REFLECTION OF A SINGLE WAVE

In our virtual experiments with interference and diffraction of the waves on the water surface we used small vibrating balls. These balls excited the waves which consist of periodic circles followed each other. In this case the reflected wave is seen not clear because it interferes with incident wave. It is convenient to explore and visualize the reflection of the waves and the passing them through the semitransparent wall using the wave,  which consists of a single circle propagating from the point source. Such wave can be obtained by one-shot submersion of a needle into the water. However, single wave on the water surface will be accompanied by several "satellite" waves of smaller amplitude. More sharp single wave can be achieved with electrical spark discharge in air. In this case so called shock wave will appear, which consists of a very steep wave crest with a flat and slightly sinuous valley adjoining to its back side. This wave of anomalously high density propagates with higher speed as compared to the normal waves. Because of high density of the air in the crest, shock waves can be photographed as shadow pictures.

Animation shows the single circular wave excited by a point source and reflected partially by semitransparent wall. The other part of this wave is passing through the wall. We see in animation that reflected wave is symmetrical to the passing one relatively to the wall. This can be explained by Huygens principle according to which every element of the wave front generates the secondary waves. The tangency to all these waves will coincide with the wave front in the next moment of time (the waves reflected back are not considered). Both reflected wave and passing one are the tangency to the secondary point sources at the wall. These sources generate the symmetrical waves in both directions. So the passing wave repeats the incident wave with smaller amplitude and reflected wave coincides with the wave excited by a fictitious point source located on the opposite side of the wall symmetrically to the real one. 

Next animation shows the case when the single wave is reflected consequently by two parallel walls. Every reflected wave are symmetrical to the incident one, but of smaller amplitude. For this reason we can consider the reflected wave to be excited by a fictitious point source located on the opposite side of the wall at the same distance as the real one. Herewith the fictitious source for every next reflected wave will be the mirror reflection of the source  (real or fictitious) of the incident wave.