Re: [Phys-l] Sun's image due to reflection by not a pinhole.

[John Denker <jsd@av8n.com>]

On 04/30/2009 06:42 AM, Anthony Lapinski wrote:

> Not sure my (high school) students have ever heard of "convolution,"

Gaudeamus igitur !
  (That's Latin for "party on".)

Think how much easier it is when the students have never heard the
word.  Contrast that with, say, conservation of energy, where the
students arrive knowing the vernacular meaning of energy and the
vernacular meaning of conservation, both of which must be unlearned
before they can learn the physics meanings.

Besides, the word isn't important.  The idea is important.  And 
the idea is simple.

> Seems to be an "advanced" calculus topic/idea, well beyond most
> introductory high school physics courses. 

Absolutely not.

============================

You can demonstrate the whole idea in less time than it takes to
tell about it.

Start with a board with three pinholes in it.  Let the arrangement
of pinholes be non-symmetric enough to be recognizable.  This
board will be called the _mask_ and will serve as the lens in a
slightly peculiar pinhole camera obscura.

Also arrange for a bright scene to serve as the _object_.  Form an
image on a screen in the usual way.

Case 1:  This the intermediate case, where each pinhole produces a
separate subimage that does not overlap with the other subimages.
Each subimage will be a clear representation of the object.

Case 2:  In this case, let the object be very small (but still bright)
so that each subimage becomes small and structureless.  In this case,
the image as a whole is a one-to-one representation of the mask.

Case 3:  This is the opposite extreme from case 2.  In this case, let
the object be large and/or let the spacing between pinholes be small.
Then there will be nearly 100% overlap between the subimages, so that
in effect there is only one image.  It is a single representation of
the object, just slightly blurred.

In all three cases, the image as a whole is the convolution of a function
representing the object with a function representing the mask.  The mask
can be considered the kernel of the convolution.

This thread started by calling attention to the two extreme cases (case 2
and case 3).  I suggest that the intermediate case (case 1) is easier to
understand.  There's nothing tricky about it.  No calculus,  No math of
any kind.  Just look at the three subimages.