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Single Slit Diffraction
Purpose:
To verify experimentally the predicted locations of intensity minima and maxima
for a single slit and to use the phenomena of interference and diffraction to
measure small dimensions
Apparatus:
He-Ne laser, optical bench and laser alignment bench, single slits, screen with
scale, magnetic holders, hair, phonograph record and/or CD (if available)
Introduction
For a single slit of width d, the diffraction pattern consists of a broad
central maximum extending between two minima located at an angle  on either side
of the perpendicular bisector of the slit.
The angle to that first minimum is
given by an equation that looks exactly like the one giving the location of the
first maximum for the double slit:
dsin = 
Subsequent minima are located at angles given by
dsinm = m, m = 1,2,3,... (but not 0!)
As for the double slit pattern,
if the diffraction pattern is
projected on a screen a distance
D from the slit and the positions
of the minima are located at points
ym along the screen, the angles are given by
m
yn
D
tanm = ym/D
If the angles are small, tan  sin, and we can substitute the location
information directly into the mathematical description of how to find the angles:
d(ym/D) = m,
m = 1,2,3,... (but not 0!)
(Note that this looks exactly like the equation telling how to find the maxima for
the double slit pattern.
You should practice deriving equations for both
situations yourself to make sure you really understand what they mean. Don't just
blindly memorize them.)
Procedure
1. Put the laser on its alignment bench and place it at one end of the 1-meter
optical bench. Place magnetic holders near each end of the optical bench to hold
the slits and the screen. The wavelength of the laser light is 632.8 nm.
2. Put the single slit slide on the magnetic holder nearest the laser.
Put the
screen on the magnetic holder near the other end of the bench.
For the
measurements to be made in this part of the experiment, the holders must not be
moved. Record their positions here and calculate the distance (D) between them.
Estimate positions to 0.1 mm.
Position of slit
__________
Position of screen
__________
D =
__________
(UNITS!!!)
3. Adjust the slit so the laser beam illuminates the slit with
slit width = .04 mm
Adjust the screen so that the diffraction pattern is positioned on the printed
scale and is parallel to the scale.
4. Record the positions of six minima,, three on each side of the central maximum.
Please note carefully that the central maximum is twice as wide as the other
maxima. Even though it's difficult, you should estimate these to a precision of
.1 mm.
Minima
_______
_______
_______
_______
_______
_______
7. To find y1, the distance from the center of the pattern to the first minimum, we
use the same basic technique as in the double slit experiment.
Except for the
minima on either side of the central maximum, the distance between successive
minima is equal to the distance from the middle of the central maximum to the
first dark spot.
If we measure the distances between dark spots, the average
distance is equal to y1. When doing the calculation, we get four differences from
our six minima. However, remember the caution from the previous page: since the
central maximum is twice as wide as the other maxima, we must divide the sum of
the five differences by six to get the value for y1.
8. Analyze your data in Part 6 to find the average value of y. You can report
the average to one more significant digit than the individual differences have.
Average value of y = y1 =
_______
(Units???)
Single Slit
2
9. Now use the given wavelength, your value of D, and the average value of y to
compute a value for the slit width d:
d = ___________
10.
Now repeat the entire procedure for the slit with
slit width = .02 mm
Position of slit
__________
Position of screen
__________
D =
__________
(UNITS!!!)
Minima
______
______
______
______
______
______
Average value of y = y1 =
_______
(Units???)
11.
Now use the given wavelength, your value of D, and the average value of y
to compute a value for the slit width d:
d = ___________
Single Slit
3
12.
Summarize your results here:
Given slit width = .04 mm
Experimental slit width = __________
Given slit width = .02 mm
Experimental slit width = __________
Do your experimentally determined widths agree reasonbly well with the given slit
widths?
How do these results tend to support or not support the theoretical
description of diffraction?
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Diameter of a hair
If a long thin opaque object like a hair is placed in the laser beam, it
produces the same diffraction pattern as the slit.
We can exploit this amazing
fact to determine the diameter of a hair, which is otherwise too small to measure
directly with ordinary tools like a micrometer. Follow the same basic procedure
as in the first two parts of this experiment. (Be sure to include units on all
measurements!)
Type of hair:
______________________
Distance from hair to screen: __________
Wavelength of laser light:
__________
Positions of 6 minima, 3 on each side of the central maximum:
__________
__________
__________
__________
__________
__________
Single Slit
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Calculation of y1:
y1 =
__________
Calculation of d, the diameter of the hair:
d =
__________
Summarize the results.
How does the size of the hair compare with the width of
the slits used in the first two parts of the experiment? If more than one type of
hair was measured, is there any apparent trend in the sizes? In other words, are
all the hairs basically the same diameter, or is there a variation depending on
color or some other property of the hair?
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Other Investigations
The interference pattern formed by a large number of slits is also quite
interesting. Your instructor may have other objects for you to measure, such as
the spacing between grooves in a phonograph record or the spacing between rows of
dots on a CD. Please follow any extra instructions that may be given.
Single Slit
5