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Interference and Diffraction
Purpose
a. To study examples of interference in light waves.
b. To understand the interference pattern produced when light passes through a single slit.
c. To understand the interference pattern produced when light passes through a double slit.
Theory
When a monochromatic and coherent light passes through a single or double slit, it creates a
diffraction/interference pattern on a screen placed beyond the slits. The pattern formed is because of
the superposition of the waves coming from the slit (or two slits). The position on the screen
directly opposite the slits
is defined to have
location y = 0. Other
positions on the screen
are characterized by
their distance y away
from this origin.
Alternatively, a position
on the screen is
characterized by an
angle θ formed by the
line from the slits to this
position, relative to the
perpendicular line. Note
that if the distance from
the slits to the screen is
labelled L, then y = L
tan θ.
Double slit Interference
Interference pattern due to a double slit will have dark and bright fringes due to destructive
and constructive interference of the waves coming from the two slits. When two slits separated by a
distance d produces bright spots on the screen centered at positions where the following
constructive interference criterion is satisfied:
d sin θ = n λ , where n is an integer.
For the experiments we will be doing, the angle θ is less than 10 degrees, and sin θ tan θ =
y/L. Substituting y/L for sin θ in the above equation, we get
n L
y d = ,
or, rearranging,
d
n L y
=. (1)
d
D
Fig. 1. Geometrical arrangement of slits and screen in experiment.
Single-slit diffraction
Diffraction pattern formed by a single will have a wide and bright pattern at the center with
alternate dark and bright fringes with diminishing intensity on both sides. The pattern is formed is
because of the superposition of the waves coming from all points in the slit. A single slit with slit
width D will produce dark regions on the screen at positions where the following destructive
interference criterion is satisfied.
D sinθ = n λ , where n is a non-zero integer.
Again, for our experiments sin θ tan θ = y/L. Substituting y/L for sinθ in the above
equation, we get
n L
y D = ,
or, rearranging,
D
n L y
=. (2)
Since the slits have a finite slit width in double slit experiment, it is thoughtful idea to look
back to double slit interference pattern. Thus, practically, double slit interference pattern will have
single slit effect. This is because each of the individual slits of the double slits act as a single slit
that produces single slit diffraction. As you will observe in this experiment, the real interference
pattern will have interference pattern enveloped in diffraction pattern with evenly-spaced narrower
bright fringes grouped in a few broader bands with decreasing intensity on both sides. The broader
bands are because of the single slit diffraction. We can determine the slit width from the broader
bands.
Apparatus
Various slits in the plastic slits bar of the diffraction assembly; lasers (to be shared and students can
move from station to station when it is time to use a different color laser); mount that holds
laser; black wooden target board; paper; (tape: if needed); meter stick; ruler.
Description of Apparatus
The first three items listed in the apparatus section are shown in the figure 2. You will use
lasers of different colors. Laser gives a monochromatic and coherent light. You will use a plastic
slits bar that you slide in the diffraction assembly to select single slits of different width and then
gently slide the plastic slits bar to select double slit with different slit width and slit separation.
Fig. 2. Experimental set up for interference experiment with a laser and slit(s).
Double slit selection
Single slit selection
Laser Plastic Slit slide bar
Diffraction slits assembly
Part II. Double slit
In this part of the lab, you will perform the same experiment as in Part I but with double
slits.
- Gently slide the plastic slits bar so that you select the double slit with slits’ width D = 0.
mm and distance between slits (that is; slits separation), d = 0.25 mm. Turn on the He-Ne
laser. Infront of the screen, place the target wooden board, with a piece of paper securely
taped to it, at a distance, L, of about two meters from the slit assembly. Measure L. You
should see an interference pattern that looks something similar to Fig 4. You can gently
adjust the laser sideways from rear (or front) to get a clear pattern centered on the screen and
paper sheet.
- The closely-spaced bright spots represent the double slit interference pattern. The larger-
scale pattern in which a wide central set of spots is bright, after which the spots alternately
fade and recover, represents the interference pattern of the individual slits.
- First characterize the double slit pattern. Mark on the paper the location of a central group of
BRIGHT spots, as shown by the black marks at the top of the figure. Stay within the bright
central portion of the pattern, before the spots become difficult to see due to the dark regions
of the single-slit pattern. In your case, for best accuracy, you should make your marks
directly on top of the spots.
- Next characterize the single-slit pattern. Mark on the paper the location of the DARK places
in the pattern, as shown by the gray marks at the bottom of the figure. In your case, for best
accuracy, you should make your marks directly on top of the dark spots. Use a different
color pen so that you can clearly distinguish these marks from your marks in step 3.
- Remove the paper from the target board.
- With your ruler measure the distance between the furthest-separated marks in your two-slit
interference pattern. Also record n, the number of spaces between these furthest-separated
marks. For example, in the figure above, there are eleven marks, so n is ten.
- With your ruler measure the distance between the second order dark on both sides from
the center. (If you can observe higher order dark, you can use them for better accuracy).
These marks are not evenly spaced: the central-most marks have roughly twice the
separation as other nearest-neighbor separations.
Fig. 4. Photograph of a double slit interference pattern on a screen using a red
laser
- Now, gently slide the plastic slits bar to select the double slit with slits’ width D = 0.08 mm
and slits separation, d = 0.25 mm and repeat the previous steps. Record your results in Table
Save this piece of paper with your marks as part of your lab data, to be submitted in your
report.
- Obtain the wavelength of your particular laser from your instructor. Write down the slit
width, D and slits’ separation, d that are marked next to the slits that we selected from the
plastic slits’ bar.
Part III. Double slit interference with different color lasers
- Repeat double slit interference experiment, Part II, with different color lasers. There are
several different color lasers placed at different stations. You may have go to that particular
station or switch to a new laser in your station. Follow the steps 1-3 only in Part II with
one pattern of the double slit.
Computation
Part I: Single Slit Diffraction. From the data recorded in Table 1 and for the first single slit we
used with slit width, D = 0.04 mm, determine the distance from the center of the pattern to
different order dark from your values. Since is the distance between the dark fringes on both
sides from the center, yn = n/2. Determine yn for your pattern. Using these values, your
measured L, and known slit width D, calculate the wavelength of the laser λ from Eq. 2,
D
L
yn n
Use n = 1, 2, 3,…. for first, second, third,…..order dark fringes. Compare this value with
the value of the wavelength given by calculating a percent error.
Repeat this calculation for the results obtained by using Pattern obtained with the second
single slit we used of D = 0.08 mm.
Part II: Double Slit Interference (with inherent single slit diffraction)
(a) Double slit pattern
From the data recorded in Table 2, and for the first double slit we used which had slits
width, D = 0.04 mm and slits separation, d = 0.25 mm, determine the distance between two
neighboring spots in the double slit interference pattern: y = /n. This y is the distance between
the central spot and its neighboring spot, and by setting n = 1 in equation (1) above, we see that
this y should obey
d
L
y
Use this equation, your y from above, your measured L, and your known d (the slit
separation) to calculate the wavelength of the laser light, λ. Compare this value with the
wavelength provided by your instructor and calculate a percent error.
Repeat this calculation for the results obtained by using the second pattern that we
obtained for the second double slit which had slits width, D = 0.08 mm & slits separation d =
0.25 mm.
Data Sheet
Date experiment performed: Name of the group members:
Table 1. Single slit
Distance from the slit to the paper sheet attached to wooden board in front of screen (L) =
Slit
position
1 2 3 y 1
L
yD
1 =
y 2
L
yD
2
y 3
L
yD
3
Pattern for
single slit
with D =
0.04 mm
Pattern for
single slit
with D=
0.08 mm
Average =
error =
Table 2. Double slits
Distance from the slit to the paper sheet attached to wooden board in front of screen (L) =
Double slit pattern Inherent Single-slit pattern
Slit position (^) (meters) n (^) y = /n
L
yd
(meters)
y2 = /
2
y
L
D
Pattern for
double slit with
D = 0.04 mm &
d = 0.25 mm
Pattern for
double slit with
D = 0.08 mm &
d = 0.25 mm
Average = error for D = 0.04 mm:
error = error for D = 0.08 mm:
Table 3. Double slits in different colors
Distance between the slits (d) = Slit width (D) = Distance from the slit to the screen (L) =
Color of laser (^) (meters) n (^) y = /n
L
yd
% error
