Diffraction- 1 Slit and 2 Slit
          by Kyla Marie Frohlich

Objectives:
   There were four main objectives in this laboratory.  The first was to qualitatively measure the diffraction phenomena and the second was to measure the laser wavelength from a 2-slit diffraction pattern.  The third objective was to observe the 1-slit diffraction pattern and lastly to compare the observed 1-slit pattern with a mathmatical model.

Introduction:
    In this lab, laser light was shown through several diffrent kinds of slits.    Laser light is very intense, narrow, straight, and monochromatic.  The type laser that was used in this lab was a He-Ne laser.  This type of laser emmits a red light.  When laser light is transmitted  through either a single slit or a double slit, the light beam produced contains very interesting patterns.  This phenomena is known as diffraction of light, or bending of light.  The phenomena seen in this lab will present proof that light is made up of waves (The Wave Theory).

Procedure:


Data and Results:
    The first thing that was done for this lab was to look at a double slit projection.  We did this by shining a laser beam onto a card with closely spaced double slits.  I predicted that we would see two lines on the wall that correspond with the two slits.  I was incorrect.  We actually saw many dots projected on the wall with about ten dark spots.  These are called fringes.  A graph of the intensity fringes is shown below.
 


    The next thing that we did was to look at the pattern of the fringes with different size double slits.  We saw that as the slits moved closer to each other the fringes moved further apart and as the slits moved further apart the fringes moved closer.

close slits

    slits further apart


    We then looked at a ripple tank and observed the ripple pattern with different dipplers.  The double dippler produced two sets of waves.  We were able to see that when the crest and trough of two waves met there was  wave interference and the nothing was seen.  This corresponded to the intensity fringes idea.  We then took a paddle dippler and placed a piece of plastic with two slits in front of it.  We observed that the straight-line waves that the paddle produced were turned into circular waves.  Here, each hole acts like a new source of light for diffraction and the circle waves that were formed are very similar to the diffraction seen with the laser in the double slit projection.
 


    We then measured the double slit projection from the wall.  We took three measurements and found the wavelength of the laser and the uncertainty for this measurement.  The data and calculations are shown below.

D = 1.491 m           Change in y = 7.24*10-3 m            a = 1.25*10-4 m

a/wavelength = D/change in y        1.25/wavelength = 1.491 m / 7.24*10-3 m

experimantal wavelenght = 6.07*10-3 m

relative uncertanty = ((1/2) range/average) = 0.022

experimantal wavelenght = 6.07*10-3 m  (+/-) 0.022       actual wavelngth = 6.30*10-3 m
 


    We then looked at a single slit projection.  I predicted that there would be only one spot projected on the wall.  My prediction was incorrect.  We then used slits of varying widths and found that the wider the slit, the smaller the fringes and the smaller the slit, the larger the fringes.  A CCD video camera with the lens taken off was then used to capture the single slit image and to graph the intensity vs. position.  This graph is shown below.  We found that there was one very large peak with a few smaller peaks on either side.
 
 


 
 


     A model of this peak was then constructed using the two equations shown below.
 

                   and 
 
 
 


    The graph of this model is shown below.  The model pattern was very similar to the observed pattern.  We found that by increasing the width of the slit, the peak decreased and the entire graph became more “scrunched” (less wide) and when the slit width was decreased the peak area increased and the entire graph looked less “scrunched” (more wide).
 
 







    We then took the ratio of small peaks to large peaks for the model and the observed graphs.  The ratio for the model was 18.7 and the ratio for the actual graph was found to be 20.6, giving a percent diffrence of 9.2%.  These ratios were very similar so we can conclude that the model was a very good fit to the observed data.  The two graphs did differ in two ways.  The observed intensity graph peaks did not touch the bottom of the graph and the peaks were a little shaky and not well defined.  This was due to noise.  The noise probably comes from dust on the lens and scattered laser light.
 

For more fum physics web pages on similar topics try these links:
Diffraction of Light  -  Joel Barto
Diffraction Grating  -  Shannon Pack
Laser Diffraction   -   by Joe Silberman