Physics 1051
CD Diffraction
Laboratory #6
Diffraction
Physics 1051
Laboratory #6
Contents
Part I:
Setup
Part II: The Diffraction Grating
Part III: CD Groove Spacing
Diffraction
Physics 1051
Laboratory #6
Diffraction
Part I: Introduction
One of the goals in this lab is to use a diffraction grating to determine the
wavelength of a laser pointer.
The grating equation is
m λ = d sin θ,
m = 1, 2, 3, 4.....
where m is the order number, λ is the wavelength of light, d is the slit spacing of
the grating, and θ is the diffracted angle. This expression illustrates that
constructive interference occurs when the path difference δ is an integer number of
wavelengths.
Once the wavelength of the laser is known, it will be used to determine the groove
spacing of a Compact Disc.
Physics 1051
Laboratory #6
Apparatus
•
You should have been provided with:
•
•
•
•
•
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Laser pointer
Metre sticks
CD
Diffraction Grating of known slit spacing
Mounting assembly
Some sheets of white paper
Diffraction
Physics 1051
Laboratory #6
Diffraction
Part II: The Diffraction Grating
What happens when light passes through a diffraction grating?
Put the diffraction grating in front of your eye and look around. What do you see?
Look at the lights in the room through the grating. Can you explain their appearance
using the grating equation?
QUESTION 1: Explain the appearance of the room lights by considering the grating
equation.
Physics 1051
Laboratory #6
Diffraction
Setup: Determining the Wavelength
Place your laser pointer in the groove in the
base.
Record the slit spacing written on your
diffraction grating in your Activity Log. This
is not simply the number of lines/mm!
Position the diffraction grating in the slot in
front of the laser.
Place the screen in front of two posts which are
screwed into the bench top. Use the clamps
provided to fasten the screen so that it does
not move.
Tape some white paper to the front of your
screen.
Physics 1051
Laboratory #6
Diffraction
Setup: Determining the Wavelength
Place the grating and laser assembly approximately 30 cm from the screen.
Make sure the screen and diffraction grating are parallel by measuring the screen
to grating distance on each side of the assembly.
Measure the distance between the diffraction grating and the screen
and record it along with the associated uncertainty in Table 1 of your Activity
Log.
Physics 1051
Laboratory #6
Diffraction
Making Your Mark!
Shine the laser through the
diffraction grating and make sure you
observe a diffraction pattern. If you
don’t check that the laser is passing
through the grating.
The spot that appears in the middle
is known as the zeroth order. Make a
note on the screen as to which spot
this is. Have your partner carefully
mark the centre positions of at least
6 bright spots on each side of the
zeroth order spot.
Zeroth order
Qu ick Tim e™ a n d a
TIFF (U n com pressed) decompr essor
a r e needed to see th is pictu r e.
2nd 1st
1st
2nd
zeroth order
Note: You should be able to see at least 8 higher order spots on both
sides of the central spot.
Physics 1051
Laboratory #6
Diffraction
Calculations
Remove the screen from the bench
and lay it flat on the bench top.
Measure the distance D between the
two first order bright spots. Divide this
distance by 2 to obtain the average
distance, X, between either spot and
the centre. Repeat this procedure to
obtain the average distances for each
of the six higher order spots. Record
the distances in Table 3 of your
Activity Log.
θ
L
Using your trigonometry skills, calculate the diffraction angles θ for all the
spots you have measured.
Using the grating equation, calculate the path difference δ for all the
angles you just obtained, and record the values in Table 3 of your Activity
Log.
D
Physics 1051
Laboratory #6
Diffraction
Graphical Analysis
Launch Graphical Analysis by clicking on the icon in the below.
Use it to plot δ versus m.
Calculate and display the regression line for this data set. To do so, pull down the Analyze menu
and select Linear Fit. Then double click on the box that appears and in the Standard Deviations
section check both the Slope and Intercept.
Record the slope and intercept (and uncertainties) in Table 4 of your Activity Log.
Print the graph and include it with your Activity Log.
QUESTION 2: Using the diffraction equation and the slope of your graph, calculate the
wavelength of your laser pointer. Be sure to include the uncertainty and units.
QUESTION 3: Compare your calculated wavelength with the value quoted on your laser pointer. If
they do not agree, explain why.
Physics 1051
Laboratory #6
Diffraction
Part III: Get in the Groove!
A CD consists of a series of evenly spaced
(reflective) grooves and ridges that act as a
diffraction grating.
The grooves in a compact disc are very close
together. One side of a disc can hold more
music than two sides of a vinyl record. Just
how close are the grooves?
To measure the distance between the grooves
we will inspect the diffraction pattern from your
laser of known wavelength using the
diffraction equation.
CDs are reflective and therefore the diffraction
pattern can be observed by looking at the
reflected pattern.
When you look at the side with
the grooves in it you see a
rainbow spectrum. The rainbow
spectrum is from the reflection
of white light that has been
diffracted.
Physics 1051
Laboratory #6
Diffraction
Setup: Groovy Spacing
Remove the diffraction grating from the holder and replace the paper on your
screen with a new piece. Be sure to punch a hole in the paper where the hole is in
the screen.
Place the screen in the slot in front of the laser pointer and carefully align it such
that the laser clearly passes through the hole in the screen and paper.
Fasten a CD in the clamp provided and
attach it to one of the support bars.
Slide the laser and screen assembly
onto the other support bar and tighten
the anchor screw.
See photos of the setup on the next page
Physics 1051
Laboratory #6
CD Setup Photos
Diffraction
Physics 1051
Laboratory #6
Diffraction
Setup: Groovy Spacing
Shine the laser so that it reflects from the outer
region of the compact disc, where the tracks of
the CD are approximately parallel lines.
To ensure that there is normal incidence of the laser on the CD, carefully
move the CD until the central spot is reflect back onto the incident beam.
This step is tricky but very important. Take your time! You will have
to rotate, raise/lower and tip the CD until the pattern is lined up
properly. The interference pattern on the screen should be
horizontal.
Physics 1051
Laboratory #6
Diffraction
On Your Mark!
In order to observe the second order
diffraction pattern from the CD, the distance
between the screen and the CD should be
no more than 25 cm.
The groove spacing will be calculated using
both the first and second order diffraction
maxima. If you do not see the second order
maximums consult your instructor.
It is very important to ensure that the diffraction pattern you measure lies
along the horizontal line containing the hole punched in the screen. This
shows that the apparatus is correctly aligned.
Physics 1051
Laboratory #6
Diffraction
On Your Mark!
Measure the distance between the screen and the CD and record it
along with the associated uncertainty in Table 5 of your Activity Log.
As before carefully mark the centre positions of
the first and second order bright spots on the
screen. The zeroth order spot is located at the
hole in the screen.
Remove the screen from the
slot and measure the distance, D,
between each of the higher order
diffraction spots. Half this distance
to obtain the average distance, X, from
that spot to the zeroth order and
record them in Table 6 of your Activity
Log. Shown at right is the distance
between the two first order bright spots.
1st
zeroth order
D
2nd 1st
Qu ick Tim e™ a n d a
TIFF (U n com pressed) decompr essor
a r e needed to see th is pictu r e.
1st
2nd
zeroth order
(located at the hole)
Physics 1051
Laboratory #6
Diffraction
x
Using your trigonometry skills, calculate the diffraction
angles for all the spots you have measured.
θ
L
Calculations
Calculate the groove spacing, d, using the
diffraction equation and the information you
have just obtained for m=1 and m=2.
QUESTION 4: Calculate the average groove spacing of your
CD. Be sure to include the uncertainty and units.
Physics 1051
Laboratory #6
Diffraction
What did you learn?
Answer the following questions in your Activity Log.
QUESTION 5: What would happen to the interference pattern if you
increase the track width of the grooves on a CD? Why?
QUESTION 6: Why can a CD be used as a diffraction grating? That is, how
is a CD similar to a diffraction grating?
QUESTION 7: What is the smallest value of d for which an interference
pattern is produced? Could this interference pattern be
observed in our experimental setup? Explain.
Physics 1051
Laboratory #6
Diffraction
Wrap it up!
Check that you have completed all the Tables of your Activity Log.
Make sure that you have answered all the Questions completely,
Attached to your Activity Log should be your graph of path difference δ versus
order number m.