Single and Double Slit Diffraction
Reading Assignment:
Halliday, Resnick, and Walker: Chapter 37 (especially 37.2, 37.4, 37.6, 37.7)
Fundamentals of Optics by Jenkins and White
Optics by Hecht and Zajac
Geometrical and Physical Optics by Longhurst.
Introduction:
When a beam of light passes through a narrow aperture it spreads out into the
region of the geometrical shadow. Such an effect is known as diffraction. We will be
studying diffraction from various types of apertures in the first part of this experiment.
Diffraction by a single slit
The diffraction pattern obtained from a single slit is shown in figure 1. The
intensity as a function of angle  is given by
2
  a sin   
2
 sin    
 sin  




I  Io
 Io 

 a sin  
  





Figure 1: The single slit diffraction pattern
where
Eqn. 1
 
a sin 

Eqn. 2
a is the slit width and  is the wavelength of the light used. Io is the intensity at  = 0,
corresponding to the principal maximum. The diffraction pattern is formed in a direction
which is perpendicular to the length of the slit. The positions of the diffraction minima in
the pattern are found from the condition  = ±π, ±2π, ±3π, … which yields the
formula
sin    m

a
m = 1, 2, 3, ...
Eqn. 3
Diffraction by a double slit
Figure 2: The double slit diffraction pattern
Consider a diffracting aperture consisting of two long parallel slits each of width
a and separated by a distance d. The transmitted intensity is given by
  a sin 
 sin  
I  4I o  
 a sin 



2


2
2
  cos d sin    4 I  sin   cos 2 


o
 
   

  


Eqn. 4
where  was defined in eqn. 2 and
 
d sin 

Eqn. 5
The factor of 4 arises from the fact that the amplitude of the wave is twice what it
would be if one slit were covered. The "diffraction'' term in eqn. 4 is recognizable as
the intensity distribution for a single slit and serves as the envelope for the "interference''
term cos2 which describes the interference between the diffracted beams from each slit.
The appearance of the intensity as a function of sin for the case d = 3a is shown in
figure 2. If a is small, the diffraction pattern from either slit will be essentially uniform
over a broad central region and interference fringes will be evident in that region.
Diffraction minima are located at
sin    m

a
,
m = 1, 2, 3, ...
Eqn. 6
while the interference minima are located at

sin   m  1 2  ,
d
m = 1, 2, 3, ...
Eqn. 7
If the slit width a is kept constant and the separation d is increased (or decreased)
the nature of the interference pattern changes, though the diffraction envelope itself
remains unaltered. The number of interference fringes in the central diffraction maximum
is (2d/a) -1. (The factor of 2 comes from identical patterns on either side of the central
point. The term –1 arises because the m=+0 and m = -0 are the same)
Single and Double Slit Diffraction
Goals:
 To examine the diffraction pattern formed by laser light passing through single
and double slits.
 To verify that the positions of the minima in the diffraction pattern match the
positions predicted by theory.
Materials Needed:




Diode laser (OS-8525) with power
supply
Optics bench with centimeter scale
Single Slit Disk (OS-8523)
Multiple Slit Disk (OS-8523)
Activity 1: Diffraction from a single slit.
1. Set up the laser on the optical bench and turn it on.
is 670 nm.
The wavelength of the laser
Do not look into the laser or point it toward someone's eyes.
2. Fix the single slit disk in the lens holder and install it on the optics bench (about 3
cm from the laser). You should be able to see the diffraction pattern on the screen.
3. Choose the slit width a = 0.04 mm by rotating the slit disk until the desired single
slit is centered. Also, set the aperture bracket to position #3.
4. Adjust the position of the laser beam from left-to-right and up-and-down until the
beam is centered on the single slit.
5. Repeat the measurement with some other slit width a. Record the new width and
copy the graph to the template.
6. For the 0.04 mm slit, determine the distance from the slit to the light sensor, as
well as the distances between the first order (m=1) minima and the second order
(m=2) minima. Enter these values in the template.
Analysis.
For the slit with a = 0.04 mm, calculate the slit width from the data collected in the
following way:
1. Divide the distances between side orders by two to get the distances from
the center of the pattern to the first and second order minima. Record those
values of y in the table provided in the template.
2. Using the average wavelength of the laser (670 nm for the Diode Laser),
calculate the slit width twice, once using the first order (a1) and once using
the second order (a2) minima. Record the results in the table.
3. Calculate the percent differences between the experimental slit widths and
0.04 mm. Record in the table.
4. Does the distance between minima increase or decrease when the slit
width is increased (or decreased, depending upon which one you used)?
Activity 2: Double Slit Diffraction.
1.
Place the Multiple Slit Disk in its holder about 3 cm in front of the laser.
2. Select the double slit with the 0.04 mm slit width and 0.25 mm slit separation.
3. Count the number of bright fringes within the central peak.
Analysis.
1. Compare the intensities of the single and double slit diffraction patterns. Is the ratio
equal to the one given by theory?
2. According to the formulae given in the introduction, how many bright fringes
should there be in the central maximum? Does your answer agree with the one
given in point 4 above? Explain.
3. Calculate the slit width from the data collected in the following way:

Divide the distances between side orders by two to get the distances from
the center of the pattern to the first and second order minima. Record those
values of y in the table provided in the template.

Using the average wavelength of the laser (670 nm for the Diode Laser),
calculate the slit width twice, once using the first order (a1) and once using
the second order (a2) minima. Record the results in the table.

Calculate the percent differences between the experimental slit widths and
0.04 mm. Record in the table.