- #1

There are many diagrams like the following

which demonstrate that if A acts as a point source of wavelets, then we will have constructive interference in the case that ##i=r## as shown, as we can show with a little geometry that the path difference is zero.

However, surely this isn't the only option, since we can let the path difference between the two waves shown equal any multiple of ##\lambda## a consequently obtain many different orders. If we accept Huygens principle and apply it to a smooth reflector, we should obtain reflection across many different angles.

So why is it that only the zeroth order is included in the law of reflection?

Previously, I thought that we could only get the "scattering" required with a reflective diffraction grating, however Huygen's principle seems to imply that the diffraction grating principle is correct even for a smooth plane mirror - is this right?

which demonstrate that if A acts as a point source of wavelets, then we will have constructive interference in the case that ##i=r## as shown, as we can show with a little geometry that the path difference is zero.

However, surely this isn't the only option, since we can let the path difference between the two waves shown equal any multiple of ##\lambda## a consequently obtain many different orders. If we accept Huygens principle and apply it to a smooth reflector, we should obtain reflection across many different angles.

So why is it that only the zeroth order is included in the law of reflection?

Previously, I thought that we could only get the "scattering" required with a reflective diffraction grating, however Huygen's principle seems to imply that the diffraction grating principle is correct even for a smooth plane mirror - is this right?