Re: [Phys-L] Lower limit for a slit width?

[John Denker <jsd@av8n.com>]

On 05/15/2014 05:56 AM, Paul Lulai wrote:
> Quote: " we do not see much of a diffraction pattern with a very
> narrow single slit, because there are no minima on the screen in this
> case"
>
> Question: Is this simply because, using Hyugen's Principle, we've
> approached such a narrow opening that we don't have multiple point
> sources traveling through the opening to interfere with each other?

I wouldn't have said it that way.  No matter how small the slit,
you can always put a gazillion Huygens-style point sources in 
the slit.

It is simpler and more accurate to say something like this:  For
a small slit, no matter where the receiver sits, there is not much
/phase difference/ between the various point sources.

To get an accurate reconstruction, there is a minimum number of
sources you need, but no maximum.  You need /at least/ many per
wavelength, but beyond that the more the merrier.

Between ourselves we can say that we are doing an integral.  We
approximate the integral by a sum, and then pass to the limit 
where it is an infinite sum of infinitesimal terms.

  In high-school language, one must employ the usual euphemisms
  and circumlocutions:  The area under the curve is approximated
  by a sum of rectangular strips.  As the strips get thinner and 
  more numerous, the approximation gets better and better.......

When the slit is small, the curve in question is very nearly a
triangle, so you'll get the right answer for the area no matter
what you do.  The /minimum/ number of strips is small in this case,
but increasing the number of strips never hurts.

Note the contrast:
  -- In general, a large number of strips is required.
  -- In the special case of a small slit, a large number of strips 
   is not required, but it never hurts.

=========================
x
x  Usual disclaimer:  The Huygens construction is a useful heuristic,
x  but it cannot possibly be correct in general.
x    http://www.av8n.com/physics/white.htm#sec-huygens