The purpose of this lab is to explain the phenomenon that occurs when light (a laser) passes through a tiny grating.

 
 

The grating itself is made up of several uniformly placed slits (distance between slits is equal whether it is above and below or left to right) each slit is of equal size.

GRATING:

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This uniformity of the grating's grove spacing is used as a measure of the quality of the grating. When a laser is aimed at a wall we just see a small dot, when a grating is placed in the path of the laser we see several distant and evenly spaced dots.  The dots are sown at intervals forming a full circle around the grating.  Most of the light from the laser will go straight through the laser forming a high intensity dot where the wavelength has a angle of zero (q = 0.0).  The configuration of the dots show a first order (the single high intensidy dot) a second order (the dots to the left and the right of the high intensity dot).

Next we used a grating with a known pitch (groves per mm - the spacing of the grating) of 600/mm to try to find out the wavelength of a laser.  Aside from the pitch we also needed the angle theta (the angle which the grating diffracts the laser).  To find theta we measured the distances of the first and second order dots (Y1 and Y2) Then we took the average of these two which in this particular case yielded Yavg=64.88cm as well as the distance to the wall from the grating D=1.56m.  With these two values it is easy to find theta (q) by using the following formula:

So q=0.3941, and sinq=0.384

Next to find the wavelength the following system can be used:

Wavelength or l = 0.000641m

Now that we have the wavelength, it can be used to find the unknown pitch of another grating by modifying the equations above.  The Yavg of this grating is 30cm and the distance is 55cm from the grating to the wall.  So q is 0.4788, thus the sin of q is 0.4788.  Using the wavelength (l pertains to the laser not the grating) and the sin of q can be plugged into the wavelength above can find d.  d can be easily turned into the pitch which is 745.8/mm.