Re: Diffraction

[brian whatcott <inet@INTELLISYS.NET>]

At 21:31 9/24/99 -0500, Cliff wrote:

> Can't the single slit be considered in the same way as two slits if one
> considers each half of the slit separately?
>
> Cliff Parker

You notice that I provided a vivid (if unwitting) illustration of
the problem of using a plausible discussion of two zones in a slit.

 You need to pick the CENTERS of the two zones to represent the phase
of each ray. (This can be thought of as an ad hoc just-so story,
if you are at all rigorous in your need for proofs, but is very much
better than no explanation.)

You can readily see that the phase of an oblique ray in fact varies
across the width of such a large ray. To make this approach more
rigorous, it can be developed by dividing the slit into smaller
and smaller strips of width delta x, and considering the phase
shift between adjacent strips.

Reckoning from one edge, the phase of one of these strips is
evidently

(2pi/lambda)x sin theta

  theta, ray's angular difference from normal.

   x is distance from slit edge.

  lambda, the monochromatic light's wavelength.

  2pi, the amount of phase change per wavelength.

The total amplitude of the beam at some angle, for a
particular instant is the summation of the contributions
from all these little strips with phase taken into consideration.

 This leads without undue complication, to an expression
linking the amplitude function of slit width, with the
 (sin alpha)/alpha factor to express variation with angle:
alpha being pi times the slit width times sin theta,
 the diffraction angle, all divided by wavelength.

But after peeking at Cliff's follow-on note this morning, I see
that he has this respectable approach already in mind....

(this development follows Starling & Woodall, 'Physics')


brian whatcott <inet@intellisys.net>
Altus OK