Bouncing off a surface

See how the reasoning about a photon works out in examples to understand the idea of a photon.

Underneath the rules

Placing a mirror in between source and detector for a photon to explore does suggest some waypoints to define paths. The special paths in this space are those with waypoints on the mirror. So explore contributions from triplets of these paths.

Arrows from triplets near the middle of the mirror line up. Arrows from triplets near the end of the mirror curl up. More precisely, where the inbound path segments hit the mirror at about the same angle as the outbound path segments leave the mirror, the arrows line up. This lining up predicts a high chance of detecting each photon. So lots of photons.

Where the inbound angle = outbound angle the arrows from these paths contribute a lot, elsewhere they don't. So elsewhere can be more or less ignored. Mirrors reflect so that inbound angle = outbound angle: you could cover or remove most of the rest of the mirror and it would make almost no difference to the brightness for this arrangement of source, mirror and detector. For other arrangements, such covering of the mirror would make a difference.

You might see a law written for mirrors: angle of incidence = angle of reflection. That's what you've just predicted, but now you know why there is such a rule. It's not just a law—there is a reason for the law.