CHAPTER IX.

INTERFERENCE.

Net Result of Two Different Forces—Liquid and Tidal Waves-Why Single Interferences are not Traceable in Light-Interference of Sound Waves-Thin Films of Turpentine, Transparent Oxide, Soap, Water, and Air-Colour Dependent on Thickness of the Film-Proved to be Dependent also on Reflection from both Surfaces-Spectrum Analysis of Films-Soap Films and Sound Vibrations-Fresnel's Mirrors-Fresnel's Prism-Irregular Refraction-Diffraction-Gratings-Telescopic Effects-Other Simple Experiments in Diffraction-Striated Surfaces-Barton's ButtonsNature of Interference Colours-Measurement of Waves-The Size of Molecules of Matter.

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93. Net Result of Two Different Forces Motions. We have now to study a class of experiments which most of all clearly demonstrate the true wave character of the phenomena which constitute Light. We know that dif ferent separate motions can act upon one another, so as either to combine and strengthen, or to neutralize and destroy each other, simply because the actual motion of any particle must result from the net sum, difference, or other result of the forces which act upon it. Take a billiard ball travelling in a direction and at a rate resulting from some stroke of the cue; if we impart another impulse in the same direction the velocity will be increased; while if the ball be met by a second force of the same amount it is brought to a standstill.

94. Interference of Liquid Waves.-The same must result in the case of any series of vibrations of equal amplitudes and periods, such as constitute a wave. If we drop two stones at some distance apart into the same pond, the circular

waves from one will cross those from the other. At some points the crests will coincide, and reinforce each other; at others the same particle of water is elevated by one wave

The conse

and depressed by the other; there it is at rest. quence is a beautiful pattern caused by the intersecting ripples. Fig. 91 shows such a pattern caused in an elliptical bath of mercury by a drop or point introduced at one of the foci. They can be beautifully shown by the vertical attachment (§ 10) to the lantern, laying over the condenser a glass plate to which is cemented a circular tin wall, making a circular tank some 6 inches in diameter and an inch deep, with a glass bottom, On focusing the surface, and then touching it with a pointed wire some distance from the centre, the intersections of the original and reflected waves will be beautifully depicted upon the screen.

95. Interference of Tidal Waves.-The same thing is true of tidal waves, a remarkable example of which is found in the channel between England and Ireland. The flood-tide, sweeping round from the Atlantic to the north and south of Ireland, meets about a line which usually passes just across the south of the Isle of Man. There the two currents destroy one another, and there is practically none, while the rise and fall of the tide is greatest. But going back from this point to north and south, there are also two points, near Portrush, in Antrim, at the north of the Irish Channel, and near Courtown, in Wexford, at the south, where the falling tide meets the next rising tide; at these points, therefore, there is practically no rise or fall of tide whatever, while the current is at the maximum. The same is true of the vast tidal waves that sweep round the globe. At certain times the sun-wave agrees with the moon-wave, and then we have the greatest tidal motion; at others the sun's wave opposes the moon's wave, and we have the least motion.

96. Single Interferences not Traceable in Light and Sound. But here we must make a very important distinction, the want of which has caused many a student difficulty. In the foregoing cases we could trace the interferences

of single waves, because their motions were large to us, occu pied considerable time, and thus enabled us to trace them most clearly in the grand tidal waves, which are longest of all. The student is at first apt to fancy that, in a similar way, rays from any two points of light must be constantly destroying one another by interference, much as in Fig. 92, supposed to represent the rays from two lighthouses. And to some extent they undoubtedly do so. But they can only thus act on each other at the detached points where the undulations cross; and in the case of light and sound the vibrations are so enormously rapid and numerous that

FIG. 92. Two Lighthouses.

comparatively few extinctions of this kind are not sensibly missed.

But if we can bring a whole wave series to act upon another exactly similar whole wave series, then any effect at one point in any wave of the series is repeated throughout the series, and the effect becomes visible. In the case of sound we can get similar wave series pretty easily by employing exact unisons; and so it will be found, if a tuning-fork be struck and held close to the ear, that on turning it round on the stem there is a position in which the sound is nearly or quite extinguished. This position differs, as it should do, with the key of the fork, but with either an A or a C fork

is when the two prongs are at an angle of nearly 45° with the direction of the ear. If the fork is steadily rotated, the sound will be alternately extinguished and reinforced, according to the phases in which the waves from each prong encounter one another.

A moment's reflection shows us that in the case of light, as a rule, we can only get the exact similarity necessary by employing two beams of light from the same original point of emission, or very nearly so; but if we can bring two such exactly similar series of waves again together, or so close together that the ether-atoms set in motion by each can act upon each other, while the paths of the rays are sufficiently parallel for many successive undulations to come into the same relations, then we ought to get effects which shall be visible to us. There are several methods of effecting this object.

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97. Colours of Thin Films.-The simplest and one of the most striking is reflection from a thin film." If a pencil of light a strikes any thin transparent film at B, we know that a large part is reflected at a similar angle to c. But the rest is refracted to D, where (unless at the angle of total reflection) a portion passes through and is lost to us, while another portion is reflected to E and thence refracted to F. It is evident the ray E F must be precisely similar to the ray B C in the periods of its waves, and also precisely parallel to it; and, if the film be thin enough, it should also be near enough to it to cause interference. As to the phenomena we ought to expect, remembering that every colour has its own wave-length, and reverting to the wave-slide shown in Fig. 71, we see there how the retardation of the central section of that slide by a given distance brings the long waves into contrary phases, while the short waves of half the length, at the same time, exactly coincide. A very little thought shows that with waves of all various lengths, only