| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
Chuck wrote about the shape of the "spot of light." You are writing
about the "image of the sun."
On Apr 30, 2009, at 9:42 AM, Anthony Lapinski wrote:
I've always wondered about this solar image thing. Using a rectangular
mirror, the image of the sun "nearby" (few meters away) is
rectangular,
but "far away" (over 15 m) is circular. I thought it had something
to do
with the fact that a mirror has an infinite focal length.
Not sure my (high school) students have ever heard of
"convolution," and
I myself am unfamiliar with the term.
Is there another ("basic") explanation to use when trying to explain
this
optical phenomenon to students?
Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
writes:
On 04/30/2009 03:34 AM, chuck britton wrote:
I had students outside on a sunny day with round and/or rectangular
mirrors reflecting sunlight onto the brick wall.
Some wondered why square mirrors made a round spot of light.
Some didn't care (of coarse).
If the 'screen' is CLOSE to the mirror - the 'spot' of light is
square.
OK.
Is this 'correctly' viewed as near-field and far-field domains??
I wouldn't have said that.
It seems much simpler to describe it in terms of a convolution.
If this were a spectrometer, we would say that the "intrinsic
lineshape" (round) is convolved with the "instrumental lineshape"
(square). The concept of convolution is so very broadly useful
that it is worth spending some time on.
There are lots of pedagogical models you can use to help get the
students up to speed. For example, compare a square array of
small round things to a round array of small square things.
You can also collect additional partially-independent data by
using other instrumental shapes. For example, use tape to put
a "black belt" on some of the square mirrors:
M M k k M M
M M k k M M
M M k k M M
M M k k M M
M M k k M M
where "M" stands for mirror and "k" stands for black. The idea
is to emphasize the difference between the intrinsic shape and
the instrumental shape.
Also be sure to do the intermediate case, not just the asymptotic
near case and the asymptotic far case.
In a non-calculus course you can define convolution without
mentioning integrals, but if any of the students have heard of
integrals you should make that connection.
If they've done any AC circuits you should mention that the
input/output relationship of a simple RC circuit is a convolution.
Another simple, familiar example: the potential due to given
distribution
of charges is a convolution. Some guy named Green had something to
say
about this, several decades before Maxwell wrote down the Maxwell
equations.
And the importance of Green functions continues to this day, with
innumerable applications from quantum field theory to civil
engineering.
I get multiple hits from
http://www.google.com/search?q=%22green+function%22+site%3Anobelprize.org
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
- - - - - - - - - - - - - -
Ludwik Kowalski, a retired physics teacher and an amateur journalist.
Updated links to publications and reviews are at:
http://csam.montclair.edu/~kowalski/cf/ http://csam.montclair.edu/~kowalski/my_opeds.html
http://csam.montclair.edu/~kowalski/revcom.html
Also an ESSAY ON ECONOMICS at: http://csam.montclair.edu/~kowalski/economy/essay9.html
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l