44. Emissive and Absorbing Power

Following G. KirchhoffG. Kirchhoff, Gesammelte Abhandlungen, 1882, p. 574. we call the quantity $I_{2}$ , i.e., the intensity of the pencil emitted from the second medium into the first, the emissive power $E$ of the second medium, while we call the ratio of $J_{2}$ to $J$ , i.e., that fraction of a pencil incident on the second medium which is absorbed in this medium, the absorbing power $A$ of the second medium. Therefore $E = I_{2} (≦ I), A = \frac{J_{2}}{J} (≦ 1) . \Label [e q n] (47) \upshape (47)$

The quantities $E$ and $A$ depend

(a) on the nature of the two media,
(b) on the temperature, the frequency $ν$ , and the direction and the polarization of the radiation considered,
(c) on the nature of the bounding surface and on the magnitude of the surface element $d σ$ and that of the solid angle $d Ω$ ,
(d) on the geometrical extent and the shape of the total surface of the two media,
(e) on the nature and form of all other bodies of the system.

For a ray may pass from the first into the second medium, be partly transmitted by the latter, and then, after reflection somewhere else, may return to the second medium and may be there entirely absorbed.

With these assumptions, according to equations [eqn:(46)] (46), [eqn:(45)] (45), and [eqn:(43)] (43), Kirchhoff's law holds, $\frac{E}{A} = I = d σ \cos θ d Ω 𝖪_{ν} d ν, \Label [e q n] (48) \upshape (48)$

i.e., the ratio of the emissive power to the absorbing power of any body is independent of the nature of the body. For this ratio is equal to the intensity of the pencil passing through the first medium, which, according to equation [eqn:(27)] (27), does not depend on the second medium at all. The value of this ratio does, however, depend on the nature of the first medium, inasmuch as, according to [eqn:(42)] (42), it is not the quantity $𝖪_{ν}$ but the quantity $q^{2} 𝖪_{ν}$ , which is a universal function of the temperature and frequency. The proof of this law given by G. Kirchhoff l. c. was later greatly simplified by E. Pringsheim.E. Pringsheim, Verhandlungen der Deutschen Physikalischen Gesellschaft, 3, p. 81, 1901.