Advanced Undergraduate Experiment Research Articles

A paraxial cloak with four lenses of different focal lengths

We demonstrate cloaking with four lenses of different focal lengths. To achieve this, we compute the separation distances between lenses such that the effective ABCD matrix is equal to just a propagation in free space. Previously, calculations using this method have been restricted to two pairs of lenses with equal focal lengths. Our computations, on the other hand, have no such restrictions: we generalize even with an asymmetric case. We derive expressions that show the dependence of the distances on the lenses and their focal lengths. Furthermore, we propose a way to minimize the length of this cloak. Our equations reduce to the Rochester cloak when its restriction is imposed. A general paraxial cloak could be useful in advanced undergraduate experiments in optics because (i) the limit imposed by the focal length has been lifted, and (ii) there is a pedagogical benefit of doing experiments with lenses beyond the usual imaging experiments, such as reinforcing concepts in Gaussian optics.

Improving undergraduate labs

Toni Feder’s news story “Undergraduate labs lag in science and technology” (Physics Today, April 2017, page 26) is a welcome analysis of the challenges facing advanced undergraduate physics laboratories and current efforts to provide effective solutions for undergraduate physics programs at US colleges and universities.The Advanced Laboratory Physics Association (ALPhA) sponsors a laboratory immersion program in which physics faculty receive three days of dedicated instruction and hands-on experience with modern advanced undergraduate physics experiments. The goal is to provide enough training so that participants can implement the experiments at their own institutions.Since the inception of the program, I have participated in nine immersions. Each was excellent, and I have implemented at least one experiment—and in one case, five—from each immersion I attended. The topics have been fascinating, and they included single-photon tests of quantum mechanics, external-cavity diode lasers, laser-induced fluorescence, Compton scattering, precision laser interferometry, Fourier methods, and saturated absorption spectroscopy.At my small undergraduate institution—10 physics majors per year on average—the primary obstacle I faced in implementing those experiments was locating funds to purchase the equipment. Fortunately, the Jonathan F. Reichert Foundation started the ALPhA immersions equipment grant program, which has been a godsend to me and my students. Its support has allowed me to acquire a Leybold x-ray diffraction apparatus, a TeachSpin diode laser spectroscopy instrument, a Stanford Research lock-in amplifier, and a TeachSpin Fourier Methods system.As a direct result of the efforts of ALPhA and the Reichert Foundation, I have implemented 13 advanced undergraduate physics experiments at my institution. Additionally, I proposed a new course, Advanced Laboratory in Physics, which was offered for the first time in the fall of 2017.Some friends and colleagues suggest that after 30 years of professorial experience I should be thinking about retiring. I disagree. I am more excited now than ever, because I see my students’ enthusiasm as they perform the new experiments. I look forward to many more years in the best job on the planet. Section:ChooseTop of page <<© 2018 American Institute of Physics.

One step beyond the electric dipole approximation: An experiment to observe the 5p → 6p forbidden transition in atomic rubidium

An advanced undergraduate experiment to study the 5P3/2→6P3/2 electric quadrupole transition in rubidium atoms is presented. The experiment uses two external cavity diode lasers, one operating at the D2 rubidium resonance line and the other built with commercial parts to emit at 911 nm. The lasers produce the 5s→5p→6p excitation sequence in which the second step is the forbidden transition. Production of atoms in the 6P3/2 state is observed by detection of the 420 nm fluorescence that results from electric dipole decay into the ground state. Lines whose widths are significantly narrower than the Doppler width are used to study the hyperfine structure of the 6P3/2 state in rubidium. The spectra illustrate characteristics unique to electric dipole forbidden transitions, like the electric quadrupole selection rules; they are also used to show general aspects of two-color laser spectroscopy such as velocity selection and hyperfine pumping.

Scaffolding Students’ Skill Development by First Introducing Advanced Techniques through the Synthesis and 15N NMR Analysis of Cinnamamides

An advanced undergraduate experiment involving the synthesis and characterization of a series of six unique cinnamamides is described. This experiment allows for a progressive mastery of skills students need to tackle more complex NMR structure elucidation problems. Characterization of the products involves IR spectroscopy, GCMS, and proton, carbon, and nitrogen NMR analyses. Understanding the principles of advanced NMR techniques, including nitrogen NMR spectroscopy, is highly relevant to advanced organic chemistry students.

Detection of the cp4 epsps Gene in Maize Line NK603 and Comparison of Related Protein Structures: An Advanced Undergraduate Experiment

A flexible, rigorous laboratory experiment for upper-level biochemistry undergraduates is described that focuses on the Roundup Ready maize line. The work is appropriate for undergraduate laboratory courses that integrate biochemistry, molecular biology, or bioinformatics. In this experiment, DNA is extracted and purified from maize kernel and leaf samples collected from a Roundup Ready maize grower’s field. A small segment of DNA (108 base pairs) specific to the Roundup Ready transgene that codes for CP4 5-enolpyruvylshikimate-3-phosphate synthase (CP4 EPSPS) is amplified with polymerase chain reaction (PCR) to detect the presence of the gene in the maize samples. Students additionally choose a protein closely related to CP4 EPSPS as determined by amino acid sequence alignments. The selected amino acid sequences are submitted to an online protein modeling program where students compare their protein with the herbicide-resistant enzyme found in Roundup Ready crops. This experimental paradigm gives students a physical appreciation for the central dogma of biology, as they are exposed to products derived from the replication, transcription, and translation events belonging to a genetically modified crop. The PCR portion of the laboratory allows students to perform an in vitro replication of a portion of the NK603 transgene and identify the segment via ultraviolet radiation. In direct connection to the PCR portion, the protein structure elucidation gives rise to the central ideas of evolution—that slight changes in the genetic code of DNA, translated into proteins, produce novel protein structures with significantly different function.

Vibrational spectra of N2: An advanced undergraduate laboratory in atomic and molecular spectroscopy

We describe an advanced undergraduate experiment to demonstrate molecular spectroscopy by measuring the vibrational energy spacing of nitrogen molecules in the gas phase. We show how the use of a simple and readily available AC discharge tube and a handheld spectrometer allows students to observe and measure the radiative collisional phenomena in the gas, and to scrutinize the resulting emission spectrum for an instructive analysis of the quantized vibrational potential of neutral as well as ionized N2.

Hammett Parameter and Molecular-Modeling Correlations of Substituent Effects on Esterification Kinetics

The effect of substituents on the rate of reactions is taught extensively throughout organic chemistry. The Hammett equation is useful in quantifying this dependence; however, there are relatively few experiments that investigate this relationship. We describe an advanced undergraduate experiment suitable for exploring the substituent effect on esterification kinetics of trifluoroacetic acid with a variety of alcohols. We find a negative correlation between the Hammett substituent constant and the rate of the esterification, indicating a slower rate of reaction for the substituted alcohols. The decrease in measured rates is also correlated with the calculated charge on the oxygen atom for the substituted alcohols. The combination of the experimental data with the theoretical calculations should increase the student’s understanding of substituent effects on reaction rates.

An Advanced Undergraduate Chemistry Laboratory Experiment Exploring NIR Spectroscopy and Chemometrics

An advanced undergraduate chemistry experiment for an instrumental analysis course or analytical chemistry course is described to familiarize students both with NIR spectroscopy and chemometrics. Students measure NIR spectra of toluene, heptane, and isooctane solutions in the 6400�5150 cm-1 region of the electromagnetic spectrum and develop an accurate and precise (±0.6% absolute) chemometrics calibration model to predict component concentrations. Experimental exercises are described to examine the calibration model and discern its limitations. Selective substitution experiments pinpoint the CH2/CH3 ratio and the aromatic ring as a key factors in the calibration model. Further exercises show how alterations of sample and analysis conditions adversely effect quantitation using the tailor-made chemometrics calibration model.

Fluctuations near a phase transition in liquid crystals

The increase in molecular orientational fluctuations as a phase transition is approached is an interesting and dramatic phenomenon, but associated undergraduate experiments are rare. We present an advanced undergraduate experiment on light scattering from the molecular orientational fluctuations in liquid crystals. In the high-temperature, disordered phase of a liquid crystal, small clusters of parallel-oriented molecules form spontaneously and scatter light. The size of the fluctuations and the consequent light scattering increase dramatically as the temperature is reduced approaching the weakly first-order phase transition to the ordered liquid crystal phase. We discuss a simplified theory that captures the essential physics.

Macroscopic coherence effects in a mesoscopic system: Weak localization of thin silver films

We present an advanced undergraduate experiment on weak localization in thin silver films with a thickness between 60–200 Å, a mesoscopic length scale. At low temperatures, the inelastic dephasing length for electrons exceeds the film thickness, and the film becomes quasi-two-dimensional. In this limit, theory predicts corrections to the Drude conductivity due to the coherent interference between the wave functions of the conducting electrons, a macroscopically observable effect known as weak localization. This correction can be destroyed by the application of a magnetic field, and the resulting magnetoresistance curve provides information about electron transport in the film.

Crystallographic Study of Manganese(III) Acetylacetonate: An Advanced Undergraduate Project with Unexpected Challenges

An advanced undergraduate crystallographic experiment is proposed that integrates the well-tested protocol for synthesis of manganese acetylacetonate, Mn(acac)3, with a new low-temperature characterization of the crystal structure of the synthesized complex. Standard synthesis of Mn(acac)3 was followed by crystallization trials to obtain single crystals suitable for X-ray structural determination. Surprisingly, single crystals of a new crystalline form (δ) were obtained. When cooled to 100 K, single crystals of the δ form underwent an irreversible solid–solid phase transition to another new form (e). The discovery of these new crystalline forms was a highly stimulating experience for the students involved. The goal to investigate the Jahn–Teller behavior of the high-spin Mn(III) complex, Mn(acac)3, was more than successfully achieved with the recognition of an unusual orthorhombic distortion (OD) of the coordination polyhedron. This experiment not only introduces crystallography, one of the most powerful ...

A study of electric dipole radiation via scattering of polarized laser light

We have developed an advanced undergraduate experiment to explore electric dipole radiation in the optical frequency domain. A polarized laser beam is used to illuminate an aqueous suspension of skim milk, and the light scattered from the suspension is measured in the plane perpendicular to the laser beam as a function of the angle θ with respect to the polarization direction and as a function of the perpendicular distance R from the laser beam. When the length of the scattering region, d, is much smaller than R, the measurements agree very well with the sin2 θ/R2 dependence of electric dipole radiation. Increasing the scatterer concentration increases the background of multiply scattered light and decreases the degree of polarization of the scattered light with no appreciable change in the observed sin2 θ/R2 dependence. We discuss variations of the experiment for different instructional needs and describe how an understanding of dipole radiation helps students to appreciate a number of optical phenomena.

Spin-Coating of Polystyrene Thin Films as an Advanced Undergraduate Experiment

A simpler version of the well-established technique of spin-coating thin polymer films on glass slides is described. Starting with simple instrumentation and using an ordinary, commercially available cooling fan (a "CPU cooler"), a method of spin-coating an expanded polystyrene foam on glass slides is described. Making thin films of commercially available polystyrene on glass slides is also included for comparison. An interferometric technique is used to measure the film thickness employing a UV–vis spectrophotometer. FTIR spectroscopy is used to verify the identity of the polymer on the glass slide. Using the Beer–Lambert law of absorbance, the film thickness is also calculated from the FTIR spectra of films. A comparison is made between the interferometric and FTIR methods for thickness measurements. An organic dye is doped into a film and a UV–vis spectrum is used to identify the dye.

Quantitative Determination of Nicotine and Cotinine in Urine and Sputum Using a Combined SPME-GC/MS Method

An advanced undergraduate experiment for the analysis of nicotine metabolites in urine and sputum is described. Students use solid-phase microextraction (SPME) coupled with gas chromatography/isotope dilution/selective ion monitoring/mass spectrometry to identify and quantify volatile and semi-volatile metabolites produced in response to nicotine exposure. Nicotine and cotinine were chosen as target analytes because smoking trends continue to increase on college campuses despite the well-known risks associated with this activity. Solid phase microextraction is an ideal technique for this analysis because of its simplicity, making it amenable for introduction into the undergraduate laboratory. Also, sample preparation and handling steps are minimized, thereby lessening potential contamination or matrix exposure. Furthermore, the use of isotopic dilution for sample quantification is illustrated.

Determination of the Active Principle in a Syrup by Spectrophotometry and Principal Component Regression Analysis. An Advanced Undergraduate Experiment Involving Chemometrics

An advanced analytical chemistry laboratory experiment concerning the determination of the mucolitic bromhexine in a commercial syrup is described. It involves the following steps: (i) preparing nine calibration mixtures and recording their absorption spectra in the region 285-348 nm, (ii) recording spectrophotometric data for four synthetic unknowns and two commercial samples, and (iii) processing them with the multivariate calibration technique of principal component regression (PCR). The theory of PCR is discussed, and a Visual Basic 5.0 for Windows 95/98 program is made available to students for data processing. The program allows students to perform cross-validation and to obtain and save relevant statistical information (root mean square deviation, correlation coefficient, and relative error of prediction), as well as calibration spectral factors and spectral residuals for each test sample, all of which illustrate the PCR technique in detail. The reagents used are low-cost and nontoxic; the experiment is simple and gives students an insight into a real practice that integrates chemistry, instrumentation, and computer techniques.

Simultaneous Determination of Two Antibiotics in Tablets by Spectrophotometry and Principal Component Regression (PCR) Analysis. An Advanced Undergraduate Experiment Involving Chemometrics

An advanced analytical chemistry laboratory experiment involving the simultaneous determination of the antibiotics sulfamethoxazole and trimethoprime in commercial tablets is described. It involves the following steps: (1) preparation of nine calibration mixtures and the recording of their absorption spectra in the region 200–320 nm, (2) dissolution of the tablet contents and the recording of spectrophotometrics data, and (3) processing the data with the multivariate calibration technique of principal component regression (PCR). The theory of PCR is discussed, and a Visual Basic program is made available for data processing. The latter program allows students to obtain and save relevant statistical information (root-mean-square deviation, correlation coefficient, and relative error of prediction), as well as calibrate spectral factors and spectral residuals for each test sample. This program helps to illustrate the PCR technique in detail. The reagents used are of low cost and nontoxic; the experiment is simple and provides students with insight into a the real practice of integrating chemistry, instrumentation and computer techniques.

An Advanced Undergraduate Experiment in 2-D NMR

The concurrent use of one-dimensional (1H-NMR) and two-dimensional (1H-1H-COSY and 1H-1H-Delay-COSY) experiments can unambiguously assign each resonance in a spectrum to a particular proton. We have developed an experiment for the advanced chemistry student that utilizes long-range coupling to assign signals in the spectra of ketopinic acid, borneol, and isoborneol. Prelaboratory discussion of the spectra of camphor, hands-on use of the instrumentation, and determination of molecular stereochemistry are topics visited during the course of this experiment.

UV-Visible Spectrooelectrochemistry of the Reduction Products of Anthraquinone in Dimethylformamide Solutions: An Advanced Undergraduate Experiment

The redox properties of anthraquinone (AQ) may be used to model the behaviour of quinones in biological systems. AQ undergoes two successive one-electron reductions in aprotic solvents to form a stable radical anion (AQ.-) and a stable dianion (AQ2-) but this behaviour is altered in the presence of a proton donor. This advanced undergraduate experiment shows how cyclic voltammetry, digital simulations of cyclic voltammograms, and UV-visible spectroelectrochemistry may be used to examine the reduction behaviour of AQ in dimethylformamide (DMF), both in the absence and presence of benzoic acid.The cyclic voltammetry of AQ in DMF shows two reversible one-electron reductions. This allows the UV-visible spectra of AQ.- and of AQ2- to be determined using an optically transparent thin layer electrode (OTTLE) cell. AQH- may also be detected in the spectra if there are proton impurities. When benzoic acid is added to the DMF, the cyclic voltammograms are markedly altered with almost all the reduction occurring near the AQ/AQ.- potential and the corresponding oxidation at rather more positive potentials. The UV-visible spectroelectrochemistry shows AQH2 as the stable reduction product under these conditions while digital simulations of the cyclic voltammograms support a mechanism involving protonation of AQ.- followed by AQH. disproportionation.

Attaining optimal conditions: An advanced undergraduate experiment that introduces experimental design and optimization

The experiment described is a five-period exercise in experimental design and optimization performed in a junior laboratory course that integrates synthesis and analysis.

Chaos in a dripping faucet

An advanced undergraduate experiment on the chaotic behaviour of a dripping faucet is presented. The experiment can be used for the demonstration of typical features of chaotic phenomena and also allows the advanced physics student to learn about the use of microcomputers as data-taking devices. For convenience a brief introduction to the basic concepts of nonlinear dynamics and to the period-doubling route to chaos are included.