These foci share a remarkable link. Imagine that an elliptically shaped pan is filled with water. Drop a pebble at one of the foci. Waves of water will ripple out from the splash and bounce off the walls of the dish, thereby creating a wave pattern that repeatedly doubles back on itself. Waves, of course, can move through many different substances, such as water, or through the air as sound.
Modern physics considers an electron to be both a particle and a wave.
Inside an ellipse resonating with a pattern of rippling waves, the walls of the ellipse act as a lens, refocusing the center of the first ripple pattern at a second point. In effect, the ellipse makes a copy of the first focus at the second focus. But it is an attenuated copy, like the harmonic of a musical note. Eigler wondered if the same effect would play out on an atomic level. This was the mirage.