It is necessary to explain a little more in detail how it comes to pass that the wave-line is thus bent. Imagine a row of soldiers, _ab_, marching over smooth grass, but going towards a very rough field, the line of separation SS between the smooth and the rough field being oblique to the line of the soldiers (see Fig. 25). Furthermore, suppose the soldiers can march 4 miles an hour over the smooth grass, but only 3 miles an hour over the rough field. Then let the man on the extreme left of the line be the first to step over the boundary. Immediately he passes into a region where his speed of marching is diminished, but his comrade on the extreme right of the row is still going easily on smooth grass. It is accordingly clear that the direction of the line of soldiers will be swung round because, whilst the soldier on the extreme left marches, say, 300 feet, the one on the extreme right will have gone 400 feet forward; and hence by the time all the men have stepped over the boundary, the row of soldiers will no longer be going in the same direction as before—it will have become bent, or refracted. This same action takes place with waves. If a wave meets obliquely a boundary separating two regions, in one of which it moves slower than in the other, then, for the same reason that the direction of the row of soldiers in the above illustration is bent by reason of the retardation of velocity experienced by each man in turn as he steps over the dividing line, so the wave-line or wave-front is bent by passing from a place where it moves quickly to a place where it moves more slowly. The ratio of the velocities or speeds of the wave in the two regions is called the _index of refraction_. We can, by arranging suitably curved reflecting surfaces or properly shaped shallow places in a tank of water, illustrate all the facts connected with the change in wave-fronts produced by reflection and refraction. We can generate circular waves or ripples diverging from a point, and convert them, by reflection from a _parabolic_ reflector, into plane waves; and again, by means of refraction at a curved or lens-shaped shallow, converge these waves to a focus. Interesting experiments of this kind have been made by means of capillary ripples on a mercury surface by Mr. J. H. Vincent, and he has photographed the ripples so formed, and given examples of their reflection and refraction, which are well worth study.[12] We do not need, however, elaborate apparatus to see these effects when we know what to look for.