166.

Let us next consider the temperature of the radiation in the other media, which lie between the separate refracting or reflecting spherical surfaces. In every one of these media the radiation has a definite temperature, which is given by the last formula when referred to the real or virtual image formed by the radiation in that medium.

The frequency $\nu$ of the monochromatic radiation is, of course, the same in all media; moreover, according to the laws of geometrical optics, the product $n^{2}F\Omega$ is the same for all media. Hence, if, in addition, the total intensity of radiation $I_{\nu }$ remains constant on refraction (or reflection), $T$ also remains constant, or in other words: The temperature of a homocentric pencil is not changed by regular refraction or reflection, unless a loss in energy of radiation occurs. Any weakening, however, of the total intensity $I_{\nu }$ by a subdivision of the radiation, whether into two or into many different directions, as in the case of diffuse reflection, leads to a lowering of the temperature of the pencil. In fact, a certain loss of energy by refraction or reflection does occur, in general, on a refraction or reflection, and hence also a lowering of the temperature takes place. In these cases a fundamental difference appears, depending on whether the radiation is weakened merely by free expansion or by subdivision or absorption. In the first case the temperature remains constant, in the second it decreases. Nevertheless regular refraction and reflection are not irreversible processes; for the refracted and the reflected rays are coherent and the entropy of two coherent rays is not equal to the sum of the entropies of the separate rays. (Compare above, [sect:104.] Sec. 104.) On the other hand, diffraction is an irreversible process. M. Laue, Ann. d. Phys. 31, p. 547, 1910.