Another very interesting case of reflection is that occurring inside an elliptical mirror. When light diverges from one of the two foci of such a mirror, all the rays are brought accurately to the other focus. If rays of light come to a focus from all directions, it is evident that the wave surface must be a sphere, which, instead of expanding, is collapsing. This is very beautifully shown in the photographs. The sound wave starts in one focus and the reflected wave, of spherical form also, shrinks to a point at the other focus. (See [Fig. 5].)
Fig. 3. A Wave Reflected from a Portion of a Sphere.
Fig. 4. A Wave from a Cylindrical Mirror.
In the next series the wave starts outside of the field of the lens, and enters a hemispherical mirror. We know that a concave mirror has the power of bringing light to a focus at a point situated half-way between the surface of the mirror and its center of curvature. If the light comes from a very distant point, and the mirror is parabolic in form, the rays are brought accurately to a focus; which means that the reflected wave is a converging sphere,—a condition the opposite of that in which spherical waves start in the focus of such a mirror. If, however, the mirror is spherical, only a portion of the light comes to a focus. On examining the pictures we see that the reflected wave has a form resembling a volcanic cone with a bowl-shaped crater. See the third and fourth pictures of the series. The bowl of the crater shrinks to a point half-way between the surface of the mirror and its center of curvature, and represents that portion of the light which comes to a focus, while the sides of the cone run in under the collapsing bowl, and eventually cross. (No. 6 of the series.) From now on the portion which has come to a focus diverges, uniting with the sides of the cone, the whole passing out of the mirror in the form of a horseshoe.
Fig. 5. A Wave from an Elliptical Mirror.
Fig. 6. A Wave Starting Outside the Field of the Lens.