On Fri, Mar 30, 2012 at 4:54 PM, John Griessen <john@industromatic.com> wrote:
> On 03/30/2012 11:19 AM, Nathan McCorkle wrote:
>>
>> does the smaller focal length allow less
>> overall divergence to occur? As in, if the focal length were longer,
>> the rays would have a longer time to diverge?
>
>
> Yes, but you think of the focal length as negligibly short.
Why? Its not negligibly short, the distance is measurable and matters.
>
> You take care of whatever divergence has happened by unmagnifying it
> to a small spot with a short focal length lens system.
>
I meant divergence after the final lens, the length between the lens
and the focus, not divergence before the lens (as those rays would
merely pass the lens)
> For the original question, You choose a fatter beam to get the near in
> effects where divergence varies less, see
> http://en.wikipedia.org/wiki/File:GaussianBeamWaist.svg
>
> You use the fat beam in the part of the sketch called Zr
>
I only posed 1 question. Zr isn't the fat part, its the thinnest part
of the beam, that diagram looks like rays coming to a focus, from left
to right, which pass through the focus.
> "where the origin of the z-axis is defined, without loss of generality, to
> coincide with the beam waist, and where
>
> http://upload.wikimedia.org/wikipedia/en/math/e/5/8/e58a707d1ccf4ed6cefac660633038a8.png
>
> is called the Rayleigh range."
> http://en.wikipedia.org/wiki/Gaussian_beam
>
> Then, for some light source, it might make sense to expand it to a
> collimated beam of a certain width,
> then focus down to a spot. The advantage would be that over the different
> distances,
> (as in the distances a laser cutter mirror moves to),
> the spot size would be changing less because it is in the Rayleigh range.
>
None of this really answers the 'why', which is really the main part
of my question. Describing the behavior isn't what I was looking for,
I was looking for the root/cause of the behavior.
That said, if I'm correct about
(http://en.wikipedia.org/wiki/File:GaussianBeamWaist.svg) being rays
coming to a focus and going through a focus... it seems that the
reason a wider beam with a shorter focal length produces a smaller
spot size is due to less interference as the rays converge, because
they start out in low concentration (beam gets expanded), then rapidly
head toward the focus. In the other case the rays are more
concentrate, and have a longer focus so more time to 'rub shoulders'
"
Because of this property, a Gaussian laser beam that is focused to a
small spot spreads out rapidly as it propagates away from that spot.
To keep a laser beam very well collimated, it must have a large
diameter. This relationship between beam width and divergence is due
to diffraction.
"
"
Richard Feynman[4] said that
"no-one has ever been able to define the difference between
interference and diffraction satisfactorily. It is just a question of
usage, and there is no specific, important physical difference between
them."
He suggested that when there are only a few sources, say two, we call
it interference, as in Young's slits, but with a large number of
sources, the process be labelled diffraction.
"
--
Nathan McCorkle
Rochester Institute of Technology
College of Science, Biotechnology/Bioinformatics
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