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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 2 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 4 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. 6 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 8 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.