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:

- Double Slit Prediction
- Double Slit Qualitative 1
- Ripple Tank
- Double Slit Qualitative 2
- Single Slit Projection
- Single Slit Qualitative
- Image the Pattern
- Plot Brightness Profile of the Pattern
- Model Diffraction Pattern

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