We do not need, however, elaborate apparatus to see these effects when we know what to look for.
A stone thrown into a lake will create a ripple or wave-train, which moves outwards at the rate of a few feet a second. If it should happen that the pond or lake has an immersed wall as part of its boundary, this may form an effective reflecting surface, and as each circular wave meets the wall it will be turned back upon itself as a reflected wave. At the edge of an absolutely calm sea, at low tide, the author once observed little parallel plane waves advancing obliquely to the coast; the edge of the water was by chance just against a rather steep ledge of hard sand, and each wavelet, as it met this reflecting surface, was turned back and reflected at an angle of reflection equal to that of incidence.
It is well to notice that a plane wave, or one in which the wave front or line is a straight line, may be considered as made up out of a number of circular waves diverging from points arranged closely together along a straight line. Thus, if we suppose that a, b, c, d, etc. ([see Fig. 26]), are source-points, or origins, of independent sets of circular waves, represented by the firm semicircular lines, if they send out simultaneous waves equal in all directions, the effect will be nearly equivalent to a plane wave, represented by the straight thick black line, provided that the source-points are very numerous and close together.
Supposing, then, we have a boundary against which this plane wave impinges obliquely, it will be reflected and its subsequent course will be exactly as if it had proceeded from a series of closely adjacent source-points, a′, b′, c′, d′, etc., lying behind the boundary, each of which is the image of the corresponding real source-points, and lies as far behind the boundary as the real point lies in front of it.
Fig. 26.
An immediate consequence of this is that the plane reflected wave-front makes the same angle with the plane reflecting surface as does the incident or arriving wave, and we thus establish the law, so familiar in optics, that the angle of incidence is equal to the angle of reflection when a plane wave meets a plane reflecting surface.
At the seaside, when the tide is low and the sea calm or ruffled only by wavelets due to a slight wind, one may often notice trains of small waves, which are reflected at sharp edges of sand, or refracted on passing into sudden shallows, or interfering after passing round the two sides of a rock. A careful observer can in this school of Nature instruct himself in all the laws of wave-motion, and gather a fund of knowledge on this subject during an hour’s dalliance at low tide on some sandy coast, or in the quiet study of seaside pools, the surface of which is corrugated with trains of ripples by the breeze.
CHAPTER II.
WAVES AND RIPPLES MADE BY SHIPS.