# Does ordinary refraction exert a couple on the refracting medium?

Refraction gives rise to a momentum change orthogonal to the propagation direction. This must result in an equal and opposite change to the medium at the boundary. Entry and exit cancel, and the medium experiences no net force. The problem is that the forces on the medium do not in general line up, so we have a pair of forces, opposite but parallel - i.e. a couple. Can we therefore conclude that refraction imparts a couple to a refracting medium? (and if so, has the experiment been done?).

Assuming this couple indeed exists: Since the light loses no energy and loses no momentum, and yet the medium appears to have gained rotational energy and momentum, where does the medium's extra angular momentum come from?

• Don't know the answer right off, but you must include the reflected beam in your consideration. Commented Apr 10, 2014 at 14:59

## 1 Answer

As @dmckee points out, you have to take into account the reflected wave. And also the refracted wave. When you add them up, there is a transfer of momentum perpendicular to the $surface$. No couple.

Another way to arrive at this conclusion is to notice that an infinite surface (the usual model) has perfect translation invariance. Momentum in that direction, parallel to the surface, must be conserved. There are no surface features against which a parallel force can be applied.

• I'm assuming zero reflectivity, but vanishingly small will do. In any case, I don't see how this solves the problem. There is a displacement perpendicular to the surface normal along the bottom surface between entry and exit points, and so the two forces are equal, opposite and parallel, not colinear. How is that not a couple? Commented Apr 10, 2014 at 18:12