George Gabriel Stokes (not to neglect the later work of Gustav Kirchhoff) is often given credit for having first enunciated the fundamental principles of spectroscopy.  In 1862, Stokes published formulas for determining the quantities of light remitted and transmitted from "a pile of plates".  He described his work as addressing a "mathematical problem of some interest".  He solved the problem using summations of geometric series, but the results are expressed as continuous functions.  This means that the results can be applied to fractional numbers of plates, though they have the intended meaning only for an integral number.  The results below are presented in a form compatible with discontinuous functions.
Stokes used the term "reflexion", not "remission", specifically referring to what is often called regular or specular reflection.  In regular reflection, the Fresnel equations describe the physics, which includes both reflection and refraction, at the optical boundary of a plate.  A "pile of plates" is still a term of art used to describe a polarizer in which a polarized beam is obtained by tilting a pile of plates at an angle to an unpolarized incident beam.  The area of polarization was specifically what interested Stokes in this mathematical problem.