Diffraction Lab – General documentation
Deliverable
Individual worksheet report
Equipment needed
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3 laser pointers per group (class split into 10 groups rather than 15)
Single Slit, Double Slit and Diffraction Grating cards for groups
o Table 1 does Double Slits A and B with all three laser pointers
o Table 2 does Double Slits B and C with all three laser pointers
o Table 3 does Single Slits A and B with all three laser pointers
o Table 4 does Diffraction Grating (300 and 600 lines/mm) with all three lasers
o Table 5 does Double Slits A, B, C and Single Slits A, B with one laser pointer
Lab Jacks or blocks to position heights (x10)
Large sheets of paper for recording patterns
Tape
Clamps for laser pointers (x10)
Posts and table clamps (x10)
Estimated Time needed for the activity
To be determined – hopefully 45 minutes
Pre-lab questions
1. What are some modern technology applications of interference and diffraction?
2. Which size slit will produce a wider diffraction pattern: 0.01 mm, or 0.05 mm? Why?
3. Which grating will yield a wider diffraction pattern: 300 lines/mm or 600 lines/mm? Why?
4. Sketch the actual diffraction patterns that correspond to the single and double-slit intensity.
5. How could a laser be used to measure the thickness of a human hair?
Pre-lab answers
1. What are some modern technology applications of interference and diffraction?
So many answers are fine here – spectrometers, monochromators, interferometry, holography, fiber
optics – any wavelength division applications, etc.
2. Which size slit will produce a wider diffraction pattern: 0.01 mm or 0.005 mm?
0.01 mm since a smaller slit produces a wider diffraction pattern
3. Which grating will yield a wider diffraction pattern: 300 lines/mm or 600 lines/mm? Why?
600 lines/mm more lines spread light more
4. Sketch the actual diffraction patterns that correspond to the single and double-slit intensity.
The sketch should have lines (with minima) for single slit and a similar diffraction envelope with fine
structure for the double-slit. They can either draw full curves like in the lab write-up or just the
projection on the viewing screen (though they should only get full credit for drawing the pattern rather
than the intensity curves since that’s what the question asks for).
5. How could a laser be used to measure the thickness of a human hair?
The procedure here is nearly identical to the single slit – it’s just now you have a single obstacle. The
diffraction pattern results from two edges separated by a small distance (a), and this can occur for a slit
or an object with the same width.
Pre-lab discussion points
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Spend some time going over/showing the Google spreadsheet so that everyone
understands the expectations from this lab.
Review/cover laser safety – watch for eye-level beams and always point your
experiment “outward” in the room, rather than at another group.
Don’t spend too much time on the theory as we want them to experiment with
changing wavelengths and the different effects of slit widths/grating rulings.
Teaching Tips/pointers for doing lab
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General things to watch for - that students are progressing with their patterns – don’t
let any group spend too much time marking their papers. They will need some
precision, but also need to keep sight on the bigger picture.
Keep an eye towards safety here (probably most important for the instructors
themselves, moving around the classroom) – watch for stray reflections and stray
beams. Make sure groups are pointing their setups away from each other.
Post-lab discussion questions
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There are a lot of different data points that the class is gathering together here – and we
don’t want to lose the big picture because of the details – so start the overall review
discussing the general effects that different changes in our experiment will have. If you
increase your slit widths, for example, what happens to the pattern. If you increase the
wavelength, on the other hand, what happens to the pattern.
After the class is comfortable with the different effects, discuss some of the inherent
issues with our diode laser pointers – and lead, as a guided demo, one last data
collection through a grating (easiest setup) with a “red” laser pointer and a HeNe laser
(632.8 nm). Guide the class in using the HeNe laser as a calibration standard to
determine the actual wavelength of the laser pointers..
Extension Problems
1. The lab links to a nice simulation on Wolfram. Students who finish early can first use
the hallway to make measurements, but if that is still too much time, they can do
some open-ended investigation with the intensities displayed in the simulation. No
specific questions have been worked up yet…
Solutions for Extension Problems
1. Nothing to turn in or grade here – open ended investigation – so no real solutions
Rubric for grading Deliverable
Point Short report for Diffraction Lab:
NAME__KEY/Rubric____ 35 points+15 pts prelab=50 pts
PreLab (15pts) (No Abstract needed)
1. What happens when you increase the wavelength of the laser light used in the three
different patterns (diffraction gratings, single slits and double slits)?
(2 pts) Check for completeness here – students need to answer all parts. Increasing the
wavelength makes the diffraction pattern spread out more in all three cases (a sin θ = λ). If
wavelength increases, the angular spread increases.
2. What happens to the interference pattern when the single slit width is decreased?
(2pts) Larger slit width causes less dispersion
3. What happens to the interference pattern when the double slit separation is decreased?
(2pts) Increasing the slit spacing decreases the fine structure spacing
4. What happens to the interference pattern when the density of lines on the diffraction
grating is increased (more lines per mm)?
(2pts) Increase lines/mm means there will be a greater spread in the dispersion of dots
Quantitative Analysis (attach graphs where appropriate): Data located on shared Google Spreadsheet!
(20 pts) (the nominal values should be free points to record) Deduct 10 points if plots or details about
how the analysis was done are not included for deriving their values and deduct points if the graphs are
not labeled properly (but don’t deduct for each graph)
Single Slit
Wavelength Nominal a – Measured a – Nominal a Measured a –
Slit A
Slit A
– Slit B
Slit B
Double Slit
Wavelength Nominal a –
Slit A
Measured a – Nominal d
Slit A
– Slit A
Measured d
– Slit A
Double Slit
Wavelength Nominal a –
Measured a – Nominal d
Measured d
Slit B
Slit B
– Slit B
– Slit B
Double Slit
Wavelength Nominal a –
Slit C
Measured a – Nominal d
Slit C
– Slit C
Measured d
– Slit C
Diffraction
Wavelength Nominal d
Measured d
Measured d
Nominal d
Discussion Questions:
1. What are some applications of diffraction both in science labs as well as in your home?
(2pts) There are a lot of ways to answer this question again – similar to the pre-lab
question – but x-ray crystallography and atomic spectroscopy and really any
spectroscopy (astro applications, Raman/vibrational modes, etc.) are good answers.
2. Why can you hear around corners but not see around them?
(2pts) It is all about the wavelength and size scales here. A typical doorway is around a meter
wide (a little less, usually), so sound with its relatively large wavelengths will create a big
central maximum and sufficiently-loud secondary peaks – sound we can hear. That can be
enough to hear even if you aren’t in a straight line with the source. And a corner is just a very
wide doorway…
3. What are the largest sources of error in this lab?
(2pts) It is difficult to make sure the screen is perfectly perpendicular to the incident
laser source and to measure that large distance well. Also, if you don’t have the screen
far enough away, the patter can be quite small and so the percentage of uncertainty in
the measurement increases.
4. How would you improve this lab?
(1pt) Pretty open here – mostly interested in seeing what students would like to see
change/improve in the lab. Give credit for reasonable and thoughtful answers.
Lab Write up
Short report for Diffraction Lab:
NAME_________________________ Group ________
PreLab (15pts) (No Abstract needed)
1. What happens when you increase the wavelength of the laser light used in the three
different patterns (diffraction gratings, single slits and double slits)?
2. What happens to the interference pattern when the single slit width is decreased?
3. What happens to the interference pattern when the double slit separation is decreased?
4. What happens to the interference pattern when the density of lines on the diffraction
grating is increased (more lines per mm)?
Quantitative Analysis (attach graphs where appropriate): Data located on shared Google spreadsheet!
Single Slit
Wavelength
Nominal a
– Slit A
Measured a
– Slit A
Nominal a
– Slit B
Measured a
– Slit B
Double Slit
Wavelength
Nominal a
– Slit A
Measured a
– Slit A
Nominal d
– Slit A
Measured d
– Slit A
Double Slit
Wavelength
Nominal a
– Slit B
Measured a
– Slit B
Nominal d
– Slit B
Measured d
– Slit B
Double Slit
Wavelength
Nominal a
– Slit C
Measured a
– Slit C
Nominal d
– Slit C
Measured d
– Slit C
Diffraction
Wavelength Nominal d
Measured d
Nominal d
Measured d
Discussion Questions:
1. What are some applications of diffraction both in science labs as well as in your home?
2. Why can you hear around corners but not see around them?
3. What are the largest sources of error in this lab?
4. How would you improve this lab?
Interference and Diffraction
Pre-lab Questions and Exercises
1. What are some modern technology applications of interference and diffraction?
2. Which size slit will produce a wider diffraction pattern: 0.01 mm, or 0.05 mm? Why?
3. Which grating will yield a wider diffraction pattern: 300 lines/mm or 600 lines/mm? Why?
4. Sketch the actual diffraction patterns that correspond to the single and double-slit intensity.
5. How could a laser be used to measure the thickness of a human hair?
Introduction
In geometrical optics we are concerned with the ray concept of light. In this experiment,
we will observe how wave optics manifests itself in the phenomenon of diffraction.. Wave
optics are required under specific size scales – namely when a (the width of the slit or aperature)
is smaller or on the order of λ (the wavelength of light). This condition is satisfied for diffraction
patterns. The aim of this experiment will be to study the interference patterns that result from the
wave nature of light.
The unifying principle of elementary wave optics is Huygens’ principle: All points on a
wave front can be considered as point sources for the production of spherical secondary
wavelets. As the waves propagate, the position of the wave front will be the surface of tangency
to these secondary wavelets.
This principle, together with the principle of superposition, can be used to explain the
phenomenon of diffraction. The principle of superposition states that the resultant waveform is
found by adding algebraically, or super-imposing, the separate wavelets that make up the total
waveform.
You may find the following simulation helpful as you are considering different patterns:
http://demonstrations.wolfram.com/MultipleSlitDiffractionPattern/
The Diffraction Grating
A diffraction grating is equivalent to an array of closely spaced sources. A transmission
grating, for example, is just closely spaced parallel lines scratched onto a glass plate. We will
consider the geometry of a row of point sources, remembering that each point source on the
grating will act as a source of secondary wavelets that will interfere with each other (see Fig. 1).
Here d is the distance between sources and N is the total number of sources.
d
Nd





d
m
Figure 1
Figure 2
Consider any two adjacent sources, as shown in Figure 2. There will be constructive
interference, or maxima in intensity, when the phase of all wavelets is the same. This requires
that the optical path length difference, d sin  m , be an integer number of wavelengths.
Therefore,
d sin  m  m (m  0, 1, 2, )
(1)
This is commonly called the grating equation.
Intensity Variation fora Diffraction Grating
m=0
m=1
m=2
InterferencePeak
DiffractionFringes
θ=0

Figure 3
m=3
Single-Slit Diffraction
For a single-slit, we again imagine each point on the wave front as being a new point
source of radiation. Infinitesimally small distances separate these point sources and all oscillate
with the same phase. So then we have an infinite array of point sources spread over the finite
width of the slit. From this geometry the intensity of the diffraction pattern can be derived. The
intensity as a function of angle is given (without proof) by:
 sin 
I  I o 
 
2

a
 , where  
sin 


(2)
where
Io = maximum intensity (at  = 0)
a = width of the slit
 = wavelength of the light
Minima occur when sin   0 . For this condition to be true,  must equal an integer multiple of
:
  m
Since  
(m  1, 2, 3, )
a
sin  , it follows that

a sin   m
(m  1, 2, 3, )
(3)
Minima

a
Central
Central
Maximum
Maxima
m=1
m=2
Figure 4
m=3
Double-Slit Diffraction
Suppose now we have two parallel slits, each of width a, with their centers separated by a
distance d. If we cover one of the slits, then the result is a single-slit diffraction pattern, as
discussed before. If we open both slits, we obtain the same diffraction pattern as with a singleslit, but there are also finer variations in intensity caused by the double-slit interference. The slit
separation d can be found from equation (1) when the distances from the center of the diffraction
pattern to maxima of the fine structure are measured.
The intensity of the double-slit diffraction pattern is given (without proof) by:
 sin 
I  4 I o 
 
2

 d 
 cos 2  , where     sin 
  

(4)
and  is defined the same as before. Minima occur when sin   0 or when cos   0 . We
already know that when sin   0 , then a sin   m (equation 3). Note in figure 5 which
minima occur when sin   0 .
d
sin  (m  0, 1, 2, ) . When this

equation is rearranged, we obtain the grating equation in slightly different form:
When cos   0 , it must be that   m  12  
d sin  

2
 m
(m  0, 1, 2, )
(5)
This may seem to contradict what was stated above, that the slit separation can be found
from equation (1), but remember that equation (5) results from minima, while the equation (1)
results from maxima.
The interference pattern is “modulated” by the diffraction pattern just as with AM
(Amplitude Modulation) radio transmission, where the carrier wave amplitude is “modulated” by
the audio signal.
I()
Double Slit
Diffraction
Envelope
d
Interference
"Fine" Structure
a
a

d
Figure 5
a

Procedure
Be sure to avoid shining the laser light into anyone’s eyes! In this lab you will use a
series of laser pointers (red, green, and blue) monochromatic light sources. Be sure to record the
wavelength for each laser. We will also use a combination of single slits, double slits and
diffraction gratings. We will be sharing data as a class to reduce the total data collection time
and improve efficiency. There is a Google spreadsheet that will be shared for all class data. The
groups at Table 1 will focus on using all three laser pointers to measure Double Slits A and B,
the groups at Table 2 will focus on using all three laser pointers to measure Double Slits B and
C, the groups at Table 3 will focus on using all three laser pointers to measure Single Slits A and
B, the groups at Table 4 will focus on using all three laser points to measure diffraction gratings
with 300 and 600 lines/mm and the groups at Table 5 will each use one laser (Group A will use
the red laser pointer, Group B will use the green laser pointer) but will measure Double Slits A,B
and C as well as Single Slits A and B. Each group will therefore be measuring either 5 or 6
patterns, and almost all the patterns will have two sets of data so we can check consistency.
1. Set up the laser clamp and pole at your table on the side closest to the center of the room
and opposite the nearest wall or window sill where you will locate your screen. Use a
right- angle clamp to mount one of the three laser pointers. Make sure you set the clamp
on the silver strip around the middle of the laser pointer, (not on the ON/OFF button), so
that the laser is not on continuously– this will be safer and will preserve the battery as
well as lifetime of the laser pointers. Wait until you are ready to collect data before
turning on the laser.
2. Set up your viewing screen in a somewhat convenient location in the room – use just
paper or tape your paper to a portable white board depending on what makes most sense
for your location in the room. Draw a vertical line down the approximate center of your
paper so you have a common alignment for all your interference patterns.
3. Use the table to hold the targets (either diffraction grating, single-, or double-slit card) in
a lens holder. Use a lab jack or wood blocks at the table to raise or lower the metal lens
holders for alignment. Adjust the heights of your laser as necessary so that you will be
able to direct the laser through the target onto your viewing screen.
4. Record the distances (between laser, target, and screen) as well as the wavelengths of
light used.
5. When ready, have one group member hold the laser on so you can collect data.
Remember to keep the laser off when it is not being used.
6. Trace the interference patterns assigned to your group. Carefully label each pattern on
your paper to avoid confusion later.
a. When recording the patterns, you can just mark the maxima (easier to see – rather
than the minima) for each pattern directly on the sheet. Remember to be careful
and not look directly at the laser beams while you are recording your data.
b. You can use multiple sheets of paper if it is difficult to keep track of all of your
lines. You can also just shift the white board/paper vertically to record all the
interference patterns together. Remember to always aim your central maximum at
the center line on the paper, and ensure that the distance between the target and
screen does not change..
c. Qualitatively describe the differences between the patterns you measured.
Analysis
The Google spreadsheet lays out the different pieces of information that need to be shared as a
class. The different descriptions below for step 1 (only) depend on the particular pattern that
your own group measured, but after you measure your distances and record those values on the
shared google doc, do the analysis described in all the following steps for all the data the class
recorded.
1. Measure the important parameters for your patterns.
a. For the single-slit diffraction pattern, measure several xm, the distance from the
central maximum to the mth minimum.
b. For the double-slit diffraction pattern, measure several xm, the distance from the
central maximum to the mth minimum of the interference fine structure. Also
record the diffraction envelope minima.
c. For the diffraction grating pattern, measure several xm, the distance from the
central maximum to the mth interference peak (maximum).
2. Single Slit analysis: Use your data (by plotting sin θ vs m - where sin θ is approximately
xm/(distance to target), by the small angle approximation), to determine the slit width, a.
a. Compare your calculated value to the nominal slit width of the target.
b. Do you get the same value for different wavelengths?
c. Which wavelength yielded the most accurate and/or precise results? Why do you
think this is true?
3. Double Slit analysis: Determine which plots are necessary to use your data to determine
both d and a for the double-slit.
a. Compare your calculated values to the nominal slit widths and separations on the
card.
b. Does the calculation change with the different wavelengths?
c. Which wavelength yielded the most accurate and/or precise results?
4. Diffraction grating analysis: Use your data to compute a best estimate of the line spacing
for the grating. Plot sin θ vs m,. Be sure to attach your graph – what is the slope of your
line equal to? From the known grating spacing determine the wavelength used to create
the pattern and compare this to the actual wavelength used.
Discussion
What are some applications of diffraction both in science labs as well as in your home?
Why can you hear around corners but not see around them? What are the largest sources of error
in this lab? How would you improve this lab?