PASCO OS-8500 INTRODUCTORY OPTICS SYSTEM - Manual (Page 44)

Introductory Optics System 012-02744K
®
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Figure 16.2 Geometry of Single Slit Diffraction
The single slit pattern can be explained using Huygen’s theory. When a plane wave front
strikes the slit, each point on the slit acts as a point source of light. Figure 16.2 shows a point P,
far from the slit, where the distance AP = BP +
λ. Since light from point A travels one wave-
length farther than light from point B, the light from these two points is in phase at point P. But
light reaching point P from the points in between A and B will vary in phase through a full
360°. For any point from which light reaches point P at a particular phase, there will be a point
from which light arrives in the exact opposite phase. Because of this, there is complete cancel-
lation at point P, and a minima (dark fringe) will be seen at that point.
In the Figure, point P is at an angle q from the center of the slit. We make the assumption that
point P is far enough away such that AP and BP are very nearly parallel (this is true in reality, if
not in the diagram). As shown in the diagram, angle ABC =
θ , also. Therefore W sin θ = λ;
where W is the width of the slit (AB). A similar argument can be used to show that a minima
will be found at any angle such that W sin
θ = nλ , where n is any integer.
Review the two slit interference experiment. Notice the similarity between the equations for
single and double slit patterns. To measure the wavelength of light, use the same techniques
you used in the two slit experiment (
θ = arctan X/L). When measuring the distance to the
minima (x) for each color, place the Color Filter on the front of the Light Source. Use your
data to fill in Table 16.1, then perform the calculations shown to determine the wavelength of
Red, Green, and Blue Light.
➀ If the width of the slit, W, were less than the wavelength of the light being used, how many
maxima would you expect to see in the single slit diffraction pattern? Why?____________
________________________________________________________________________.
Data Calculations
Color n W X L arctan X/L Wsin (arctan X/L) =
nλλλλλ
Red
Green
Blue
Table 16.1
__
AB = W
1st
maximum
1st
minimum
P
Diffraction
Scale
zeroth
maximum
1st
maximum
1st
minimum
Zeroth
maximum
1st
minimum
1st
maximum
Retina of
your eye
Diffraction Grating
θ
B
A C
θ
P
L
x
λ
θ