Engineering a lens

Lining up and curling up are core insights in representing the calculations. Looking for arrangements where all of the contributions line up predicts great brightness. That we can make reliable predictions enables us to engineers situations where the brightness ends up where we want it, such as a lens.

The photons appear to travel more slowly in the glass – they rotate at the same rate (because the colour remains constant) – but there are more rotations in a millimetre of glass than in a millimetre of air. So inserting extra glass effectively inserts more rotations.

Separate the central waypoints so as to insert more glass. This extra glass compensates for the shorter distance. So the contributions from the ends of this new object can line up with the contributions from the centre of the new object. The new object is of course a focusing lens.

It's a different account of the lens, but it is one that uses the same theoretical framework as we have use throughout. You really are showing that the idea of photons can account for a wide range of phenomena and be useful to build things.