change in the angle of refraction for a small change in the angle of incidence near the critical angle, and cited this as the cause of the rapid increase in brightness of the reflected ray as the refracted ray approaches the tangent to the interface. Huygens' insight is confirmed by modern theory: in Eqs.() and () above, there is nothing to say that the reflection coefficients increase exceptionally steeply as θt approaches 90°, except that, according to Snell's law, θt itself is an increasingly steep function of θ. Huygens offered an explanation of TIR within the same framework as his explanations of the laws of rectilinear propagation, reflection, ordinary refraction, and even the extraordinary refraction of "Iceland crystal" (calcite). That framework rested on two premises: first, every point crossed by a propagating wavefront becomes a source of secondary wavefronts ("Huygens' principle"); and second, given an initial wavefront, any subsequent position of the wavefront is the envelope (common tangent surface) of all the secondary wavefronts emitted from the initial position. All cases of reflection or refraction by a surface are then explained simply by considering the secondary waves emitted from that surface. In the case of refraction from a medium of slower propagation to a medium of faster propagation, there is a certain obliquity of incidence beyond which it is impossible for the secondary wavefronts to form a common tangent in the second medium; this is what we now call the critical angle. As the incident wavefront approaches this critical obliquity, the refracted wavefront becomes concentrated against the refracting surface, augmenting the secondary waves that produce the reflection back into the first medium. Huygens' system even accommodated partial reflection at the interface between different media, albeit vaguely, by analogy with the laws of collisions between particles of different sizes. However, as long as the wave theory continued to assume longitudinal waves, it had no chance of accommodating polarization, hence no chance of explaining the polarization-dependence of extraordinary refraction, or of the partial reflection coefficient, or of the phase shift in TIR. Isaac Newton rejected the wave explanation of rectilinear propagation, believing that if light consisted of waves, it would "bend and spread every way" into the shadows. His corpuscular theory of light explained rectilinear propagation more simply, and it accounted for the ordinary laws of refraction and reflection, including TIR, on the hypothesis that the corpuscles of light were subject to