You are getting close.
:-)
Diffraction is not the correct answer, although diffraction does cause the spot to be larger
than it would otherwise be.
Any beam of light has a divergence -- it spreads out as you get farther away.
There is no magic that makes the divergence zero until some distance.
The angle between parallel and the outside of the beam is called the divergence angle.
There is a fundamental law of of optics called the optical invariant: The product of the image
size and the ray angle is a constant.
If the beam has a radius R, and a divergence angle A, and we focus it with a lens that has a
focal length F, then the cone of light will have an angle R/F, and the spot size at the vertex of
that angle will be A times F.
The shorter the focal length, the smaller the spot.
This is how magnifying glasses magnify.
The larger the diameter of the lens (for a given focal length) the smaller the spot.
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Get a free science project every week! "http://scitoys.com/newsletter.html"2012/3/30 John Griessen <john@industromatic.com>
On 03/29/2012 10:25 PM, Nathan McCorkle wrote:Could be due to the way a coherent beam goes a certain distance with no
I've read some equations and searched google, but I'm still not
understanding WHY expanding the beam and shortening the focal length
allows light to be focused into a smaller spot.
measurable spreading out, and then does spread out. As though coherence
causes some interaction of the particles/waves that
are shoulder to shoulder "so to speak".
Gaussian beam defines it. from http://en.wikipedia.org/wiki/Gaussian_beam
"Gaussian beam model is valid only for beams with waists larger than about 2λ/π."
They mention "radius of curvature of the wavefronts". That could be as close to
a why as I've found. I.e. -- if a wavefront is not perfectly flat in a plane,
how could it stay the same as it propagates? The main theories we use all assume
"no action at a distance", (or knowledge at a a distance either), so a part
of a curved wavefront not in line with the beam axis is going to wander off
in a different direction.
So, apart from "why a Gaussian beam is the best you can do", taking an imperfect point source
of coherent light and expanding the beam **while getting the path lengths through the lens system
to create a planar wavefront** gets you the best collimation. Then you could collimate it down
to get a beam width you wanted.
For the practical laser focusing in a CO2 laser, the light is never collimated to a planar
or even perfect gaussian beam -- it just takes advantage of the lower divergence in the
waist zone, the Rayleigh range zR by having the waist width be big--> the distance it rules the
system divergence is greater. If you get that distance to be same or more than your operating distances
you've optimized it. Next to use it as a small spot, focus with a short focal length lens.
The CO2 lasers start with a large width of tube so they don't even have the expense of
the expanding lens system -- that width gets set by the end mirrors.
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