Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- University of Nebraska - Lincoln (3576)
- Missouri University of Science and Technology (2387)
- Old Dominion University (1919)
- Utah State University (1829)
- TÜBİTAK (1382)
-
- University of Kentucky (965)
- Air Force Institute of Technology (961)
- California Polytechnic State University, San Luis Obispo (922)
- Syracuse University (908)
- City University of New York (CUNY) (663)
- University of Texas Rio Grande Valley (661)
- University of Central Florida (620)
- Portland State University (594)
- University of Nevada, Las Vegas (565)
- Technological University Dublin (541)
- Brigham Young University (502)
- Michigan Technological University (495)
- Wright State University (488)
- University of South Carolina (481)
- University of New Mexico (467)
- Chapman University (432)
- University of Arkansas, Fayetteville (357)
- Virginia Commonwealth University (339)
- Florida Institute of Technology (338)
- Cleveland State University (283)
- University of Dayton (266)
- Karbala International Journal of Modern Science (261)
- Western Michigan University (258)
- Andrews University (225)
- Dartmouth College (225)
- Keyword
-
- Physics (842)
- Department of Physics (327)
- Optics (182)
- Spectroscopy (166)
- Scattering (146)
-
- Graphene (139)
- Thin films (139)
- Galaxies (137)
- Gravitational waves (129)
- Physical Sciences (126)
- Simulation (123)
- Polarization (122)
- Electron (121)
- Plasma (121)
- Nanoparticles (115)
- Superconductivity (114)
- Radiation (113)
- Pure sciences (105)
- Quantum chromodynamics (103)
- Ionization (101)
- Machine learning (99)
- Cavity (96)
- Laser (94)
- Photoluminescence (94)
- Quantum physics (93)
- Condensed matter (90)
- Hadron-Hadron Scattering (88)
- CMS (87)
- Cosmology (86)
- Lasers (83)
- Publication Year
- Publication
-
- Physics Faculty Publications (2109)
- Physics Faculty Research & Creative Works (1939)
- Turkish Journal of Physics (1382)
- Faculty Publications (1213)
- Theses and Dissertations (1151)
-
- Physics (969)
- Physics and Astronomy Faculty Publications (841)
- All Physics Faculty Publications (658)
- Electronic Theses and Dissertations (618)
- Physics & Astronomy Faculty Publications (585)
- Physics Faculty Publications and Presentations (559)
- Physics - All Scholarship (554)
- Department of Physics and Astronomy: Faculty Publications (374)
- Kenneth Bloom Publications (369)
- Articles (366)
- Mathematics, Physics, and Computer Science Faculty Articles and Research (351)
- Publications and Research (332)
- Physics & Astronomy ETDs (299)
- Aerospace, Physics, and Space Science Faculty Publications (298)
- Peter Dowben Publications (284)
- David Sellmyer Publications (278)
- Masters Theses (274)
- Dissertations (272)
- Karbala International Journal of Modern Science (261)
- International Building Physics Conference 2018 (255)
- Physics Publications (230)
- Anthony F. Starace Publications (229)
- Doctoral Dissertations (214)
- Dissertations, Theses, and Capstone Projects (213)
- Electrical & Computer Engineering Faculty Publications (199)
- Publication Type
- File Type
Articles 32071 - 32100 of 34203
Full-Text Articles in Entire DC Network
Experimental Study Of Spin-Exchange Effects In Elastic And Ionizing Collisions Of Polarized Electrons With Polarized Hydrogen Atoms, G. D. Fletcher, M. J. Alguard, Timothy J. Gay, V. W. Hughes, P.F. Wainwright, M. S. Lubell, W. Raith
Experimental Study Of Spin-Exchange Effects In Elastic And Ionizing Collisions Of Polarized Electrons With Polarized Hydrogen Atoms, G. D. Fletcher, M. J. Alguard, Timothy J. Gay, V. W. Hughes, P.F. Wainwright, M. S. Lubell, W. Raith
Timothy J. Gay Publications
Using crossed beams of polarized electrons and polarized hydrogen atoms we have investigated the effect of spin exchange on 90° elastic scattering from 4.4 to 30.3 eV and impact ionization from 14.1 to 197.0 eV. Our results suggest that the range of validity of various theoretical approximation methods is more restricted than had been assumed previously.
Analysis Of A Rocket-Borne Resonant Scatter System For Measurement Of Atomic Oxygen, Neil B. Myers
Analysis Of A Rocket-Borne Resonant Scatter System For Measurement Of Atomic Oxygen, Neil B. Myers
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
A computer model has been developed at Utah State University for interpreting the results of a rocket-borne resonant scatter measurement system using 1304 A radiation. Atomic oxygen densities are obtained from 65 to 140 km from three rocket flights. The resolution of the system is < 0.1 km, and considerable structure has been observed. The variety of shapes exhibited by the three profiles suggest a dynamic nature to atomic oxygen density profiles in the lower ionosphere. Maximum densities between 2.6 x 1011 and 1.2 x 1012 cm-3 were observed at altitudes between 92 and 95 km.
Measuring R And D Productivity, Richard A. Pappas, Donald S. Remer
Measuring R And D Productivity, Richard A. Pappas, Donald S. Remer
All HMC Faculty Publications and Research
Measuring the productivity of an R&D organization is extremely tricky. Productivity is usually defined as a ratio of an output, like number of cars produced on an assembly line, to an input, like the wages paid the workers. While R&D may have a measurable input, the output is often intangible and difficult to quantify. This is further complicated because the return from an R&D department may not be realized for one or two decades,which means the time lag is much higher than in factory measurements. Furthermore, many researchers believe that this kind of measurement may be counterproductive,since the mere act …
Applications Of A Direct Fast Field/Reflectivity Method To Wave Propagation Modeling In Underwater Acoustic And Solid Earth Seismic Environments, Gerard Joseph Tango
Applications Of A Direct Fast Field/Reflectivity Method To Wave Propagation Modeling In Underwater Acoustic And Solid Earth Seismic Environments, Gerard Joseph Tango
LSU New Orleans Theses and Dissertations
A new method is discussed for exact rapid computation of the depth-dependent Green's function occuring in full integral solutions to the acoustic and elastic Helmholtz wave equation, allowing calculations of underwater acoustic propagation loss and full wavefield synthetic seismograms, in range-independent plane stratified media.
Feasibility Studies Of Conversion Electron Mossbauer Spectroscopy (Cems) Of Iron-Doped Inp, Edward Agyekum
Feasibility Studies Of Conversion Electron Mossbauer Spectroscopy (Cems) Of Iron-Doped Inp, Edward Agyekum
Physics Theses & Dissertations
An electron detector for conversion electron Mossbauer spectroscopy (CEMS) has been designed and built. Tests have been performed to study the effects on the electron detector resolution with respect to high anode voltage, He/CH4 gas flow rate, and counting rate. These parameters have been optimized to detect the 7.3 keV conversion electrons emitted following resonant absorption of the 14.4 keV source gamma-rays associated with the Mossbauer effect using 57Fe nuclei. CEMS spectra have been obtained using standard 57Fe enriched and natural iron samples. CEMS spectra and Mossbauer transmission spectra have also been obtained for iron-compensated InP (InP:Fe) …
Beyond The Rigid-Ion Approximation With Spherically Symmetric Ions, L. L. Boyer, M. J. Mehl, J. L. Feldman, John R. Hardy, C. Y. Fong
Beyond The Rigid-Ion Approximation With Spherically Symmetric Ions, L. L. Boyer, M. J. Mehl, J. L. Feldman, John R. Hardy, C. Y. Fong
Physics Faculty Publications
Ab initio calculations show that a spherically symmetric charge relaxation of ions in a crystal, in response to the long-range electrostatic potential, is important for understanding the splitting between longitudinal- and transverse-optic-mode frequencies, and the violation of the Cauchy relations among elastic constants.
Beyond The Rigid-Ion Approximation With Spherically Symmetric Ions, L. L. Boyer, M. J. Mehl, J. L. Feldman, John R. Hardy, J. W. Flocken, C. Y. Fong
Beyond The Rigid-Ion Approximation With Spherically Symmetric Ions, L. L. Boyer, M. J. Mehl, J. L. Feldman, John R. Hardy, J. W. Flocken, C. Y. Fong
John R. Hardy Papers
Ab initio calculations show that a spherically symmetric charge relaxation of ions in a crystal, in response to the long-range electrostatic potential, is important for understanding the splitting between longitudinal- and transverse-optic-mode frequencies, and the violation of the Cauchy relations among elastic constants.
Rapidly Quenched FeXTa100-X Alloys, C.L. Chien, Sy_Hwang Liou, B.K. Ha, K.M. Unruh
Rapidly Quenched FeXTa100-X Alloys, C.L. Chien, Sy_Hwang Liou, B.K. Ha, K.M. Unruh
Sy-Hwang Liou Publications
Binary alloys of FexTa100-x were made by high-rate sputtering. A sharply defined boundary separates the composition ranges in which crystalline alloys (93 ≤ x ≤100) and amorphous alloys (15 ≤ x ≤ 90) are formed. The amorphous alloys with Fe concentrations up to the threshold of xc ≈ 65 are nonmagnetic. For the samples with x > xc, the magnetic ordering temperature (Tc) varies monotonically with Fe content to 200 K for a-Fe90Ta10. However, the crystalline alloys, with slightly higher Fe content, are strongly ferromagnetic. Their T …
Magnetic Properties And Hyperfine Interactions Of Amorphous Fe-Hf Alloys, Sy_Hwang Liou, G. Xiao, J.N. Taylor, C.L. Chien
Magnetic Properties And Hyperfine Interactions Of Amorphous Fe-Hf Alloys, Sy_Hwang Liou, G. Xiao, J.N. Taylor, C.L. Chien
Sy-Hwang Liou Publications
Alloys of FexHf100-x (20 ≤ x ≤ 100) were fabricated by a vapor-quench method. The amorphous state, as verified by x-ray diffraction, is realized over a wide composition range of 20 ≤ x ≤ 94. The magnetic phase diagram was determined. The variation with Fe content of the magnetic ordering temperature (Tc) in Fe-Hf amorphous alloys shows a maximum at xp≈87. In contrast, the effective magnetic hyperfine field and therefore the Fe moment increases monotonically with x. Amorphous pure Fe is likely to be magnetic (Tc ~200 K) with …
Random Magnetism In Amorphous Rare-Earth Alloys (Invited), David J. Sellmyer, S. Nafis
Random Magnetism In Amorphous Rare-Earth Alloys (Invited), David J. Sellmyer, S. Nafis
David Sellmyer Publications
Several aspects of the magnetic transitions seen in rare-earth metallic glasses are discussed, particularly with reference to recent theoretical work. These include: (a) apparent double transitions observed in Gd glasses where exchange fluctuations are important, (b) evidence for a correlated speromagnetic state recently predicted by Chudnovsky and Serota, and (c) the analysis of a Tb glass with strong random anisotropy in terms of an Ising-type spin-glass transition. Journal of Applied Physics is copyrighted by The American Institute of Physics.
Anomalous Magnetic Hysteresis In An Amorphous Nd54Co36B10 Alloy, George C. Hadjipanayis, S.H. Aly, David J. Sellmyer
Anomalous Magnetic Hysteresis In An Amorphous Nd54Co36B10 Alloy, George C. Hadjipanayis, S.H. Aly, David J. Sellmyer
David Sellmyer Publications
The hysteresis and crystallization behavior of an amorphous Nd54Co36B10 alloy have been examined over a range of temperatures. Crystallization studies show a glass transition temperature around 210 °C, two crystallization peaks at around 220 and 360 °C, and two endothermic peaks at around 530 and 600 °C, respectively. ac susceptibility measurements show an ordering temperature of 38 K for the amorphous phase. Four additional magnetic phases have been observed in the crystallized samples with ordering temperatures 17, 45, 90, and 190 K, respectively. Magnetic measurements on melt-spun ribbons reveal a coercivity of 6 kOe at …
Constraint On The Optical Constants Of A Film-Substrate System For Operation As An External-Reflection Retarder At A Given Angle Of Incidence, R. M.A. Azzam, Bruce E. Perilloux
Constraint On The Optical Constants Of A Film-Substrate System For Operation As An External-Reflection Retarder At A Given Angle Of Incidence, R. M.A. Azzam, Bruce E. Perilloux
Electrical Engineering Faculty Publications
Given a transparent film of refractive index n1 on an absorbing substrate of complex refractive indexn2-jk2, we examine the constraint on n1, n2, and k2 such that the film-substrate system acts as an external-reflection retarder of specified retardance Δ at a specified angle of incidence φ. The constraint, which takes the form ƒ(n1,n2,k2;φ,Δ) = 0, is portrayed graphically by equi-n1 contours in the n2,k2 plane at φ = 45, 70° and for Δ …
Spin-Glass And Double-Transition Behavior In Gd-La Glasses, Michael J. O'Shea, David J. Sellmyer
Spin-Glass And Double-Transition Behavior In Gd-La Glasses, Michael J. O'Shea, David J. Sellmyer
David Sellmyer Publications
We report studies of high-field magnetization, field-cooled magnetization, thermoremanent magnetization, and isothermal remanent magnetization as a function of temperature in the metallic glass sytem GdxLa72-xG28 where G28=Ga18B10 for the compositions x=72, 68, 64. The first two compositions show double-transition behavior and the last one shows only a paramagnetic to spin-glass transition. The approach to saturation at intermediate fields (up to 40 kOe) is of the form 1/H1/2 as predicted by a mean field model which incorporates a small random anisotropy. The field-cooled magnetization in these samples is …
Origin Of The Peaked Structure In The Conductance Of One-Dimensional Silicon Accumulation Layers, Richard A. Webb, A. Hartstein, J. J. Wainer, A. B. Fowler
Origin Of The Peaked Structure In The Conductance Of One-Dimensional Silicon Accumulation Layers, Richard A. Webb, A. Hartstein, J. J. Wainer, A. B. Fowler
Faculty Publications
We have made extensive studies of the temperature, gate voltage, and electric field dependences of the conductance peaks in small silicon inversion layers in order to distinguish between resonant-tunneling models and a hopping model. We find that many of the peaks are consistent only with a hopping model, whereas some could be consistent with an early resonant-tunneling model. None of our structure is consistent with resonant tunneling if the recent formulation of Stone and Lee is correct.
Problems Of Channel Correlation And Statistical Bias In Photon-Correlation Spectroscopy, Richard C. Haskell, Gary L. Pisciotta
Problems Of Channel Correlation And Statistical Bias In Photon-Correlation Spectroscopy, Richard C. Haskell, Gary L. Pisciotta
All HMC Faculty Publications and Research
Correlation between channels of the normalized photocount-rate correlation function g(2)(τ) becomes significant at high count rates and leads to a number of data-analysis problems. We derive an expression for channel correlation that is valid for a detector area of arbitrary extent and compare the theoretical predictions with measured values. A data-analysis procedure is demonstrated that employs the theoretical expression for channel correlation and provides a rigorous test of an assumed fitting function. The procedure facilitates the use of the cumulant method in determining the polydispersity of scatterers. An expression for the statistical bias of g(2) …
The Impeachment And Trial Of Secretary Of War William Worth Belknap, Duane Edward Holthof
The Impeachment And Trial Of Secretary Of War William Worth Belknap, Duane Edward Holthof
Masters Theses
The purpose of this thesis is to give an account of the events which lead to the resignation of Secretary of War William Worth Belknap in 1876, to examine the circumstances surrounding his impeachment, and to study the testimony in his Senate trial.
Although Belknap was not convicted on charges of accepting bribes, most of those senators who voted to acquit him did so on the technical ground that the Senate lacked the jurisdiction to try a private citizen. The evidence in the case clearly indicated Belknap's involvement, and there seems little doubt that if Belknap did not know what …
Construction And Testing Of A New Atomic Physics Beam Line At The Western Michigan University Accelerator Laboratory, William Andrew Hollerman
Construction And Testing Of A New Atomic Physics Beam Line At The Western Michigan University Accelerator Laboratory, William Andrew Hollerman
Masters Theses
A new beam line containing a differentially-pumped gas cell and charge state analyzing magnet was constructed for the purpose of measuring a wide variety of atomic inner-shell processes, such as excitation, ionization, and charge transfer. The completed system will be able to measure these individual atomic processes using coincidence techniques. Initial testing of the beam line was performed using 40MeV S+7+Ar collisions to determine the effect of the collimating slit size on the measured x-ray cross sections. These measurements showed that the slip size on the measured x-ray cross sections. These measurements showed that the slit size affects …
Resonant Electron Transfer And K-Shell Excitation Of Lithiumlike Projectiles In Collisions With Neutral Gas Targets, Carollyn Sloan Oglesby
Resonant Electron Transfer And K-Shell Excitation Of Lithiumlike Projectiles In Collisions With Neutral Gas Targets, Carollyn Sloan Oglesby
Masters Theses
No abstract provided.
The Pauli Operator Correction In The Effective Λn Interaction, Jaleh Owliaei
The Pauli Operator Correction In The Effective Λn Interaction, Jaleh Owliaei
Masters Theses
Hypernuclear structure calculations performed for 6ΛLi, 7ΛLi, and 16Λ0 have reproduced the 1Λ=1 levels inferred from the recent (k, Π) reactions. However the 1Λ=0, groundstate of 16Λ0 is overbound by 6 MeV in these calculations, indicating a density dependence in the effective ΛN interaction in the interior of the heavier system. In this work corrections to the 16Λ0 effective interaction are introduced in terms of a Brueckner-Goldstone G-matrix with a modified Pauli operator. The G-matrix of 16Λ0 derived from that of 6ΛLi …
Small-Angle Neutron Scattering Of (Er₀.₈Ho₀.₂)Rh₄B₄, Oran Allan Pringle, Herbert A. Mook, M. Brian Maple
Small-Angle Neutron Scattering Of (Er₀.₈Ho₀.₂)Rh₄B₄, Oran Allan Pringle, Herbert A. Mook, M. Brian Maple
Physics Faculty Research & Creative Works
The (Er1-xHox)Rh4B4 pseudoternary alloy system has a minimum in the phase boundary between the superconducting and ferromagnetic phases near x=0.3. This minimum has been identified as due to the competing magnetic anisotropies of Er and Ho. It has also been suggested that there could be a Lifschitz point near the minimum. Using the 30-m SANS camera at the National Center for Small-Angle Scattering Research at ORNL, we have observed a peak in the SANS pattern for (Er 0.8Ho0.2)Rh4B4 at Q=0.065 Å-1. This peak appears for …
Lung Cancer Incidence In A Chinese High Background Area — Epidemiological Results And Theoretical Interpretation, Werner Hofmann, Robert Katz, Chunxiang Zhang
Lung Cancer Incidence In A Chinese High Background Area — Epidemiological Results And Theoretical Interpretation, Werner Hofmann, Robert Katz, Chunxiang Zhang
Robert Katz Publications
A survey of inhabitant exposures arising from the inhalation of radon and thoron daughters, and lung cancer mortality has been carried out in two adjacent areas in Guangdong province, China, designated as the "high background" and the "control" area. Annual exposure rates are 0.38 WLM/yr in the high background, and 0.16 WLM/yr in the control area, while age-adjusted mortality rates are 2.7 per 105 living people of all ages in the high background, and 2.9 per 105 in the control area. From this data we conclude that we are unable to determine the excess lung cancer rate over normal fluctuations …
Self-Consistent Phases In Topological Particle Theory, Paul Finkler, C. Edward Jones
Self-Consistent Phases In Topological Particle Theory, Paul Finkler, C. Edward Jones
Paul Finkler Papers
To be a self-contained theory, topological particle theory should explain from the basis of its own stated framework of assumptions (nonlinear self-consistency equations, pole factorization, crossing symmetry, and Hermitian analyticity} all the mathematical properties and numerical values of scattering amplitudes. This paper attempts to move the theory in this direction by showing that the phases of the zero-entropy amplitudes in the theory are, in fact, determined by the above framework of assumptions except for trivial ambiguities that appear to have no physical consequences. This extends previous work on this subject and removes the need for certain extra assumptions. Once the …
Derivation Of Discrete Invariances (T, C, And P) And The Connection Between Spin And Statistics In Topological Particle Theory, C. E. Jones, Paul Finkler
Derivation Of Discrete Invariances (T, C, And P) And The Connection Between Spin And Statistics In Topological Particle Theory, C. E. Jones, Paul Finkler
Paul Finkler Papers
For purely hadronic processes, the standard connection between spin and statistics as well as separate invariances under charge conjugation, parity, and time reversal are shown to be consequences of self-consistency in topological particle theory.
Comment On "Pyroelectric Materials As Electronic Pulse Detectors Of Ultraheavy Nuclei", R. Al-Jishi, L. L. Foldy, Rolfe G. Petschek, P. L. Taylor
Comment On "Pyroelectric Materials As Electronic Pulse Detectors Of Ultraheavy Nuclei", R. Al-Jishi, L. L. Foldy, Rolfe G. Petschek, P. L. Taylor
Faculty Scholarship
[No abstract available]
A Birefringence Relaxation Determination Of Rotational Diffusion Of Magnetotactic Bacteria, Charles Rosenblatt, Richard B. Frankel, Richard P. Blakemore
A Birefringence Relaxation Determination Of Rotational Diffusion Of Magnetotactic Bacteria, Charles Rosenblatt, Richard B. Frankel, Richard P. Blakemore
Physics
The orientational relaxation of the magnetotactic bacterium Aquaspirillum magnetotacticum is observed by the decay of the optical birefringence upon switching off an aligning magnetic field. The data yield a rotational diffusion constant Dr ≅ 0.13 s1 and information about cell sizes that is consistent with optical microscopy data.
Safety Evaluation Report Related To The Renewal Of The Operating License For The Triga Training And Research Reactor At The University Of Utah, United States Nuclear Regulatory Commission, Office Of Nuclear Reactor Regulations
Safety Evaluation Report Related To The Renewal Of The Operating License For The Triga Training And Research Reactor At The University Of Utah, United States Nuclear Regulatory Commission, Office Of Nuclear Reactor Regulations
Radioactive Materials
This Safety Evaluation Report for the application filed by the University of Utah (UU) for a renewal of operating license R-126 to continue to operate a training and research reactor facility has been prepared by the Office of Nuclear Reactor Regulation of the U.S. Nuclear Regulatory Commission. The facility is owned and operated by the University of Utah and is located on its campus in Salt Lake City, Salt Lake County, Utah. The staff concludes that this training reactor facility can continue to be operated by UU without endangering the health and safety of the public.
Photoemission, Electronic Structure, And Magnetism In Vpd3, D.K. Misemer, S. Auluck, David J. Sellmyer, Sitaram Jaswal, A.J. Arko
Photoemission, Electronic Structure, And Magnetism In Vpd3, D.K. Misemer, S. Auluck, David J. Sellmyer, Sitaram Jaswal, A.J. Arko
David Sellmyer Publications
Electronic and magnetic states in the ordered compound VPd3 have been investigated with photoemission measurements and self-consistent band-structure calculations. The linear combination of muffin-tin orbitals method was used to study VPd3 in a hypothetical cubic crystal structure and the actual tetragonal crystal structure, and the calculations were performed for both paramagnetic and spin-polarized configurations. The results for the cubic structure are in agreement with earlier calculations, while the results from the tetragonal structure are in much better agreement with the photoemission and other measurements.
Summary Abstract: Capacitance-Voltage Characteristics In Modulation Doped Heterojunction Fets, George B. Norris, David C. Look, W. Koop, J. Klem, H. Morkoç
Summary Abstract: Capacitance-Voltage Characteristics In Modulation Doped Heterojunction Fets, George B. Norris, David C. Look, W. Koop, J. Klem, H. Morkoç
Physics Faculty Publications
No abstract provided.
Crossover From The O(2) To O(1) Universality Class In Equilibrium Polymerization, Rolfe G. Petschek
Crossover From The O(2) To O(1) Universality Class In Equilibrium Polymerization, Rolfe G. Petschek
Faculty Scholarship
Equilibrium polymerization systems in which directed rings are formed correspond to O(2) vector models of magnetism and ones in which undirected rings form correspond to O(1) models. In this paper it is shown that a system in which polymers tend to form directed rings but there is a finite free energy for misdirected bonds corresponds to an O(2) model with a uniaxial anisotropy which causes it to crossover to an O(1) model.
Explicit Equations For The Polarizing Angles Of A High-Reflectance Substrate Coated By A Transparent Thin Film, R. M.A. Azzam
Explicit Equations For The Polarizing Angles Of A High-Reflectance Substrate Coated By A Transparent Thin Film, R. M.A. Azzam
Electrical Engineering Faculty Publications
Simple explicit equations are derived that determine the angles of incidence at which the parallel and perpendicular polarization components of light are extinguished on reflection from a transparent film coating a high-reflectance (metallic) substrate. The polarizing angles obtained from our approximate expressions are in excellent agreement with those determined by iterative numerical solution of the exact nonlinear equations that govern such angles. For the approximation to be valid, the intensity reflectance of the film-substrate interface, evaluated at the critical angle of the film-ambient interface, must exceed 0.5.