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.) [Illustration: FIG. 3. A WAVE REFLECTED FROM A PORTION OF A SPHERE.] [Illustration: 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. [Illustration: FIG. 5. A WAVE FROM AN ELLIPTICAL MIRROR.] [Illustration: FIG. 6. A WAVE STARTING OUTSIDE THE FIELD OF THE LENS.] [Illustration: FIG. 7. A CASE OF REFRACTION.] We will now consider a case of refraction, and show the slower velocity of the sound wave in carbonic acid. A narrow glass tank, covered with an exceedingly thin film of collodion, was filled with the heavy gas and placed under the brass balls. When the sound wave strikes the collodion surface, it breaks up into two components, one reflected back into the air, the other transmitted down through the carbonic acid. An examination of the series shows that the reflected wave in air has moved farther from the collodion film than the transmitted wave, which, as a matter of fact, has been flattened out into a hyperboloid. Exactly the same thing happens when light strikes a block of glass. We have rays reflected from the surface, and rays transmitted through the block, the waves which give rise to the latter moving slower than the ones in air.