is then easy to compute how much nearer one dark band is to S1 than it is to S2. If the band chosen is the first one, this difference in distance is half a wave-length; if it is the second, the difference is three half-wave-lengths. From this difference of path the wavelength is obtained. The method does not give accurate results, because one cannot measure the distance between the dark bands with a high degree of accuracy; but results correct within 5 or 10 per cent can be obtained.

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650. The Fresnel biprism. Fresnel devised another and, in many respects, a more simple method of showing interference of light. A piece of glass was made with a double bevel on one side (P, Fig. 439). A plate of this kind is called a biprism. Light going through half of it is bent in one direction, and that going through

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