Download Chapter 17 A modern optics laboratory for undergraduate students

Chapter 17
A modern optics laboratory for undergraduate
students in science and engineering
CRISTIAN BAHRIM
Department of Chemistry and Physics, Lamar University, P.O. Box
10046, Beaumont, TX 77710, USA. E-mail: [email protected]
A new modern optics laboratory for senior undergraduate students in science and
engineering was developed at Lamar University. The laboratory consists of one
conceptual lab (about colors and optical illusions), five fundamental labs (on
interference, polarization, blackbody radiation and photoelectric effect) and four
advanced labs on atomic spectroscopy (based on dispersion and diffraction of light).
These labs address fundamental questions about the nature of light and discuss
important technological applications, such as transparency of dielectrics,
spectroscopic analysis, etc. Two research oriented lab activities are offered at the
end of the semester as experimental learning. After the completion of this modern
optics laboratory and course, the students are better prepared for optics related jobs
in industry and many of them find interest in continuing studies in the field of optics
and photonics in graduate schools.
MOTIVATION AND GOALS
As part of Physics Curriculum at Lamar University (LU), a set of laboratory activities
associated to a new fundamental optics course were developed. The course uses an
excellent textbook, “Optics” by Eugene Hecht [1], and intends to discuss fundamental
concepts of modern optics with applications in the optics related fields and technology.
The course has been offered for the first time in fall 2003 and again in spring 2005. In
each semester we had seven undergraduate students enrolled with majors in either
physics or electrical engineering (EE), or both. This is a senior-level undergraduate
course with prerequisites of calculus-based University Physics II (electricity, magnetism
and basic elements of optics) [2] taken at sophomore level and a Modern Physics course
[3] taken at junior level. This course was created at the students’ request with majors in
science and engineering of having a fundamental optics course. It helps them to further
take advanced courses focused toward applications in optics, such as “Fiber Optics
Communication” which is offered by the Department of Electrical Engineering. The
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course covers advanced topics in optics and photonics for scientists (i.e. laser cooling,
superluminal information, light-gravity interaction) and engineers (i.e. fiber optics,
storage of information in a bulk of matter, transparency of dielectrics).
The primary goal of this laboratory course is to lead the undergraduate students to
the discovery, through experimental investigation, of the dual character of light (photon
and wave), and to understand the link between the two characteristics of light through
spectroscopic measurements. Experiments of spectroscopy show in a very clear way that
a photon is actually a wavetrain and brings the modern physics into a modern optics lab.
Another goal is to teach certain experimental techniques of optics, like interferometry and
spectroscopy, which are widely used in industry and research, today.
Previous physics courses briefly introduce the wave characteristic [2] and the photon
[3] characteristic of light, but in a very basic and qualitative way. Our Modern Physics
course [3], which has no lab associated, introduces the photon as being a ‘bundle of
energy’, and next, it discusses applications, like the light-atom/molecule interaction, as
the photon would have a well-defined energy. In reality the photon is a short duration
wavetrain, a concept which is typically discussed in graduate courses. However, an
undergraduate student who is familiar with Heisenberg’s uncertainty principle from
Modern Physics [3] has the necessary basis for a correct understanding of the photon.
Typically the basic topics covered in an undergraduate optics lab are geometric
optics (refraction, reflection and image formation with mirrors and lenses) and wave
optics (interference, diffraction and polarization of light). Sometimes the photoelectric
effect is introduced as the best and easier experiment that shows that light is a photon.
We are familiar with such optics lab courses offered by other universities. For example,
the Department of Physics and the Department of Electrical and Computer Engineering
(ECE) at North Dakota State University (NDSU) offers a Physics/ECE 457/657 course
(which was introduced in fall 2001) [4] and the New Jersey Institute of Technology
(NJIT) offers an “Introduction to Optical Science and Engineering” course (called OPSE
301) [5]. Both courses are offered to a similar student population as we do, but they do
not require as prerequisite a Modern Physics course.
I consider that a fundamental optics course offered at senior undergraduate level
should go deeper into the dual character of light. Most of the textbooks identify
experiments that show separately the wave characteristic or the photon characteristic of
light, and explore several applications (fiber optics, interferometry, etc.). Because the
wave and the photon characteristics of light are studied separately, many students
understand the statement “light has a dual character: it is a wave or a photon”, like it
would be two different faces of the same object. In reality the two characteristics of light
co-exist. The link between the wave and the photon concepts can be observed in the best
way when an experiment of atomic spectroscopy is performed. However, this topic is
rarely included in optics textbooks for undergraduate students, but there is a significant
literature on atomic spectroscopy at advanced level. The atomic spectroscopy represents
a technique which allows a simultaneous analysis of light as a photon and as a wave. A
spectroscopic measurement has the advantage of giving the most complete information
about the nature of light: the light is a short duration wavetrain when is emitted by atoms,
but it propagates as a wave, and therefore, it can be diffracted by a grating or decomposed
with a dispersive transparent dielectric. Also, the spectroscopic method is important for
industry and research because it is one of very few non-destructive methods that can be
used to analyze the composition of various materials by the light emitted.
The course addresses many fundamental questions in the field of Optics and
Photonics, such as: What does it mean that light has a dual character: it is a wave, as well
as a particle? Is the photon a localized particle such as a traveling elementary particle or
the picture is actually more complex? Based on concepts of quantum physics, the student
can understand the difficulty that one experiences when is trying to give a definition for
the particle of light. This difficulty was pointed out by Einstein, more than a half of
century ago: “Every physicist thinks that he knows what a photon is. I spent my life to
find out what a photon is and I still don’t know” (see [1], page 7). Today, based on
Heisenberg’s uncertainty principle one can better understand the characteristics of light
as a particle: the photon is a short duration wavetrain with a width related to the lifetime
of the upper atomic state involved in a transition. A photon can be “stretched” by
pressure broadening, an effect that can be induced by atomic collisions within a light
source. This aspect and many others are carefully investigated in our labs. The novelty of
this fundamental optics laboratory course resides in the fact that it combines the wave
optics and photonics. The student gradually discovers not only the dual character of light,
but he gets a correct understanding of the photon as a wavetrain, and also, he can study
various applications important for industry and research.
LABORATORY
STRUCTURE
The labs offer complementary information to the theory presented in lecture, as well as
hands-on experience for students taking this course. Each laboratory activity is
scheduled for three hours. The optics laboratory is structured as follows:
Lab#1: An introductory lab about colors and optical illusions. In this lab, the
students learn about the basics of the theory of colors: the combination of colors (primary
and secondary) at reflection by a surface and transmission through a filter, using many
class demos. The structure (light sensors on the retina, blind spot, etc.) and the sensitivity
of human eye to visible light are also discussed, as well as the origin of optical illusions.
Next, the laboratory class includes a set of five basic optics experiments that give to
students the opportunity to understand fundamentals of optics: the light is a wave when
propagates through a medium and is a particle when is absorbed or released by atoms.
The theory part of each lab is extensively discussed in the lecture before lab.
Lab#2: Diffraction and interference using single and multiple narrow openings
(circular and rectangular). The students can run experiments for a wide variety of
situations from the classical Young double-slit setup, to gratings of diffraction and
simulation of the Bragg diffraction on crystals using the diffraction of light by various
nettings. The interpretation of maxima of diffraction gives information about the
geometry of the nettings. This is a computer-based experiment using a PASCO interface.
Lab#3: Polarization of light by transmission using Polaroids, where the students
can check the Malus’ law and reflection on a dielectric surface (the Brewster’s angle).
Lab#4: Interferometry of light using a Michelson interferometer helps students to
better understand the phenomenon of interference of coherent light waves, as well as the
influence of the polarization of light in the formation of an interference pattern: i.e. two
light waves perpendicularly polarized cannot form an interference pattern because the
interference term cancels out. This lab combines the phenomena of interference and
polarization of light discussed in Labs#2 and 3, and presents various applications, such as
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accurate measurements of index of refraction for gaseous and solid transparent materials,
and measurements of wavelengths by investigating changes in an interference pattern.
Lab#5: Emission of light by glowing objects with experimental verification of the
Wien’s displacement law and the Stephan-Boltzman law for the intensity of light. The lab
includes a theoretical component based on elements of quantum statistics: using the
Bose-Einstein distribution of photons inside a blackbody cavity, we derive the Planck’s
formula for radiancy. This computer-based laboratory introduces the concept of photon.
Lab#6: The photoelectric effect shows that the photon theory of light successfully
explains the absorption of light by a metal surface. In this lab, the students measure the
Planck’s constant, which is a fundamental constant in our Universe.
The second part of this laboratory class is composed by two sets of experiments of
atomic spectroscopy with two labs each. One set of experiments is based on dispersion of
light through a transparent dielectric and requires a simple spectrometer with a glass
prism. The other set uses a high-sensitivity spectrophotometer with a diffraction grating.
Labs#7&8: The light propagates as a wave through a transparent dielectric. The
classical electric dipole oscillator model proposed by Lorentz gives an elegant
explanation of this phenomenon. In this model, the electric field component of light
drives the electronic cloud of each molecule located on its path into an oscillatory motion
r
(“ E -field – electric dipole interaction”) with an angular frequency, ω. The electronic
r
cloud of molecules opposes practically no inertia to the driving E -field, and oscillates
immediately in resonance with it. The molecules oscillate either in-phase (if ω < ω0) or
r
out-of-phase (if ω > ω0) with a driving E -field depending on the value of the molecule’s
natural frequency, ω0.
In this experiment, the key information is the index of refraction of a dielectric,
which is the optical response of the material. First, the students should measure the index
of refraction for a transparent glass prism using a method of minimum deviation, should
plot the curve of dispersion, n = f(λ), for glass, and should understand the challenges in
the correct identification of the emission lines. Next, the students use the dispersive
curve to calculate some characteristics of the glass prism (such as the density of electrons
and the resonant wavelength) and to prove that the light passes as a wave through glass,
in a much shorter time than if the light would be absorbed and re-emitted by molecules.
The method of minimum deviation is spectacular for students, who discover that
when a prism is rotating in front of a light source, the spectrum rotates in a direction let’s
say counterclockwise, until it reaches a position after which the spectrum starts to rotate
clockwise. This turning point corresponds to the angle of minimum deviation of the
incident light by the prism. This method gives a very accurate curve of dispersion for a
transparent dielectric, which allows identifying impurities in unknown sources of light.
Figure 1 shows the curve of dispersion for a crown glass using six visible lines of
Helium atom (388.8 nm, 447.1 nm, 471.3 nm, 492.2 nm, 501.6 nm, 587.6 nm, 667.8 nm
and 728.1 nm) and four Balmer lines of Hydrogen (410.2 nm, 434.0 nm, 486.1 nm, 656.3
nm). We choose H and He atoms because of their abundance in the Universe and their
spectral purity. The Lorentz model leads to a linear equation (in λ-2) for dispersion
(n
(
2
2
2
) = −C λ + C λ ,
m ) (q N ) is the slope and C λ
−1
−1
2
−2
−2
o
(1)
−2
o
where C = 4 π c ε o
is the intercept. In equation (1),
N is the electronic density of the molecules in dielectric, c is the speed of light in free
space, ε o is the electric permittivity of free space and m is the mass of the electron. The
equation (1) is known also as the Cauchy’s dependence. Using a linear regression, the
students can find the natural wavelength, λo, of the dielectric and the electronic density of
the molecules, N. In figure 2, for a crown glass the slope C is (0.00736 ± 0.00007) x 10-6
nm2, the intercept C λo−2 is 0.7843 ± 0.0003 and the resonant wavelength λo is 96.8 nm.
From this experiment the students (1) understand why a dielectric material is
transparent to visible light, (2) find out that a dielectric is typically opaque for a radiation
λo in the near UV spectrum, and (3) calculate the speed of light, v, through a dielectric for
various wavelengths in visible, plotting v = f (λ ) (see figure 3). Thus, the students can
discover that in a normal dispersive material the red light travels faster than the blue light.
FIGURE 1
THE CURVE OF DISPERSION.
FIGURE 2
THE CAUCHY’S DEPENDENCE.
FIGURE 3
THE SPEED OF LIGHT IN GLASS.
Knowing v and measuring the length L of the geometric path traveled by light through a
glass prism, the student can discover that light propagates much faster than the lifetime of
any excited state of the molecules in the crown glass. This result proves that light travels
as a wave rather than a photon (which always travel at speed c!) through a glass prism.
It is also important that during these measurements, the students can experience and
understand the difficulties arising from the interpretation of an emission spectrum:
1. For most transparent dielectrics of practical concern n decreases as λ increases
across the visible range (see figure 1). Also, the rate of increase for n is greater at
shorter λ. Studies indicate that larger n, stepper the curve of dispersion. Therefore,
the spacing between various wavelengths will be non-uniform: for visible light, the
violet end is spread out more than the red end. In consequence, the measurements in
the blue-violet region of the visible range will be more accurate since the lines are
better resolved than the red end of the spectrum where the lines are much closer.
2.
Another difficulty in the correct identification of various wavelengths comes from
the variation in intensity of light transmitted through a dielectric material due to
Rayleigh scattering: Iscattered varies as λ-4. The violet and blue colors are scattered
more than the red color. In consequence, a violet line appears weaker here, than in a
normal spectrum resolved with a diffraction grating, for example. This creates a real
challenge when spectroscopic tables [6] are used for identifying emission lines.
3.
Also, the curve of sensitivity of human eye has a maximum around 550 nm, which
makes difficult the identification of λ close to the boundaries of the visible range:
380 and 780 nm.
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Labs#9&10: Computer-based atomic spectroscopy using a diffraction grating. In
this lab the students analyze simultaneously the light as a wave and a particle. The light
is a photon when is emitted by atoms in a gas discharge at low pressure and high
temperature. The Heisenberg’s uncertainty principle (∆t ⋅ ∆E ≈ h ) , which is fundamental
in quantum mechanics, helps to understand that a photon is a wavetrain of short duration
within a Lorentzian envelope. The width of the wavetrain, Γ ∼ 1/∆t, is proportional with
the energy width (or the uncertainty), ∆E, of the excited state in the transition that
releases the photon. The more frequent are the collisions between atoms in a source of
light, the larger ∆E, and also, the shorter the lifetime of the upper state in atomic
transitions, and in consequence, the larger is the width of the photon emitted. In thermal
collisions, the average lifetime of atoms is about 10-12 seconds, which is much shorter
than the natural lifetime of an isolated atom (≈ 10-8 seconds). Therefore, the width of the
photon can reach a few nanometers and can easily be resolved with a spectrophotometer.
An atomic gas at high temperature and low pressure (i.e. an atomic discharge tube)
that obeys the Maxwell-Boltzman statistics is a perfect candidate for spectroscopic
analysis. The Maxwell-Boltzman statistics considers that the population of atoms on
excited states, n, is given by N n = N max exp(− En kT ) , where En is the energy of upper
atomic state involved in the transition and kT is the averaged kinetic energy of atoms in
thermal equilibrium at temperature T. Using a few new concepts, a senior undergraduate
student can easily understand that the analysis of light emitted by a gaseous discharge
source gives information about (1) the distribution of atoms on various excited states, n,
in the source of light, (2) the temperature of atoms, (3) the averaged speed of atoms, and
(4) the quantum rules in optical transitions (n → n’). The analysis of atomic transitions
using the quantum selection rules and Grotrian diagrams [7] allows understanding the
origin of the polarization of light, which is a concept introduced already in Lab#3.
The emission lines in visible and near IR is recorded with a PASCO educational
spectrophotometer connected through an interface to a computer. The Data Studio
software allows the analysis of the spectrum and it plots the intensity of light as a
function of position (or wavelength) in the spectrum. An important industrial application
of optics spectroscopy is the identification of impurities in various sources of light.
Figure 4 shows the spectrum of water vapor in visible and near IR. The Balmer lines
of Hydrogen in visible at (1) 410.2 nm, (2) 434.0 nm, (3) 486.1 nm, (4) 656.3 nm (which
is a very high peak, and therefore, it is truncated), and two IR lines of Oxygen at (5)
777.0 nm and (6) 844.6 nm are indicated.
From the classical Maxwell-Boltzman
distribution, the students can derive:
 N  hc  1
1 

.
−
(2)
ln n  =


 N n '  kT  λ n ' λ n 
Equation (2) allows to estimate the
temperature of atoms, T, in a discharge
tube, and the averaged kinetic energy of
atoms, kT, by measuring the relative
population of atoms (which is indicated
by the high of peaks in figure 4) and the
FIGURE 4
wavelengths λn and λn’ for two optical
THE RELATIVE INTENSITY OF LIGHT IN
transitions: n → n” and n’ → n”.
THE VISIBLE AND IR SPECTRUM FOR
WATER VAPORS
As source of light we use spectral tubes 26 cm long with a capillary-thin region of 10
cm which provides a sharp, bright spectrum. The energy supplied to initiate and stabilize
the discharge is about 36 eV, so the discharge can effectively ionize many atoms, in
particular those close to the electrodes. The kinetic electrons induce excitation in atoms
by collisions. Next, atomic collisions will stimulate the emission of radiation which is
finally detected with a photodiode.
We use a PASCO photo-detector, Model CI-6604, which includes a photodiode with
a response in a wide spectrum ranging from vacuum wavelengths of 320 nm through
1100 nm. The spectral response curve of the photodiode is given in the instruction
manual and it is used for calibration. However, the measurement proposed here it uses
relative intensities and no absolute calibration is necessary for the peaks of the emission
lines. To give an example, for a Hydrogen gas discharge we find a kinetic temperature of
the atoms in the middle of the capillary tube of about 3050 Kelvin.
The atomic gas is assumed to be in a local thermodynamic equilibrium (LTE)
because of the high electron density, and also, because it is optically thin in the middle of
the capillary region where the light is detected (figure 4). It is reasonable to assume that
LTE model is correct for the description of stable collisional-dominated plasmas [8]. The
relative high frequency of the electron-atom collisions keeps the atoms in LTE.
Therefore, the Maxwell-Boltzman distribution can be applied in order to get the average
kinetic energy and the kinetic temperature of the atoms in the middle of the capillary
region of the discharge tube, where the LTE is the best preserved. The pressure
broadening induced by atomic collisions enlarges the width of the emission lines up to a
few nanometers and it makes their identification and characterization relatively easy with
our spectrophotometer of 1 nm resolution.
The experience acquired in labs#7-10 allows the investigation of other sources of
light using the same spectroscopic methods. The students can learn certain techniques for
identifying impurities in sources of light by using spectroscopic measurements in
combination with spectroscopic tables [6] and Grotrian diagrams [7]. Also, the students
can be involved in new research projects of atomic and molecular physics, like the
investigation of the pressure broadening effect on the photon’s width, which can be done
by fitting any isolated peak from figure 4 with a Lorentzian function.
Typically in undergraduate optics labs the wave and the photon characteristics of
light are studied separately [4, 5]. Our set of fundamental optics labs allows a gradual
discovery of the dual character of light and it leads to a correct interpretation of the
photon as a wavetrain. In addition, our experiments of spectroscopy allow analyzing the
characteristics of light simultaneously, making this optics lab “modern” in its content.
TEACHING STRATEGY AND ASSESSMENTS
In my opinion an effective model of teaching at undergraduate level should be based
on more interactive classes as suggested by Eric Mazur [9]. This optics laboratory
applies successfully Mazur’s peer instructional model allowing open discussions
between students moderated by the instructor. A laboratory activity is the best suited for
a non-traditional, discussion-oriented learning experience. My model of teaching new
concepts is based on the interaction with students. All optics labs have an introductory
theoretical component, which requires a maximum concentration from students’ part. A
lack of attention at this stage creates difficulties for students in running the experiments
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in a limited time, and individual work with certain students is required. The best way to
keep the students’ attention focused on and to make them to understand the new
phenomena and the related physical concepts is by encouraging open discussions
moderated by the instructor. In this way the misconceptions can be rapidly eliminated.
Also, these discussions awake an interest in each student for experimental testing of the
new concepts and it gives to students a sense of discovery. After this introductory part of
the optics lab, groups of two students are formed. Each team proceeds to the
identification of the experimental setup as described in the handout. Open discussions
between students moderated by the instructor clarify the strategy needed to run the
experiment. At the end of the class, the students do the analysis of their results, draw the
conclusions, and turn in reports. The teacher evaluations have shown positive
appreciations regarding the lab activities we have offered. All students have declared that
they agree or strongly agree with the way this class was organized. Also, they have
mentioned that they gained considerable knowledge on the subject, which proves to me
that an experimental-based learning technique is very effective for understanding optics.
The most important assessment of this optics laboratory course in terms of its
effectiveness is the interest and ability of students to run sophisticated optics experiments
later, in a senior project or research-oriented programs in optical science and technology
(i.e. optics communications, interferometry, spectroscopy, etc.). After the completion of
the optics course, two of my best students have taken with me classes of special topics on
“Advanced photonics” (with a subject focused on the storage of light in materials) and
“Atomic spectroscopy” (with a subject focused on the analysis of impurities in various
sources of light). One of my students, Joseph Young an electrical engineer and physics
major was the recipient of a Barry M. Goldwater scholarship award for year 2005, in part
because of a successful research project on atomic spectroscopy we have done together.
Also, he has presented an experiment on “Computer-based atomic spectroscopy” to a
student research conference where he has received an award. Recently, he got a McNair
Scholars special recognition for outstanding research in optics. Another student has
started a research project under the McNair Scholars program on the topics ‘slowing
down light in dielectrics’. I anticipate that both research projects will lead to publications
in peer-review journals. Also, in parallel with the lab activities listed above, we offer
various research projects for students in the Honors program at LU. A very interesting
honors project about a ‘computer-based experiment on interference and diffraction’, with
simulation of Bragg diffraction on crystals, was run by another student, Joseph Hunt.
This laboratory integrates a strong research component to the basic education in
optics and it has as goal to form a group of savvy students in optics and photonics at LU.
Teaching both modern physics and optics to the same students gives me the opportunity
to add many advanced topics on photonics (such as laser cooling, GRIN fiber optics,
superluminal and subluminal light, holography, etc.) to fundamentals of the theory of
light. Encouraged by the positive response of my undergraduate students to the present
laboratory, an advanced optics laboratory course at graduate level is underway.
REFERENCES
1.
Hecht, E., Optics, Addison Wesley, San Francisco, 2002.
2.
Halliday D., Resnik R. and Walker J., Fundamentals of Physics, 6th ed., John Wiley & Sons,
Inc., N.Y., 2003.
3.
Krane, K., Modern Physics, 2nd ed., John Wiley & Sons, Inc., N.Y., 1996.
4.
32nd ASEE/IEEE Frontiers in Education Conference, S4A-8 by O.F. Swenson, D.A. Rogers,
F.M. Patterson, and A. Campiglia.
5.
http://www.njit.edu/v2/Directory/Centers/OPSE/
6.
Reader J., Corliss Ch. H., Wiese W. L. and Martin G. A., Wavelengths and Transition
Probabilities for Atoms and Atomic Ions. Part 1 and Part.2, U.S. Department of Commerce,
N.S.R.D.S.-N.B.S. 68, 1980.
7.
Bashkin S. and Stoner J., Atomic Energy Levels and Grotrian Diagrams, Elsevier, N.Y., 1975.
8.
Lochte-Holtgreven
Amsterdam, 1968.
9.
Mazur, E., Peer Instruction. A User’s Manual, Series in Educational Innovation, Prentice Hall,
New Jersey, 1997.
W.,
Plasma
Diagnostics,
North-Holland
Publishing
Company,
Cristian Bahrim received the M.S. degree in Physics from the University of
Bucharest in 1991. He received his Ph.D. degree in Physics from University of
Paris-Sud in 1997. He was a post-doctoral fellow at Kansas State University,
the department of Physics between 1998 and 2001. Since 2001, he has been an
Assistant Professor of Physics in Lamar University and beginning with 2005 he
holds a joint-appointment in the department of Electrical Engineering at Lamar
U. Research interests include quantum mechanics, atomic physics and optics.