Reflection and refraction of light from a moving block of glass

Abstract

For a block of glass moving with speed $\ensuremath{\beta}c$ we present calculations which give the changes in the laws of reflection and refraction of light from the laws which hold when $\ensuremath{\beta}=0$. In particular we show (i) that changes in the critical internal reflection condition, although formally of order $\ensuremath{\beta}$, are obtainable by measuring the refraction angle to $O(\ensuremath{\beta})$; and (ii) that the reflection coefficient depends not only on the polarization plane of the incident light but also on whether the plane of incidence does, or does not, include the direction of motion of the glass block. For instance, for light incident in a plane perpendicular to the direction of motion there is no Brewster angle for either plane of polarization, while for light incident in a plane containing the direction of motion at least one (and sometimes both) planes of polarization possess a Brewster angle. We have done these calculations in order to demonstrate that the shearing of one medium relative to another can have profound effects on the reflection and refraction of light. A major point here is that even when it might appear a priori that $O({\ensuremath{\beta}}^{2})$ phenomena are unobservable in the laboratory, the present calculations show that this is not always so.