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

[Paul Nord <Paul.Nord@valpo.edu>]

Quick reactions to the discussion:

1. If the source has parallel rays, then you have a plane source that fills
the field of view.  The intensity wouldn't drop off at all.  (I'll add a
horrible story of some injuries to a firefighter who was helping with a
controlled burn weather measurement.  They also had some surprising damage
to equipment on a pole that they thought should have been "far enough" from
the fire.)
2. Thinking of the mirror as "scattering" the light is not useful.  You'll
get some light lost through absorption and some scattering.  But the only
interesting rays are those that come from the source to the detector.
These will be 90% of the original light for a typical mirror.  Whether
light is lost to absorption or some other method, the result will be the
same.
3. The 0 to 50 cm distance reported is suspect.  If you're really looking
at the reflection of an object, you need to add the distance from the
object to the mirror.  You couldn't get zero.  If the light source is
another meter away, then the distance is really 1.0 to 1.5 m.
4. I'm surprised that they can collimate the acceptance of the detector
over a few cm with an angle of incidence that's as small as 10º.  That
geometry sounds tricky.
5. The photography reference may be confusing apparent surface brightness.
This does not vary with distance.  This is what allows a photographer to
use a portable light sensor without knowing anything about the placement of
the camera, optics, etc.  You just need to know the light intensity at the
location of the photographic subject.

Paul

On Wed, Dec 8, 2021 at 3:20 PM John Denker via Phys-l <
phys-l@mail.phys-l.org> wrote:

> 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.
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