Double Slit Interference Wave Interference Interference and Diffraction Lab 4 Link for the lab instructions: https://docs.google.com/document/d/e/2PACX-1v

Double Slit Interference Wave Interference Interference and Diffraction Lab 4 Link for the lab instructions:

https://docs.google.com/document/d/e/2PACX-1vSLw2sxabGu_IlE4SU2On8wDAh7lmThw_Bp8OFZ7lOEhnTW_lgIeBtONrw4gaXyOLUqPJn0rfjc2tgH/pub

a word document attached for the same instruction,

requirements as in the instructed in the link/word doc.

answering questions, objective included. Lab 4 – Interference and Diffraction
Objectives
•
•
Understand how interference and diffraction patterns are formed, how they are modeled, and how they
differ.
Understand which variables affect each t ype of pattern.
Writeup Requirements
Overview – 4 pts, Data & Analysis – 6 pts, Questions – 8 pts, Lab 4 Survey – 2 pts
Preparation
Diffraction and interference patterns are two different demonstrations of what is fundamentally the same physics:
wave interference. It is traditional to call the phenomena produced by light passing through a single or many slits
diffraction patterns. The phenomena produced by light passing through two slits are called interference patterns.
The mathematical models that describe each are very similar even though the geometries of each system are
different.
Part 1: Wave Interference
Procedure
Watch the lecture video here!
Watch the lab demo video here.
Please open the following simulation, which will help illustrate wave interference phenomena.
Wave Interference – Interference | Double Slit |
Diffraction
First, we will look at how two point sources of light interfere with one another.
1. Select “Interference” from the main menu.
2. Select light as the source (note: in the panel at the right, the “light” is the bullet shape circled in red at the
bottom right), and then check the “screen” box (also circled in red at the right).
3. First, turn on just one of the point sources (by pressing the green button). You will see a light wave
propagate away from the point source. (Note: light is an electromagnetic wave; what is represented by
the crests and troughs is the magnitude of the electric field.)
4. Now, press the pause button at the bottom of the screen, and use the ruler tool to measure the distance
between two adjacent crests of the wave pattern (this distance is the wavelength). The ruler tool is
pictured at top-left in the panel at right: it looks like a tape measure and can be dragged using the mouse
cursor out of (and in fact back into) this virtual toolbox. The ruler tool will start to function as soon as you
drag it out of the virtual onscreen toolbox.
1. What wavelength did you measure for your light source?
2. Press play to resume the simulation and turn on the second light source: what do you observe?
Part 2: Double-Slit Interference
Now, we will look at how a double-slit barrier can cause wave interference. Prepare a table like the one shown
below:
Table 4-1. Measurements for the double-slit interference experiment.
D=
Case
Color
d (slit separation, nm)
λ (nm)
y1 (nm)
y2 (nm)
1
Green
2000
2
Green
3200
3
Red
3200
1.
2.
3.
4.
Select “Slits” from the main menu at the bottom of the screen.
Select light as the source and check the “screen” box.
Select “two slits” from the drop-down menu.
Set the slit width parameter to 200 nm, and set the slit separation parameter (which we call d) to 2000
nm. (Leave the double-slit barrier near the center of the screen.)
5. Turn on the green light source, and observe the wave interference, as well as the bright and dark fringes
that appear on the “screen” (this is the interference pattern).
6. Use the ruler tool to measure the distance from the double-slit barrier to the screen (we will call this
distance D). Record this value in your table.
7. Pause the simulation, and use the ruler tool to measure the wavelength of the light. Record this value in
your table, then resume the simulation.
8. Measure and record the distance from the central bright fringe to the first one above it (we will call this
distance y1).
9. Measure and record the distance from the central bright fringe to the second one above it (we call this
distance y2).
10. Increase the slit separation parameter to 3200 nm. Once the interference pattern is clearly visible,
measure and record y1 and y2.
11. Increase the wavelength of the light source by moving the color slider from green toward red.
12. Once the interference pattern is clearly visible, record y1 and y2, and pause the simulation to measure and
record the new wavelength.
3. How did increasing the slit separation affect the interference pattern?
4. How did increasing the wavelength affect the interference pattern?
Now, we can try to explain the double-slit interference patterns mathematically. Our aim is to develop a simple
model that describes the location of the dark spots or fringes that appear in the pattern.
As before, d describes the slit separation distance, D is the distance from the double-slit barrier to the screen
where the interference pattern appears, and λ is the wavelength of the light.
Take a careful look at Figure 4-1, particularly the zoomed in section. Shown are two paths, one from the upper slit
to a bright fringe, the other from the lower slit to the same bright fringe. For constructive interference to occur,
the difference in these two path lengths must be an integer multiple of the wavelength. We call this integer m,
which represents the order of the fringe. The distance from the center of the pattern to the mth bright fringe is
called ym. (Previously, we had measured y1 and y2.)
Figure 5-1. Description of a double slit interference pattern. Peaks represent bright spots. The constructive
interference occurs when the distances from the first slit to the screen and the second slit to the screen differ by a
whole wavelength multiple. The two angles labeled  can be considered equal when the distance to the screen, D, is
much greater than the slit separation.
See the zoomed-in region in Figure 5-1, and note that this is approximately a right triangle. Using some
trigonometry, the variables d, , λ, and m can be related as:
(4-1)
This equation can be used to predict at what angles the bright fringes will appear. Another useful trigonometric
result is:
(4-2)
For each of the three cases from Table 5-1, determine the values for y1 and y2 by plugging in the results
recorded for λ, m, d, and D into Equations 4-1 and 4-2. Compare these calculated values to the measured values
with a percent error. (Give an example calculation to show how you did this.)
(Note: when analyzing the results from this simulation, you cannot make the approximation that sin(θ) ≈ tan(θ);
the screen is too close to the double slit barrier for this to be valid.)
Case
Calculated y1
% error
Calculated y2
% error
1
2
3
Consider the case that the distance from the double-slit barrier to the screen is much larger than the distance
between the bright fringes (in this case, D >> ym). This is generally true in an actual double-slit experiment.
5. Calculate the angle, , for D = 1 m and y = 1 cm.
Next calculate sin() and tan(). Are they approximately equal (it would introduce error if they are
not)?
6. Show how this approximation can be used to simplify Equations 4-1 and 4-2 to obtain the following
formula for the double-slit interference pattern: ym=mλD/d.
7. For the green laser wavelength and screen distance D used in the video, calculate the distance of the first
fringe (m=1) when the slit spacing is d=0.25 mm.
Part 3: Diffraction
Diffraction is an application of an early wave theory of light developed by the Dutch physicist and mathematician
Christian Huygens (1629-1695) and French physicist Augustin-Jean Fresnel (1788-1827). Once light passes through
a slit, it acts as though it is being emitted anew from a point source. The slit has a real, if small, width, thus there
are many such point sources in a line within the slit. The light emitted from any one point can interfere with the
light emitted from another point because of slight differences in the distances between the screen and the points.
Procedure
We will be using the same simulation as before.
1. Select “Diffraction” from the main menu at the bottom of the screen.
2. In this simulation, a beam of light is passing through an aperture, or small hole, in the middle of a light-
blocking barrier. Turn the light on to see the diffraction pattern.
8. What do you observe?
9. How is the diffraction pattern you see similar to the double-slit interference pattern, and how is it
different?
3. Try varying the diameter of the aperture, and observe how the diffraction pattern changes.
10. What is the relationship you observed between the spacing of the bright fringes and the diameter of the
aperture?
4. Now, we will try to approximate a single-slit experiment.
5. Change the shape of the aperture to rectangular (see the icon to the right).
6. Adjust the width to its minimum ( 0.04 mm), and the height to its maximum (0.40 mm).
11. What happens to the spacing of the single-slit diffraction pattern when you increase the wavelength to
780 nm?
12. What happens to the spacing of the single-slit diffraction pattern when you increase the slit width?
Experimental Results
The set-up shown in Figure 4-2 was used to perform both a single-slit diffraction experiment, and a double-slit
interference experiment.
Figure 4-2. Experimental set-up for obtaining an interference pattern.
The results of these experiments are shown in Figure 4-3 below. In both cases, the slit width, a, was 0.08 mm, the
distance from the double-slit barrier to the screen was 83 cm, and a 650 nm light source was used. (Note that in a
real double-slit experiment such as this, the single-slit diffraction pattern will be visible in addition to the
interference pattern—this is because a double-slit barrier is just composed of two single slits.)
Figure 4-3. Experimentally obtained diffraction/interference patterns.
13. Which image (A or B) in Figure 4-3 represents single slit diffraction, and which represents double-slit
interference?
14. Is the sin(x) = tan(x) approximation appropriate to use here? (See Q5 and Q6.)
Use the measurement scale shown, and the parameters given, to determine the double-slit separation distance, d.
Do this using 3 different fringes, and take the average of your results (the values should be fairly close). You will
need to rely on what you have learned in this lab. Record your results in a table like Table 4-2.
(Note: the diffraction pattern will obscure some of the bright fringes of the interference pattern, so some of the
bright fringes will appear to be missing. When counting the order of a fringe, assume that the fringes are evenly
spaced, and count the obscured fringes as well.)
Table 4-2. Determining the double-slit separation distance.
m (fringe order)
ym (m)
d (m)
daverage =
Complete the Post Lab 4 Survey on D2L once you have
submitted your report. This is located in the Quizzes section.

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