# CD Diffraction by fjhuangjun

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```									          Physics 1051   Laboratory #6   Diffraction

CD Diffraction
Physics 1051   Laboratory #6   Diffraction

Contents

Part I:   Introduction

Part II: The Diffraction Grating

Part III: CD Groove Spacing
Physics 1051          Laboratory #6            Diffraction

Part I: Introduction

n this lab a diffraction grating is used to determine the wavelength of a
laser pointer which is, in turn, used to determine the groove spacing of a
CD.

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.
Physics 1051           Laboratory #6   Diffraction

Apparatus
You should have been provided with:

•   Laser pointer
•   Metre sticks
•   CD
•   Diffraction Grating of known slit spacing
•   Mounting assembly
•   Some sheets of white paper

Caution: You will use a laser in this experiment.
If not used carefully, it may result in permanent eye damage.
Do not shine it in anyone’s face.
Do not point it around the room.
a a grade of 0 in the lab.
Physics 1051          Laboratory #6             Diffraction

Part II: The 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.

QUESTION 1:        Describe the appearance of the room lights when
looking through the diffraction grating. Explain the
appearance of the room lights.
Physics 1051             Laboratory #6   Diffraction

Setup: Determining the Wavelength
Place your laser pointer in the groove in the
base.
Determine the slit spacing, d, using the
number written on your diffraction grating.
Record this in Table 1 of your Activity Log.
d 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 2 of your Activity
Log.
Physics 1051            Laboratory #6                                                                                                                                      Diffraction

Shine the laser through the diffraction
grating and make sure you observe a                         Zeroth order
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
Q           u               i       c       k           T               i   m                   e           ™                   a           n           d               a

T   I   F       F           (   U       n           c           o       m                       p           r       e           s       s           e           d       )           d               e       c       o               m           p       r       e       s   s   o   r

a       r   e           n       e           e           d           e       d           t           o                   s       e           e           t       h           i       s               p           i   c       t   u       r       e       .

centre positions of at least 6 bright spots
on each side of the zeroth order spot.
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.
θ          Y
L
Measure the distance Y 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.
Physics 1051         Laboratory #6            Diffraction

Calculations continued

Using your trigonometry skills, calculate the diffraction angles θ
for all the spots you have measured and record them in Table 3.
Using the grating equation (refer to introduction), calculate the
path difference δ for all the angles you just obtained, and record
the values in Table 3 of your Activity Log.

Be sure you are using the right numbers in the diffraction
equation. You may need to refer to the introduction to recall what
each symbol represents.
Physics 1051            Laboratory #6               Diffraction

Graphical Analysis
Launch Graphical Analysis by clicking on the icon in the below and 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 the results in Table 4 of your Activity Log.
Before proceeding, have an instructor come check your graph, fit, and slope
Print the graph and include it with your Activity Log.
QUESTION 2:           Using the diffraction equation and the slope of your
graph, determine 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         When you look at the side with
we will inspect the diffraction pattern from your   the grooves in it you see a
rainbow spectrum. The rainbow
laser of known wavelength using the diffraction     spectrum is from the reflection
equation.                                           of white light that has been
diffracted.
CDs are reflective and therefore the diffraction
pattern can be observed by looking at the
reflected pattern.
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   Diffraction

CD Setup Photos
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
i.e. central spot reflects back through the hole.

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

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

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.

Measure the distance between the screen and the CD and record it
along with the associated uncertainty in Table 5 of your Activity Log.
Physics 1051          Laboratory #6                     Diffraction

As before carefully mark the centre positions of the first and                                                                                                                                                                                                                                                               1st
second order bright spots on the screen. The zeroth order spot is
located at the hole in the screen.
zeroth order

Remove the screen from the slot and
measure the distance, Y, between each of
the higher order diffraction spots.
Record these values in Table 6 of your
Activity Log.                                               Y
Halve this distance to obtain the average
Q           u               i       c       k           T               i   m                   e           ™                   a           n           d               a

T   I   F       F           (   U       n           c           o       m                       p           r       e           s       s           e           d       )           d               e       c       o               m           p       r       e       s   s   o   r

a       r   e           n       e           e           d           e       d           t           o                   s       e           e           t       h           i       s               p           i   c       t   u       r       e       .

distance, X, from that spot to the zeroth
order and record them in Table 6 of your
Activity Log.                                 2nd 1st                1st                                                                                                                                                                                                                      2nd
Shown at right is the distance between the
two first order bright spots.                         zeroth order
(located at the hole)
Physics 1051           Laboratory #6          Diffraction

Calculations

Using your trigonometry skills, calculate the diffraction

θ
angles for all the spots you have measured.

L
x
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.

You may approximate the uncertainty using
δdave/dave = δλ/λ+ δX1/X1+ δL/L
Physics 1051         Laboratory #6           Diffraction

What did you learn?

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 s 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.

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