CHAPTER XVI.

PRINCIPLE OF INTERFERENCE.

CONSEQUENCES OF

FRESNEL'S EXPERIMENT.

92. WHAT happens if two wave-systems meet on the same fluid surface?

If from a vessel held above a flat pan containing mercury two fine streams of mercury are allowed to fall, each produces around the point where it strikes the surface of the fluid a circular system of waves. As the two wave-systems decussate they divide the surface into a regular network of small elevations and depressions, a representation of which is attempted in fig. 136.

If the light of the sun or of the electric lamp be allowed to fall upon the surface of the mercury, the reflexion upon a screen will also furnish a representation of this delicate phenomenon.

It is not difficult to explain the effects observed. At all points where two wave crests meet, the surface of the fluid, if the two waves are equal, rises to twice the height, and where two depressions meet it sinks to double the depth. At those points on the contrary where a wave crest is cut by a sinus, the upheaving and depressing forces are in equilibrium, and the fluid remains at rest at its original level.

In a fluid set in motion by two or more equal or unequal wave systems, every particle, speaking gene

rally, undergoes a change of place, which is the sum of all the movements impressed upon it by the several systems of waves at the same moment. Of course, by the

wordsum' the so-called algebraic sum is meant, that is to say, the elevations are regarded as positive, the depressions as negative values.

In other words, it may be said that every wave system superimposes itself upon, or adds itself to, a surface already moved by waves, as it would do were it acting alone on the surface at rest. Every wave system forms itself unhindered by those already present, and

spreads after it has crossed these upon the still quiescent surface of the water as if it had suffered no interruption. We see, for example, the slight wave rings excited by the falling rain drops form on the larger waves raised by a steamboat just as well as upon the sea at rest. It may be observed again that these waves, when they traverse an area rippled by the breeze, take the small waves on their back, and having passed beyond this region leave these last behind with their original form unaltered.

The important law just laid down, to which the processes taking place in the co-operation or interference of two or several systems of waves are subjected, is termed the principle of interference.'

93. Returning to the simplest case of interference of two equal systems of waves represented in fig. 136, it appears that an explanation can be given of the movement occurring at each point of the surface of the fluid, if, instead of the waves themselves, the wave rays are kept in view. If we consider, for example, the points 5....5' lying along the wall of the vessel, the two rays which may be conceived as drawn from the two middle points of the exciting cause of them to the central point O are equal to each other in length; the oscillating movements which proceed simultaneously from each of these centres meet therefore in the point O under equal conditions and produce the greatest possible effect. In the laterally situated point 1, on the other hand, two rays meet which are about half a wave different; the forces which they exert upon the point are therefore equal and opposite; the point consequently remains at rest. The same occurs at 3 and 5, where the difference between the rays cor

responds respectively to 3 half and 5 half wave-lengths. At the points 2 and 4, on the contrary, where the rays respectively differ one or two entire wave-lengths, and thus meet under equal conditions of oscillation, the liveliest movement takes place. The intervening points are maintained in less active movement by pairs of rays of all possible degrees of accordance and opposition.

The points 1, 3, 5,.... 1', 3', 5'.... thus remain at rest under the action of the two systems of waves. That which in waves of fluid is rest, is in waves of sound silence, and in waves of light darkness.

It is scarcely necessary to expressly mention here that this affords a complete explanation of Fresnel's mirror experiment, and that fig. 136 is a sketch of it. If, for example, the two points of light produced by the mirrors M and N (fig. 134) be regarded as centres of origin of light waves, and the wall 5′.... 5 as the screen for receiving them; and if it be further considered that the waves of light expand, not only circularly in one plane, but like a sphere into the surrounding æther, it will be understood that, in consequence of the interference of the two systems of waves, vertical dark lines must appear at the points 1, 3, 5. . . . 1', 3′, 5', and bright striæ at the points 2, 4. . . . 2′, 4'.

But why, it may perhaps be now asked, should the two points of light be employed in a roundabout way after their reflexion in the two mirrors? Would it not be simpler to put aside the mirrors, and use, instead of the images M and N thrown by them, two luminous points like the points of a glowing platinum wire ? The answer to this question is obtained from the fact that the two wave systems, in order that they should pro

duce dark lines in the given points of the screen, must proceed simultaneously, and in a precisely similar manner, from the two luminous points. But we are unable so to conduct the process of light production in two luminous bodies, or even in two points of a single luminous body, as to make the undulating movement proceeding from one exactly accordant with that of the other; in each of them, after a short period, interruption of the movement, augmentation and diminution of the liveliness of the flame, and other disturbances take place, which do not occur coincidently in the other. Hence the lines of interference are only partially formed, and in rapidly changing parts of the screen giving to the eye the impression that it is equally and uniformly illuminated. Two independent and separate luminous points therefore, on account of the inequality of these wave systems, present no interference lines. The equality required for this purpose is obtained with the greatest certainty by making the two wave systems spring by mirrors or by any other appropriate means from the same source. The irregularities to which the process of light production is subjected, whatever may be the light used, take place concordantly and simultaneously in both systems of waves, and consequently exercise no influence upon the accordance and opposition of the rays which are now conditioned only by their difference of path.

94. Fresnel's experiment may now be repeated, with this difference, that a red and a blue glass are placed alternately before the aperture of the Heliostat. It is then seen that with blue light the lines are closer together than in the red, that is to say, the corresponding series of dark lines are in the former case nearer to