Re: [Phys-L] Inverse Square for reflected light

[John Denker <jsd@av8n.com>]

On 12/8/21 1:38 PM, Scott Goelzer wrote:

> Some dubious sites and forums that all boil down to 'if the rays
> leave parallel then inverse square doesn’t work'.

It depends on what you use for the abscissa!

1) Quasi-simple constructive suggestion: Use the method of images.

Specifically: A small source plus a condenser (collimator)
is isomorphic to an N-times bigger source N-times farther
away. Similar words apply to the detector.

N could be quite large. The famous thin-lens formula applies.
  http://labman.phys.utk.edu/phys222core/modules/m8/thin_lenses.html

When you include the factors of N, the effective path length
is a lot larger than the apparent size of the apparatus as it
sits on the tabletop. So moving stuff a moderate distance is
only a tiny percentage change in the effective length.

As the final step in the argument: To first order everything
is linear.

2) Even simpler suggestion: Get rid of the collimators.

That will be a loss in terms of brightness, but it will be
a huge gain in terms of simplicity.

3) Even better: Teach the students to change one thing at
a time when the going gets tough. (That is not good advice
in general, if you understand what's going on, but it is
a useful last-ditch fallback.)

Specifically:
  a) Try it with no mirror *and* no collimators.
  b) Try it with collimators but no mirror.
  c) Try it with mirror but no collimators.
  d) *Then* try it with both.