UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
ATOMIC SPECTROSCOPY EXPERIMENT (ATM)
Version 2007.1 January 2007.1
Copyright © 2007 The Regents of the University of California. All rights reserved.
Watch the two videos on this experiment, Atomic Physics: Part 1 and Part 2.
Student's Name
Partner’s Name
Pre-lab Discussion Questions
It is your responsibility to discuss and answer the questions for this lab with a professor or GSI before
the first day of your scheduled laboratory period for the Pre-Lab Questions and on the 3rd & 5th
day of this experiment the answer the Mid-Lab Questions. This signed sheet must be included as
the first page of your report. Without it you will lose 1/3 of a letter grade for Pre-Lab and or MidLab. You should be prepared to do and discuss at least the following items before you come to
lab. If you find it difficult to find the proper texts and articles to refresh your memory, you may
find it useful to watch some of the online videos, which are designed specifically to help you in
this experiment. They are titled Energy Levels, Transitions, Light Sources and Detectors, Optical
Instruments, Atomic Physics. For the pre-lab, be prepared to do the following:
1. Draw an energy level diagram for hydrogen. Show the transitions which produce the Balmer
series. What is the formula that gives the wavelengths of these lines for the simple Bohr hydrogen
atom? How do the Bohr model and energy level derivation differ from the better quantum
mechanical methods?
2. Draw an energy level diagram for helium. Show the transitions which produce the red and yellow
lines. Note the differences between the energy level structures and splittings for hydrogen and
helium.
3. Draw an energy level diagram illustrating the Zeeman effect in the red line of helium. When a 1
tesla magnetic field is applied to helium, what happens to levels and transitions that produce the
red line of helium?
4. Draw a sketch of the diffraction grating spectrometer showing the placing of the optical elements
and the path and focussing of the light as it goes from the source through the spectrometer and to
the film or photomultiplier. Explain how the grating functions. Calculate a representative value for
the resolving power.
5. Draw a sketch of the Fabry-Perot interferometer showing the placing of the optical elements and
the path of the light as it goes from the source through the interferometer and through the
telescope. Calculate the resolving power. Why is it necessary to use the interferometer instead of
the grating when observing the Zeeman Effect?
Staff Signature
Completed on the first day of lab? (circle)
Date
Yes / No
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
Mid-lab Reviews
On day 3 of this lab, you should have successfully produced a photograph and a strip-chart plot of the
Balmer-series lines, and made an estimate of the Rydberg constant. Show them to a GSI and ask for a
signature.
Staff Signature
Completed on the third day of lab?
Date
(circle)
Yes / No
On day 5 of this lab, you should have successfully observed the Zeeman splittings of the helium lines
and estimated a value for the Bohr magneton. Demonstrate this to an instructor and ask for a signature.
Staff Signature
Completed on the fifth day of lab?
Date
(circle)
Yes / No
INCLUDE THESE SHEETS AS THE FIRST PAGES OF YOUR REPORT
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
Physics 111 Advanced Lab
ATM 2007.1
Student Evaluation of Experiment
Now that you have completed this experiment, we would appreciate your comments. Please take a few
moments to answer the questions below, and feel free to add any other comments. Since you have just
finished the experiment it is your critique that will be the most helpful. Your thoughts and suggestions will
help to change the lab and improve the experiments.
Please be as specific as possible, using both sides of the paper as needed, and turn this in with your report.
Thank you!
Experiment name: ___________________________________________
Date: ______________
How was the write-up for this experiment? How could it be improved?
How easily did you get started with the experiment? What sources of information were most/least helpful in
getting started? Were the reprints appropriate? Did the Pre-lab discussion help? Did you need to go outside
the course materials for assistance? What additional materials could you have used?
What did you like and/or dislike about the experiment?
Would you recommend this lab to fellow student? Why or why not?
What advice would you give to a friend just starting this experiment?
If the course materials were available over the Internet (WWW, FTP, etc), would you (a) have access to
them and (b) would you prefer to use them this way?
Please circle the abbreviations of the other labs you
have done.
ATM BRA BIO
COM CO2 GMA HAL
HOL
JOS
LIF
LLS
MNO MUO
SHE
NLD
NMR
RUT
OPT
Overall quality of this experiment?
1
Poor
2
3
4
Average
5
Good
XRA
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
ATOMIC SPECTROSCOPY EXPERIMENT
I.
REFERENCES
111-LAB Reprints:
1. "Atomic Spectra & Atomic Structure", Herzberg, Gerhard; Dower Publisher, 1944, New York.
Preface +pp. 1-257. #QC451.H43; This is an old text, but gives a good perspective on how the
theory developed.
2. "Ultraviolet Radiation, "Black" and Otherwise", Scherberger, R.F.; Eastman Organic Chemical
Bulletin: vol. 49, No. 2, 1977, pp. 1-2.
3. Harnwell, G.P., and Livingood, J.J., Experimental Atomic Physics, Chapter 7--"Line Spectra", 1st
edition, McGraw-Hill, pp.224-288. #QC173.H38.
4. Jenkins, Francis Arthur, Fundamental of Optics, Chapter 14--"Interference Involving Multiple
Reflections", 4th ed., McGraw-Hill, 1976, pp.286-314. #QC355.2.J461.
5. Fowles, Grant R. Introduction to Modern Optics, "Quantum Mechanics of the Hydrogen Atom",
Chapter 7.5, pp. 235-242. #QC356.F65
6. "Experiments in Modern Physics" by Melisinos cp.1966; pp. 280-327. #QC33.M4
7. "Magneto-Optics and Electronics ", Chapter 32, Fundamental of Optics, 4th ed. Jenkins F.A. & White
H.E., 1957. Pp. 679-686. #QC356.J4
8. RCA Photo Multiplier Tube (PMT) Manual
Other References:
9. “Introduction to Atomic Spectra”, H. E. White,. This classic text was written by one of our own
faculty members, and is still useful after 65 years.
10. “Optics”,Hecht and A. Zajac, Optics.
11. “Atomic Energy Levels and Grotrian Diagrams”, Bashkin and J. M. Stoner,
12. “Atomic Energy Levels”, C. M. Sitterly, (1949). Easiest place to find exact values of energy levels
and transition energies for the red and yellow lines of helium.
13. “An Introduction to Error Analysis”, John Taylor, , 2nd Edition Essential for data analysis.
14. o; “Experiments in Modern Physics”, A. C. Melissinos and Jim Napolitan 2nd Edition
II. INTRODUCTION
Atomic spectroscopy is the field of physics that was the proving ground for the quantum mechanics
of atoms and their energy level structures. In this experiment we observe the atomic spectra of hydrogen,
helium, and mercury, and correlate the data with known energy levels.
It is important that you become familiar with light sources, geometrical optics (how to get light into
the spectrometer), learn a little about diffraction, actually see what the spectra look like, and record each
spectrum photographically and photoelectrically. See Appendix A in the back of this manual.
Your report—written or oral—should include enough physics to make the experiment
understandable to one of your classmates who has not done the experiment, and enough experimental
details to show that you have done all the right things. Include photographs, recorder traces, diagrams,
and whatever else is needed for clarity and completeness. Your written report should include answers to
all the Pre-Lab questions.
Spectroscopy predates quantum theory, so some of the diagrams you see in early texts are not
labeled correctly. Look for simplicity and correctness which you can check with current quantum
mechanics books.
We think of an isolated atom as having an energy level structure described by the quantized energies
that its outermost or optical electron can assume. When this electron is excited by collisions or by
electromagnetic radiation, the atom emits radiation of characteristic wavelengths when the electron
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
returns to its unexcited state. These characteristic wavelengths are called spectral lines, because they
appear as sharp lines when the radiation is examined with a spectrometer. We say that when an atom
makes a transition between two energy levels it emits a spectral line. In principle we can use quantum
mechanics to calculate these energy levels if we can write down the proper Hamiltonian.
When the atom is placed in a magnetic field a new term is added to the Hamiltonian. It is a
perturbation which splits each energy level into several levels, called Zeeman levels after a Dutch
physicist. The optical electron circulating around the nucleus is like a rmagnetic dipole in a magnetic field,
r
and the energy added by an external magnetic field is therefore – μ ⋅ B . Each different orientation results
in a different energy, and a single level is split into as many levels as there are orientations of the dipole
in the field. The splitting energy is much less than the energy difference between the two energy levels
which produce a spectrum line. A classical description would have a continuous distribution of
orientations, but a quantum mechanical description allows only a finite number of possible orientations.
When an atom in an external magnetic field is excited and then radiates energy, a single spectral line
becomes several spectral lines spaced very close together, with spacings which are characteristic of the
magnetic moment of the electron and the magnetic field strength. This splitting of spectral lines in a
magnetic field is called the Zeeman effect. The radiation of these lines is elliptically polarized. When the
radiation is viewed perpendicularly to the magnetic field, some lines are linearly polarized parallel to the
field direction, and the others perpendicularly to the field direction. When viewed parallel to the field,
some lines are right circularly polarized, the others left circularly polarized, and some are missing
entirely. Linear and circular polarizations are special cases of elliptical polarization.
From your experience with quantum mechanics you will note that perturbations are only
approximately linear, and are not always simply calculable as implied above, especially when the
perturbation energy becomes comparable to other energies in the Hamiltonian. We will only work with
the linear Zeeman effect here. Also, in the early days of the Zeeman effect, the terms "normal" and
"anomalous" were used, but not any longer except in an historical approach in physics texts.
The key to the explanation of the Zeeman effect lies in how the magnetic moment of the atomic
electron is related to its mechanical angular momentum. Qualitatively, the magnetic moment is given by
r
μ=
r
r
e
g j , where j is the total angular momentum and g is the Lande g-factor which relates the
2me
magnetic moment to the angular momentum.
r r The energy levels are then split into as many levels as the
quantum mechanical scalar product j ⋅ B can have. The product looks like μ 0 gm j B , where
μ 0 ≡ eh / 2 me is called the Bohr magneton. The symbol m j represents the magnetic quantum number,
and has half-integral values between –j and +j. The extra energy resulting from the magnetic field is
ΔE = μ0 gmj B
Many atoms, such as helium, have more than one optical electron, in which case the angular
momentum symbol is an upper case J, and the quantum number MJ can be integral or half-integral,
depending upon whether the number of optical electrons is even or odd.
III. PREPARATION: BALMER SERIES
A. 1.
Draw an energy level diagram of hydrogen and show the Balmer series transitions with their
corresponding wavelengths and energies. Show what the spectrum ought to look like. You can
construct the principal levels from the simple energy expression for hydrogen which you learned
in quantum mechanics class, but other texts show more complete diagrams with the angular
momentum states designated. References are books by Bashkin & Stoner, Herzberg, and White,
and the tabulation by Sitterly (see REFERENCES). Refer to the CRC Handbook for wavelengths
and relative intensities. You may need to review spectroscopic notation.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
A. 2.
ATM 2007.1
Draw an energy level diagram of mercury and show the transitions likely to be observable
(yellow, green, blue, and violet lines).
You could make a copy of all these diagrams out of books, but they have so much detail you
would lose sight of only the few lines it is possible to observe in a simple experiment. Keep your
diagrams simple.
B. Read carefully the operating instructions for the spectrometer in Appendix I. This is a very expensive
piece of equipment, and the instructions are simple enough that there should be no reason for causing
damage! Be sure to pay particular attention to the cautions listed. If you have to force something the
slightest bit on this piece of equipment, something is not right. Ask someone how to turn a knob if it
doesn't want to turn. Also note that our spectrometer has a grating of 300 grooves/mm. Multiply the
dial number by 6 to get the correct wavelength.
C. Read about the function and operation of the photomultiplier tube (PMT) in any text on radiation
detection and measurement. (See, for example, Knoll in the laboratory or RCA PMT Manual).
IV. PROCEDURE: BALMER SERIES
A. Look over the equipment and locate the spectrometer, light sources, photomultiplier tube (PMT),
power supply, and digital multimeter.
The spectrometer disperses the light into its various colors and forms an image of the entrance slip, in
light of each color in the source. The spectrometer has two sets of optics: one set forms images, and
the other disperses the light - spreads it out with each color of light traveling in a different direction
from all the others. The dispersing element in our spectrometer is a diffraction grating. The image forming optics are two concave mirrors. Light from an entrance slit which acts as the source of light
is collimated by the first mirror (the slit is at the focal plane of the mirror) and directed toward the
grating. The grating disperses the light and reflects it back to the second mirror, which in turn
focuses the light on the exit slit at the photomultiplier detector or onto the Polaroid film, depending
on which way the plane mirror is positioned.
Now be very careful, and take the top off the spectrometer - unscrew the black knobs; they don't
come off, but get very loose. Lift off the top. Do not touch or breathe directly on the mirrors or
grating - your breath is full of noxious chemicals which stick to glass and aluminum surfaces and
make them cloudy. Locate the entrance and exit slits, collimating and camera mirrors, and grating.
Observe how the grating turns as the wavelength region is changed. Replace the top. It may help to
draw a sketch to see just where the light is going, and why.
B. Turn on the scope that is set up to monitor the output of the photomultiplier tube (PMT).On the
Power Supply make sure that the HIGH VOLTAGE switch is on STDBY, that the POLARITY
switch is set to NEGATIVE, and that the voltage is set to 1000 volts. You may have to change this
voltage later, but do not exceed 1500 volts! Turn on the Power Supply, and when the STDBY/RESET
light comes up, switch the voltage on.
C. 1. Wear the plastic safety goggles, although none of the radiation is dangerous.
Turn on the mercury lamp and place it about 30 cm from the slit. Open the entrance slit to about 1
mm. Open the shutter by turning the shiny elbow until it points toward the source.
Set the spectrometer wavelength to zero (for zeroth order diffraction). Remember that in order to
change the wavelength setting manually, you must set the SPEED CONTROL KNOB between
any two settings. To do this, pull the SPEED CONTROL KNOB out and then turn it half way
between any two settings.
Set the diverter mirror to the film holder position "S" (to the right) and look at the diffracted light
– put your eye where the polaroid film will be placed. You may have to move your head around
in front of the film holder in order to bring the line into view. You should see a blue line at the
center of the film holder (change the grating angle if it is not).
Copyright © 2007 The Regents of the University of California. All rights reserved.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
Position the light source on the spectrometer axis by moving it sideways until the blue line is in
the center of the diffraction grating. If there is not enough light to see the grating outline, take off
the spectrometer cover.
Put up a lens between the source and the slit and focus the light from the source on the slit. The
blue line should now be expanded to cover the entire grating. If it is not, ask an instructor to help
you. The source is now properly positioned for observing spectra.
To see a spectrum line, you must move your eye back away from the film holder until you can
focus on the position where the film will be. Or, you can use another lens as a magnifier by
placing it between your eye and the film holder. It may help to draw a picture of the optics, to be
sure you understand what is happening.
Observe the effect of varying the entrance slit width by using the micrometer on the top of the
entrance housing, but don't worry about setting it for now.
C. 2. Switch the diverter mirror to the PMT position ("O", to the left), and look at the output of the
PMT. The source lamps run on AC, and therefore the light output is modulated at 120 Hz; we can
see the output of the PMT modulated as well.
You may have to decrease the wavelength setting slightly to get the light into the PMT. What
does this tell you about the calibration of the spectrometer? Observe the effects of varying the
position of the light source, lens, slit width, and high voltage (not exceeding 1500V). Everything
is positioned properly when your output is a maximum, but is not "clipped."
C. 3. Switch the diverter mirror back to the film holder position, and increase the wavelength setting
until you see sharp lines in the visible spectrum of mercury corresponding to first order
diffraction. The counter should read about 610. Now choose the proper slit width. There is a way
to calculate it on the basis of theory, but in practice you simply want narrow yet bright lines. Too
large a slit gives bright lines that have a rectangular profile, while too narrow gives the proper
line shape (Gaussian) but with reduced intensity. Observe the effects of a slit width that is too
narrow or too wide, but end up with a choice that will give you good pictures. Once you have
made a choice, you should set the micrometer on the PMT housing to the same width.
D. 1. Photograph the mercury spectrum. Use the Polaroid 4X5 sheet camera available. Instructions for
loading the film are below; you should put the camera in the camera holder before you load the
film. You will have to choose a way to start and stop exposures to the film. Remember to change
the position of the film by about 10 mm between each exposure, increasing exposure times as
suggested below. You should get no fewer than three exposures on each piece of film, and you
should be able easily to get five to six. Keep in mind that you will want to compare this mercury
spectrum to the hydrogen spectrum, so record any information necessary to do this before
changing any settings. Try different exposure times, something like 1 sec, 3 sec, 10 sec (increase
times by a factor of 3 with each exposure), changing the position of the film by about 10mm for
each exposure. Identify and label the wavelengths of the most prominent lines, referring to the
references for these wavelengths.
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Page 7 of 25
UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
Exit slit shown to the right without camera mounted.
Slide the camera down into the holder with the develop
leveler outward toward you.
Below is the correct mounting of the camera into the holder.
4 inch x 5 inch sheet film Polaroid Camera
See top shinny level it is in the L = Load position; you load the film in this postion only.
Load the film: Hold film with the words "THIS SIDE TOWARD LENS" toward the source of the
light. If you put the film in wrong then call for help from one of the Staff.
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Page 8 of 25
UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
Push the film into the top end of the camera all the way down untill it stops. Note: take care not to
buckle the film. The film should be even with the top of the camera.
To take a picture: Now withdraw the outer envelope, the outer paper envelope covers the film
negative, untill it comes to a stop. The number 57 should now be fully visible, DO NOT pull it
any out any further. Now open and close the shutter manually to expose the film; i.e., you should
have at least four to six exposure lines on each piece of film. See example below.
Example below of five different exposures and the labelling of the lines on the photo. What
numbers should you use to label them? Below is only an example.
Now that you have exposed the film, reinsert the film envelope cover carefully until the end of
the envelope is even once again with the top of the camera. Now move the develope level to the
"P" position. Firmly hold down the camera with your left thumb at the "L" position and then hold
the film packet firmly with your right hand thumb and forefinger and and pull the film all the way
out. Pull smoothly at medium speed, without slowing down or stopping. You will feel a slight
resistance toward the end as the metal end reaches the rollers. Now the film will develop in about
30 seconds, don't forget to coat thefilm with the coaters provided.
D. 2. Use the LabView automatic scan drive and chart recorder to record the mercury spectrum. The
output of the PMT should be fed into the two wire sens ”HI” and “LO” inputs of the DMM. Be
sure that the terminator is attached on the BNC tee at the DMM input. Open the ATM chart
recorder VI for Labview. The computer does not control the power to the drive motor on the
spectrometer. You will need to enter the initial wavelength counter reading on the spectrometer
into the program and select the appropriate scan speed. It is recommended that you start the
spectrometer scan a few Angstroms away from your intended starting wavelength. As the
spectrometer reaches your wavelength, press the Start button to begin collection data. Before you
actually take a recording, look at the output of the PMT on the scope. Remember that your
signals should not be clipped, and that your resolution should be good enough to make out the
features of the spectrum. Make sure that your signal does not exceed the maximum range for the
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
DMM. Identify the lines with their wavelengths, and determine a correction factor for the dial
readings.
Wavelength Calibration
The wavelength scale on the spectrometer is only good to a few nanometers at worst. You can use
mercury lines to correct for scale errors. Set up the mercury lamp; get a strong mercury line and adjust
the spectrometer until the line is centered in the exit slit; the signal on the oscilloscope will be a max.
Record the scale reading, and compare with the wavelengths given below. Repeat for other mercury
lines.
When you do the Balmer lines, set each one in turn to a max on the oscilloscope. You can also look at the
strip chart recorder graph output on the computer, and calibrate it. This method is probably better for the
very weak lines.
Traditionally, wavelengths in air are measured. To use the Balmer series equation you must convert the
wavelengths you measure into wavelengths in vacuum. You can do this by using the index of refraction
of air, given by
2
2
n = 1 + 6432.8 x 10–8 + 2929810/(146 x 108 – σ ) + 25540/(41 x 108 – σ )
where sigma is the reciprocal of the wavelength in vacuum, called the wavenumber, in units of reciprocal
centimeters cm–1.
Another way is to use a table converting air wavelengths to vacuum wavenumbers (σ). Table of
Wavenumbers, Volume 1, NBS Monograph 3, May 2, 1960.
Think before you do anything, because some errors are so small as to be insignificant.
Mercury wavelengths in air and wavenumbers in vacuum
Red
6149.50
Yellow
5790.66
Yellow
5969.60
Green
5460.74
Blue
4358.33
Blue-violet
4046.56
16 256.986
17 264.401
17 327.439
18 307.479
22 938.156
24 705.376
Helium
Red
Yellow
6678.15
5875.62
14 970.074
17 013.752
6562.72
4861.33
4340.47
4101.74
3970.072
3889.049
3835.384
15 233.377
20 564.758
23 032.505
24 373.020
25 181.336
25 705.931
26 065.615
Hydrogen
alpha
beta
gamma
delta
epsilon
E. 1. Set up the hydrogen source. Record the lines in the spectrum (photograph and chart), and measure
their wavelengths by using the spectrometer readout calibrated as mentioned above. You should
be able to see at least SIX lines in the Balmer series. Check with an instructor if you cannot.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
E. 2. Identify lines of the Balmer series and make a plot of 1/λ vs. 1/n2. Fit the plotted points to a line,
determine the Rydberg constant and the series limit, and estimate their errors. Follow the example
given in Section 2.9, page 63, of Lyons. Do not neglect this error-analysis treatment of your data.
Spectrum of Mercury
1
0.1
Intensity
0.01
0.001
0.0001
0.00001
0.000001
350.00
400.00
450.00
500.00
550.00
600.00
Wavelength (nm)
V. ADDITIONAL QUESTIONS: BALMER SERIES
A. What elements in the equipment set upper and lower limits on the wavelengths that can be observed?
What are these limits?
B. Calculate the dispersion and resolution of the spectrometer when used in the first order at a
wavelength of 546.1 nm (mercury green line). The parameters of the spectrometer are given in the
manufacturer's manual. Compare to the dispersion on your photograph, and to the dispersion and
resolution on the strip chart record.
VI. PREPARATION: ZEEMAN EFFECT
Let us take a specific example of the Zeeman effect. We will draw an energy level diagram, show the
splittings of the levels, show the spectral lines emitted and their polarizations when viewed perpendicular
to the magnetic field. Refer to figure 1 on the following page.
At this point we need to get an idea of the magnitude of the Zeeman effect. It is derived from the
following: νλ = c energy E = hν = hc / λ = hcσ , where σ = 1 / λ is called the wavenumber, given in
reciprocal centimeters, 1/cm or cm–1. Because E ∝ σ , it is an accepted practice to use cm–1 as the unit of
energy. An increment of energy is then Δσ , and the energy of Zeeman splittings is Δ σ = g mj L B .
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
–5
ATM 2007.1
–1
Here L is called the Lorentz unit and is approximately 5 x 10 cm /gauss. One electron volt is
approximately 8000 cm–1. [Look up all the exact numbers before you make any calculations]. For
example, if we have a field of one tesla, a g-factor of 1.5, and a J-value of 2, we have a level split into 5
components, each one 0.75 cm-1 from its neighbor. For practice, compute the separations of the Zeeman
lines shown in the Figure below. You will see that the line separations are less than the level separations,
because it is the difference in g-factors that is important.
Fig 1: Structure of the Zeeman multiplet arising in a transition from a 3S1 to a 3P2 level.
The mercury green line at 546.1 nm is an example of such a transition. [after Melissinos, p. 294]
Can we observe the Zeeman lines, in a practical case? Yes, if the lines are separated by more than
their widths, and if we have a spectrometer of high enough resolution. A spectrum line has finite width (a
frequency spread) because the energy levels are not infinitesimally sharp (natural width) and because the
atoms are in thermal motion (doppler width). The doppler width is by far the larger in ordinary light
−7
sources, and has an approximate magnitude of 7 × 10 σ T / M , where T is the absolute temperature
and M is the gram atomic weight. For example, the green line mercury at 546.1 nm in a discharge tube at
room temperature has a doppler width of 0.016 cm-1. (Run through this calculation yourself–it will give
you good practice in juggling units).
Your goals for this lab are to see the Zeeman effect in action and to learn something about the FabryPerot interferometer. Experimentally this is one of the easiest labs to perform, but treat it as an
opportunity to learn more about the realities of quantum physics. Take the time to do a good job and to
understand fully what is going on. And don't leave your calculations and write-up until the last minute
just because you think they will be easy; many students err here and receive poor grades on this easy lab
just because they are rushed at the end. The same applies to presenting your oral report. There are lots of
good quantum questions that can be asked.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
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VII. APPARATUS: ZEEMAN EFFECT
A. To observe the Zeeman effect we must put a light source in a magnetic field and observe the radiation
with a spectrometer which will resolve the Zeeman lines. We are going to use a discharge tube, an
ordinary electromagnet with iron pole pieces, a lens, a Fabry-Perot interferometer, and a telescope,
arranged as shown in Figure 2.
Fig 2: Apparatus
The lens is present merely to get light into the interferometer; it plays no part in resolving the
spectrum lines. The interferometer forms fringes at infinity, as will be discussed below, and the
telescope is used to magnify and view these fringes. It is possible to dispense with the telescope if
you can focus your eyes at infinity but the fringes will look smaller and be harder to see.
B. The Fabry-Perot interferometer (see Ref. 3). Also look at Video #27 Optical Instruments.
The Fabry-Perot interferometer works on the principle of multiple amplitude division of a wavefront
and recombination of these wavefronts, each of which has traveled a different optical path length. We
can represent these wavefronts by rays, as shown in figure 3.
Fig 3: Fabry-Perot interferometer
The interferometer itself is nothing but two plane parallel partially-reflecting films. In our case they
are multi-layer dielectric coated mirrors supported on two flat quartz discs, called plates, or
substrates.
The optical path difference between two adjacent rays is δ = 2t cos θ , and the order
of interference n is this path difference divided by the wavelength. When all the rays
are added together, the intensity distribution is
I=
I0
,
4R
2 Δ
1+
sin
2
(1− R)2
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
where Δ = 2π
ATM 2007.1
2t cos θ
λ
is the phase difference between adjacent rays, and R is the reflectance of a single coating. The
interference fringes are circles. The smallest wavenumber difference (energy) that can be resolved is
given by
δσ =
1
,
2tN R
where NR = π
R
.
1−R
There is also a wavenumber interval called the free spectral range, the wavenumber difference in two
lines which will give a ring of exactly the same radius (fringes at the same angle theta, but differing in
order by 1. It is also approximately the reciprocal of the path difference between adjacent fringes of
the same wavelength.
The F-P interferometer used in this experiment is a very precise and expensive piece of equipment.
Do not touch its optical surfaces or attempt to clean it—if you think it's dirty, ask the staff for
assistance. The only adjustments you need make are are its horizontal and vertical orientations,
controlled by the two large graticulated knobs. Its spacing “t” is 8.11 mm, and its reflectance R is
0.90.
VIII. EXPERIMENT: ZEEMAN EFFECT
A. Procedure
1. Before you turn on the helium lamp, turn on the cooling air. If the lamp gets too hot it breaks.
The air valve is located in 286 LeConte on the east wall next to the BSC parts—it should be
adjusted so that the indicator ball is between 40 and 50 on the scale.
2. Make sure that the black POWERSTAT is set to zero, and then turn it on.
3. Then turn on the box marked 'HIGH VOLTAGE'. Increase the voltage on the POWERSTAT until
the He tube begins to glow brightly.
4. The Fabry-Perot interferometer is already adjusted. The plates are flat and parallel to a fraction of
a wavelength .
5. Set up the optical system with the helium lamp as shown above, but without the red filter, and
adjust the position of the lens until you see sharp circular fringes in the telescope. Make sure that
the lamp cooling air is on and watch the lamp carefully; if it gets too hot, it will melt.
6. Observe, record, and explain what happens when you do the following, using your eye without
the telescope; move the position of the lens; tilt the F-P plates; raise and lower the interferometer.
With the telescope in place, change the position of the telescope; shift the telescope sideways.
7. Put in the red glass filter; adjust the system until the fringes are sharp. Turn on the magnetic
field. To control it, use the LAMBDA DC POWER SUPPLY. Turn the OUTPUT VOLTAGE
VDC knob to zero, and the CURRENT LIMITER IDC knob to 2 Amps. Turn on the power
supply. Increase the VDC control until you see the fringes start to split. If the lamp flickers or
goes out, increase the voltage on the POWERSTAT. Can you explain why this happens? The
lamp is just a tube filled with He gas, and electrons are accelerated through the tube by an electric
field from the high voltage. As they travel through the tube, they collide with He atoms, and
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
excite them. When these de-excite, they emit the characteristic He lines. Now what happens when
we add a transverse magnetic field? Rotate the polarizer and note the behavior of the lines. Don't
be discouraged if you see fuzzy fringes and bizarre behavior. With a little experience your skill
will improve until you can produce and see the proper Zeeman effects.
8. Rotate the polarizer until only the sigma components are observed; increase the field strength
until the fringes show equal spacings between the rings. What fraction of an order did the
magnetic field shift the frequencies of the Zeeman components of the line? [1/2, 1/3, 1/4, or ? We
take one order to be the spacing between two unsplit lines – no magnetic field.] Repeat several
times, so you can make some estimate of the error in your measurements. Measure the magnetic
field strength with the gaussmeter. The He discharge tube is mounted on a track so that you can
slide it back out of the center region of the magnet and position the meter probe where the tube
usually sits.
Before taking any readings with the gaussmeter, zero it by using the Zero Gauss Chamber located
in the unit, and the Zero Adjust and Differential Zero Balance knobs, and then calibrate it using
the 1000 gauss Probe Reference Magnet and the Calibrate and Differential Zero Balance knobs.
You may have to repeat both steps several times in order to have the meter both zeroed and
calibrated correctly. Make sure that you calibrate the meter on the scale that you will use to make
your measurements.
9. Turn the magnet through 90 degrees, and look at the lamp through the hole in the pole piece. What is
the effect of removing the Polaroid?
Setup the Video Camera:
10. After you have the Zeeman apparatus set up, you can get an even better view of the fringes (and take
some snapshots for your write-up) by replacing the telescope with a zoom lens and video camera.
Attach the camera to the FireWire cable and run Prosilica Viewer on the PC from the start menu.
(You will need to turn the computer monitor around 180 degrees to see what you are doing.)
Temporarily remove the filter, lens, polarizer, and interferometer and line the camera up on the
window in the center of the electromagnet. Then put all of the other optics back in place and align
each component vertically with the aid of the camera. Zoom out all the way and set the focus to
infinity. You can use the micrometer adjustment knobs on the Fabry-Perot mount to center the fringes
in the field of the camera.
Select Camera->Controls from the Prosilica Viewer menu. Click the 'Auto Expose' button to have the
computer set a reasonable exposure time. If you select the 'Auto' button in the exposure controls, the
computer will continually adjust the exposure for a decent picture. (This is often useful, but
sometimes produces an annoying flicker. Use manual exposure if the image flickers badly.) You can
increase the gain of the camera by selecting the 'ADC' tab of the camera control window. It is best to
leave the gain as low as possible since camera noise increases with gain.
To take a snapshot, select Camera->Snapshot and then select the snapshot window from the View
menu. Save the snapshot as a tiff file in your 'My Documents' folder by selecting File->Save.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
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Fig 4: Captured Image From Fabry Perot Interferometer
B. Calculations
1. Using your observations, calculate the ratio of energy level splitting to magnetic field, expressed
in cm–1/gauss. Always use these units. While others such as joules/gauss are correct, they are
never used by practicing spectroscopists. Compare to the value of the Bohr magneton based on
universal constants (m, e, h, etc.). The thickness of the spacer is 8.11 mm, and its reflectance R is
0.90
C. Something more complex and interesting (and yes, a required part of this lab)
D. Use the spectrometer to see what lines are actually present in helium. Set up the system to use the
prism spectrometer as a filter to isolate the red, yellow, and blue lines, and observe the splitting
with the interferometer.
The trick here is to focus the light from the lamp on the slit of the prism spectrometer and
opening the slit up all the way to let in as much light as possible. Then closing it down to see the
yellow line in the center of the eyepiece.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
Setup using the Prism Spectrometer
1. Find the levels which give rise to the 587.56 nm lines of helium. Work out the Zeeman pattern
thoroughly enough to show you understand the problems. You will need to check out the
magnitudes of the triplet splittings. Use the spectrometer together with the interferometer to
observe the Zeeman effect in this line, and compare to the calculated pattern. Why don't you see a
clear pattern? Can you still see polarization effects? Originally Zeeman did not have enough
resolution or magnetic field to see components clearly, but only slight polarization effects in the
wings of the line.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
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APPENDIX I
Sections of the Operating Instructions ARC Model AM-505 Atmospheric Monochromator
SECTION III: OPERATION
3.1. Bilateral Slit Assemblies
Slit Width: The slit width of each bilateral slit assembly is adjustable from 0.005 mm to 3 mm (5 to
3,000 microns), by a micrometer knob located on the slit housing. The knob is graduated in 0.01
millimeter (10 micron) increments.
One counterclockwise revolution of the micrometer knob increases the slit width 0.25 mm (250
microns). For maximum reproducibility the slit width should be set in a counterclockwise direction
(increasing slit widths) each time it is changed.
The micrometer knob should not be rotated below a reading of 0.05 or above a reading of 3.00. A
micrometer setting of less than 0.005 mm (5 microns) should not be used, because a stop is
provided to prevent the jaws from touching each other.
3.2. Wavelength Indicator
A five-digit mechanical counter is mounted on the side of the instrument housing, and indicates the
wavelength at the exit slit in Angstrom units when a 1800 G/mm grating is used. For other grating
groove spacings, simply factor the counter reading in an inverse proportion to the change in groove
spacing. For example, if a 300 G/mm grating is installed, the counter reading must be multiplied by
six to obtain the correct wavelength at the exit slit.
[***Note: the grating installed in the monochromator in 111-Lab has 300 G/mm.***].
3.3. Manual Scanning Drive
A manual scanning knob is located in the side of the instrument housing, adjacent to the
Wavelength Indicator. One revolution of this knob changes the wavelength by 20 Angstroms when
a 1800 G/mm grating is installed.
NOTE: The speed control knob must be disengaged - placed between any two speed positions before turning the manual scan knob. To change the speed control knob, first pull it out and then
turn it.
CAUTION: Do not force Manual Scanning Knob. Do not scan below a counter reading of 99990
(equivalent to -10), or above a counter reading of 8000.
3.4. Synchronous Motor Scanning Drive
A synchronous motor with a ten-speed transmission provides scanning speeds from 1 to 1000
Angstroms/minute. The various speeds are controlled by a speed control knob located on the side of
the instrument housing. The speed control knob is labeled with the scanning speed directly in
Angstroms per minute with a 1800 G/mm grating installed. For other grating groove spacings,
factor the speeds in the same manner as the wavelength counter. To set the desired speed knob
position, pull the speed control knob out and rotate until the desired position is in line with the dot
on the instrument housing; release the knob to engage the transmission. To scan manually, set the
speed control knob between any two speed positions.
A scan power and direction switch is also located on the side of the instrument housing. The switch
is labeled "H" (higher), "OFF" and "L" (lower).
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
ATM 2007.1
To scan to lower wavelengths move the scan switch to the "L" position, and to scan toward higher
wavelengths move to the "H" position. Scans should be made to higher wavelengths for maximum
reproducibility and accuracy.
3.5. Moveable Diverter Mirror
A moveable diverter mirror directs the beam either straight through, "O" position, to the PMT, or to
the side slit in the "S" position. A knob on the top of the instrument indexes the mirror to either the
"O" or "S" position. To change the mirror position, gently rotate the knob to the desired "S" or "O"
position; a click will be heard and felt when the mirror indexes into position.
***FOR FURTHER INFORMATION, SEE THE COMPLETE MANUAL IN THE 111-LAB
(ATM) Atomic Spectroscopy REPRINTS on reserve in the Physics Library or online.***
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Appendix A
OPTICS
An understanding of optics and optical instruments is required for ATM, CO2, HOL, LIF, and
MNO. In each case, the text by Melissinos is an excellent exposition for specific instruments.
The best general reference is Jenkins and White, Principles of Optics, although any current
optics book is of help, including some at the sophomore physics level.
LENSES
We need a lens when we want to form an image of an object. Here’s what you should know
about lenses. The correct singular spelling is lens, although the plural is lenses.
Positive lenses can form real images, as in a camera.
M+
M−
A lens has a focal length, which can be found by forming an image of a distant object, such as
the sun, and measuring the distance from the lens to the image. The focal plane is a plane
perpendicular to the axis and placed at the focal length away from the lens. Off axis objects are
focused on the focal plane.
diameter D
F
F
focal plane
f
f /# = f /D
The ratio of the focal length to the diameter of the lens is a measure of how “fast” the lens is,
which can be thought of as how much light the lens collects. For example, a lens 50 mm in
diameter with a focal length of 250 mm is called an “f five lens”, or to have an “f-number of
five”, written f/5.
i
I
object
o
O
O
F image
I
F
o
i
The relationship between focal length, object distance, and image distance is given by
1/o + 1/i = 1/f. To form a real image, o must be greater than f. A real image is inverted, upside
down, when compared to the object. The ratio of object size to image size is i/o. The smallest
distance between object and image is 4f – four times the focal length.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
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The quality of the image – how accurately it represents the object – depends on the type of lens
and on its f/number. A simple single element lens suffers from spherical aberration. Light
passing through the outer zone (near the outer edge) of the lens has a shorter focal length than
light passing through the central zone or portion of the lens. As a consequence, the image is
fuzzy when a large f/number single element lens is used to form an image.
F (central rays)
F
(outer rays)
A single element lens also suffers from chromatic aberration. Different colors of light have
different focal lengths – blue the shortest, red the longest. Every image has a colored halo around
it, although often it is not noticeable.
white
violet
red
An achromatic doublet lens has two elements cemented together, one a positive lens and the
other a negative lens. The chromatic aberration is almost completely corrected for, and at the
same time spherical aberration is reduced nearly to zero. Whenever possible, use achromatic
doublets.
The drawings illustrate how a lens might be used. Calculate in advance where a lens should be
placed, but remember that the final placement is always determined experimentally.
MIRRORS
Optically speaking, mirrors and lenses are interchangeable. Take any given positive lens, split it
in half, coat the flat surface with a reflecting material, and you have the equivalent of a concave
mirror. The focusing properties are the same, the equation 1/o + 1/i = 1/f is the same. The light
path is the same except that it is folded. BUT, a mirror has spherical aberration, which is not
easily correctible, and it has no chromatic aberration (an important advantage)
O
F
I
SPECTROMETERS
A spectrometer is used to discover what frequencies or wavelengths are present in radiation. It
contains a dispersive element, which separates out radiation according to frequency, often by
changing the direction of propagation of some other parameter of the light to make the separation
observable.
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For example, white light incident on a prism is dispersed at different angles according to the
wavelengths present in the radiation, as illustrated. A single ray is deviated according to
wavenumber, with red deviated the least and violet the most in the visible spectrum.
red
red
white
violet
red
violet
violet
When a wavefront rather than a ray is incident on the prism, the dispersed wavefronts overlap, so
an optical system is necessary to separate the dispersed wavenumbers. A useful optical system
has an entrance slit, and forms an image of this slit at the output, where we can put a
photographic film or a scanning detector.
f
entrance
slit
slit
image
f
For a very small entrance slit, the width of the exit slit (the image of the entrance slit) is
dependent on the width of the wavefront rather than on the width of the slit, because of
diffraction. It’s like a single slit diffraction pattern, where the angular half-width of the patter is
given by sinθ = d/wavelength. The physical width of the diffraction patter of the slit is given
by fθ.
In practice, the entrance slit if set to the same width as the diffraction pattern width for a
vanishingly small entrance slit. Any larger slit increases the width of the diffraction pattern and
any smaller one reduces the amount of light admitted to the spectrometer.
Most spectrometers use a diffraction grating instead of a prism, but the optics are the same.
DIFFRACTION GRATINGS
In several of our 111 laboratory experiments we need to disperse a beam of light into its various
colors. We could pass it through a prism and see the colors, but more commonly we use a
diffraction grating to produce a spectrum as described above. It is inserted into an optical system
in place of the prism in the previous example.
The grating disperses the light according to wavelength, with red light dispersed the most and
violet the least. The grating equation is mλ = d sinθ. We customarily use gratings in the first
order.
m=2
λ
)θ
1
0
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When a diffraction grating is placed in the system shown, the central image of the slit
(m = 0 at θ = 0) remains unchanged from the “no grating” condition, but now other slit images
are formed at angles corresponding to different wavelengths of light according to the grating
equation.
We assume you learned about diffraction gratings in Physics 7. To refresh your memory and
increase your knowledge and understanding, refer to Jenkins and White, Fundamentals of
Optics. However, most gratings are reflection rather than transmission gratings. The optical
system is shown below. Remember that mirrors are like lenses except that they fold the light
path.
m=1
λ
f
G
m=1
f
f
G
When analyzing a spectrum, we want to know what wavelengths are present and their relative
intensities. The smallest wavelength separation we can observe is characterized by the resolving
power R, which is written as R = λ/Δλ = mN = W sin θ/λ. N is the number of grooves in the
grating (width of grating W = N × groove spacing). A 3 cm wide grating with 600 grooves/mm
when used at an angle of 10 degrees in the first order to view the green line of mercury at
546.1 nm has a resolving power of R = 90 000.
The dispersion is given by dθ/dλ = tan θ/λ, or the inverse linear dispersion (called plate factor)
by dλ/dl = λ/f tan θ, usually expressed in units of nanometers/millimeter. The plate factor in the
previous example when the spectrometer has a focal length of 50 cm is 6.6 nm/mm.
The Atomic Physics (Balmer Series) spectrometer is set up as shown above. The focal length is
50 cm.
The Laser Induced Fluorescence spectrometers are similar but have a focal length of 25 cm.
The grating in the Carbon Dioxide Laser is placed in the beam path between the two laser
mirrors. The beam size is small and doesn’t nearly fill the grating. The resolution is very low, but
adequate for the purpose at hand.
INTERFEROMETERS
A diffraction grating splits a single wavefront into many parts or pieces, and contrives to have
the parts interfere, thereby creating a spectrum of the radiation. The process is called wavefront
division.
An interferometer takes the entire wavefront and splits off one or more copies of it with smaller
amplitudes but the same spatial dimensions – each split-off wavefront is the same size as the
original wavefront. This process is called amplitude division. These wavefronts are then guided
to interfere with one another.
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A Michelson interferometer splits the incoming wavefront into two wavefronts of equal
amplitudes and then causes them to interfere.
L1
L2
With the optics as shown, the source can be of any size. The first lens can be omitted. At the
image plane a series of rings is formed, each of a different order of interference given by
mλ = 2t cos θ. At the center of the pattern m = 2t/λ, and m gets smaller as θ gets larger (out from
the center of the pattern). When one mirror is displaced or moved, the rings grow from the center
when the path length is increased, and collapse into the center when the path is decreased. When
the entrance aperture is circular and of a size to cover only one ring, the detector output is a
cosine curve as the path difference is changed. This cosine-curve output, one for each frequency
in the incoming light, is called the interferogram. To get the spectrum, the Fourier transform of
the interferogram must be calculated. The resolving power is given by R = 2t/λ, and the
resolution or resolving limit is given by 1/2t in cm–1. An interferometer with a mirror travel of 10
cm has a resolving limit of 0.05 cm–1, and a resolving power of 300 000.
Such a spectrometer is called a Fourier transform spectrometer, or FTS for short. The most
useful high-resolution spectrometers are of this type.
With a laser as a source of light, there is no need for either of the lenses, since the laser beam is
already collimated and the ring pattern at the output is clearly visible. This is true even when a
lens is used to expand the beam.
The Mossbauer Effect laboratory equipment includes a Michelson interferometer, sued not to
measure a spectrum but to measure distances from which can be derived speeds of travel of the
mirror.
A Fabry-Perot interferometer consists of two plane-parallel reflecting surfaces spaced a
distance t apart. Here, the wavefront is divided as in the Michelson interferometer, but into many
wavefronts whose amplitudes are steadily decreasing with each division (reflection at the
surfaces). Instead of a two-beam interference problem, there is an N-beam interference, with
N = where R is the reflectance at the surface of each of the plates.
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UC Berkeley Physics 111 Advanced Undergraduate Laboratory
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For example, when each plate has a reflectance of 0.9 (90% of the light is reflected, 10%
transmitted), the effective number of interfering beams is 30. The resolving power is 2Nt/λ,
which is N times the resolving power of a Michelson interferometer. For example, with a spacing
of 1 cm and a reflectance of 0.9, a Fabry-Perot interferometer has a resolution for the mercury
green line of 1 100 000, or a resolving limit of 0.017 cm–1.
In the Atomic Physics experiment (Zeeman Effect) we examine the circular fringe pattern
visually, although it can be photographed, and some instruments can scan by moving one plate.
The concept of overlapping orders is important here. Two wavelengths can appear at the same
angle but in different orders. When the orders differ by 1, the difference in wavelengths is called
the free spectral range. It can be expressed in either wavelengths or wavenumbers. In
wavenumbers, it is equal to 1/2t, or 0.5 cm–1 in the example given above. Melissinos has an
especially good discussion of the Fabry-Perot interferometer.
LASERS
We use Helium-Neon and Argon Ion lasers as tools in our laboratory, and we have an
experiment with a CO2 laser. Each of these gas lasers has an optical cavity. The cavity is like a
Fabry-Perot interferometer – two highly reflecting mirrors spaced widely apart, in our case
nearly a meter for the CO2 laser, about 50 cm for the argon ion laser, and 20 cm for the heliumneon laser. The line widths of the radiation for each of these lasers depend not only on the
optical characteristics of the cavity (interferometer) but also on the nature and conditions of the
active medium inside. You will have to read more specific references in order to understand how
the widths come about.
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