The first of these two relations, which states that the coefficient of reflection of the bounding surface is the same on both sides, is a special case of a general law of reciprocity first stated by Helmholtz.
H. v. Helmholtz, Handbuch d. physiologischen Optik 1. Lieferung, Leipzig, Leop. Voss, 1856, p. 169. See also Helmholtz, Vorlesungen über die Theorie der Wärme herausgegeben von F. Richarz, Leipzig, J. A. Barth, 1903, p. 161.
The restrictions of the law of reciprocity made there do not bear on our problems, since we are concerned with temperature radiation only ([sect:7.] Sec. 7).
According to this law the loss of intensity which a ray of definite color and polarization suffers on its way through any media by reflection, refraction, absorption, and scattering is exactly equal to the loss suffered by a ray of the same intensity, color, and polarization pursuing an exactly opposite path.
An immediate consequence of this law is that the radiation striking the bounding surface of any two media is always transmitted as well as reflected equally on both sides, for every color, direction, and polarization.