Scattering, Light, Particles, Waves, and Structure 
               What do they have in common? 
  Prof. Julia Thompson, University of Pittsburgh and SIUE 


I. Scattering:

  Baseballs scatter from bats. Billiard balls scatter. Sonar scatters
  from boats. Radar scatters from planes. In ultrasound, sound scatters
  from organs in your body.  Light scatters from clouds to make sunsets
  and water droplets to make rainbows. And scattering has been responsible
  for understanding the structure of atoms, molecules, nuclei, 
  and nucleons, even finding the "quark" substructure of neutrons and protons.

  Scattering is a theme which runs through much of physics. And not
  just straight-line "particle" scattering.   When the thing being
  scattered is close in "wavelength" to the thing being scattered from, we have
  to think of the thing being scattered as a wave.  Even you can be considered
  a wave... but your "wavelength" is so small that for practical purposes
  you are always considered a "particle" or "projectile" (as you have
  already noticed).


II. Light, waves, and scattering

  But in some cases wave motion is important.  Today we are going to
  observe light scattering from "apertures". (An "aperture" is just
  a hole of some certain size or shape).  Some "apertures" we will 
  use today are  diffraction
  gratings, a hair of a colleague, and finally an "unknown".  Light can be
  treated as either a
  straight line "particle" or as a wave. In cases where it is considered
  as a "wave", when it scatters, it does not scatter uniformly, but
  "bunches" up in some places, but nearly disappears in others. If you
   have already studied waves, you
   will understand this bunching and disappearing  as "constructive" and
   "destructive" interference
   of the waves from different parts of the "aperture".  
  If you have not studied waves, it will seem very odd to you, but we will
  see that it really happens, and then when (or if?) you study waves later
  you will (I hope!) remember that you really saw it happen.


  The formula which describes light scattering will be somewhat
different for different kinds of apertures but is always something
like: 

  sin(theta)  ~ n*lambda/d

where:
lambda is the "wavelength" of the light;
  and d is the size of the object  (or "aperture") being scattered from.
  For some apertures theta is the angle of bending from straight ahead at
which
  we see maxima, or the light "bunched up"; for others theta is 
the angle of bending at which we see minima, or the light nearly 
disappearing. But in all cases the light scattering pattern 
(or "diffraction pattern") spreads out more for smaller size apertures,
and spreads out more for larger light wavelengths.
  n is some integer (the bunching  happens at more than one
  place: n can be 0,1,2,..).

 III. sin( theta) ~ n*lambda/d How to measure?

  We will use some lasers, with wavelength about 620 nm, some apertures,
  and a meter stick to observe the wave scattering of light.
  We will put the aperture close to the laser, and measure some feature
if the light scattering  (or "diffraction") pattern on a
screen.  We will  measure either the "maxima"
  (places where the light is bunched up) or "minima" (places
where there is almost no light).
Put the screen some convenient distance, about a meter, away from the
  aperture, in order to give the bunched pattern space to spread out, so
  that we can measure it. From the distance to the screen (L), and the
position of the maxima (max) [or in some cases the minima (min)], we can
measure tan(theta) = max/L. 
If the angle is less than 20 degrees, tan(theta) ~ sin(theta).

"Apertures" to test:


A.  A "diffraction grating".  This is a small sheet of clear material
(plastic in our case, glass or quartz for those used in research), with 
many small lines or grooves made in the plastic, at very small spacings.
Check the nominal spacing of the grating lines (from information written
on the
grating) and use the grating spacing  to find the wavelength of your
laser. Shine the laser pointer on the diffraction grating, and use
sin(theta)  =  max/L.

B.  Next  substitute a hair from
  one of your partners and find out how thick it is, by using the
  same idea. Attach the hair to a piece of paper or cardboard
to hold it in place, and shine the laser on it. [For the
hair, the formula is slightly different: use
tan(theta) = min/L, where min is 
the distance between the straight ahead and  "minima" or dark spots in the
light scattering pattern.]
Are the hairs of your different colleagues the same?

C. For the two apertures above, look to see how the light scattering
pattern changes as the aperture is rotated (still keeping it in the plane
perpendicular to the laser ray).

D.  Finally, try the "rose colored glasses" which come with 
your kit.  What pattern do you see?  From the pattern can you 
guess something about the structure of the rose colored glasses?


 Look at a plain light through the glasses. Since different
wavelengths (lambda) are associated with different colors and  bend
differently 
(have different theta), can you say anything about why it is 
that you see a spectrum of light when you look through the glasses?


IV. How does this relate to elementary particles and my research?
  This same idea of wave scattering can be used for elementary particles,
  and one of the ideas in my field of research is to find what the smallest
  pieces of matter are and what their structure is.  You may have heard of
  "quarks"... which come in different "flavors"... up, down, strange, charmed,
  top (or truth) and bottom (or beauty).  These were all found in some
  variation of scattering.