II. Geometrical optics of variable-frequency light rays in special relativistic and nonrelativistic situations:The general law of reflection

2000 ◽  
Vol 78 (8) ◽  
pp. 747-754 ◽  
Author(s):  
W T Chyla
Keyword(s):  
Coherent Scattering ◽  
Skin Depth ◽  
Variable Frequency ◽  
Angle Of Incidence ◽  
X Rays ◽  
Reflection Point ◽  
General Law ◽  
Light Rays ◽  
Relativistic Treatment ◽  
Angle Of Reflection

The general law of reflection concerns situations when the light ray undergoes a shift of frequency at the reflection point. For example, it governs reflection of light rays from a moving mirror (either in a vacuum or in a transparent medium), reflection from a motionless mirror coated with a layer of Raman-active molecules in the coherent-scattering regime, or external reflection of X-rays from the surface of a condensed matter sample, with partial dissipation of energy within the skin depth. The general law of reflection is derived from the extremum principle for propagation of variable-frequency light rays. It states that the angle of reflection depends not only on the angle of incidence but also on the frequency shift in the reflection point and dispersion of the refractive index of the medium in contact with the mirror. The compatibility of the general law of reflection and the special relativistic treatment of reflection is examined in detail. Applications of the new law of reflection are discussed in the special relativistic and the nonrelativistic regime. PACS Nos.: 42.15-i, 03.30+p

Electromagnetic Radiation

2019 ◽  
Author(s):  
Richard R. Freeman ◽  
James A. King ◽  
Gregory P. Lafyatis
Keyword(s):  
Electromagnetic Radiation ◽  
Energy Transport ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
X Rays ◽  
Field Equations ◽  
Radio Frequency Radiation ◽  
Relativistic Treatment ◽  
Time Variations ◽  
Radiation Science

Electromagnetic Radiation is a graduate level book on classical electrodynamics with a strong emphasis on radiation. This book is meant to quickly and efficiently introduce students to the electromagnetic radiation science essential to a practicing physicist. While a major focus is on light and its interactions, topics in radio frequency radiation, x-rays, and beyond are also treated. Special emphasis is placed on applications, with many exercises and homework problems. The format of the book is designed to convey the basic concepts of a topic in the main central text in the book in a mathematically rigorous manner, but with detailed derivations routinely relegated to the accompanying side notes or end of chapter “Discussions.” The book is composed of four parts: Part I is a review of basic E&M, and assumes the reader has a had a good upper division undergraduate course, and while it offers a concise review of topics covered in such a course, it does not treat any given topic in detail; specifically electro- and magnetostatics. Part II addresses the origins of radiation in terms of time variations of charge and current densities within the source, and presents Jefimenko’s field equations as derived from retarded potentials. Part III introduces special relativity and its deep connection to Maxwell’s equations, together with an introduction to relativistic field theory, as well as the relativistic treatment of radiation from an arbitrarily accelerating charge. A highlight of this part is a chapter on the still partially unresolved problem of radiation reaction on an accelerating charge. Part IV treats the practical problems of electromagnetic radiation interacting with matter, with chapters on energy transport, scattering, diffraction and finally an illuminating, application-oriented treatment of fields in confined environments.

scholarly journals From Femtoseconds to Hours–Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

2021 ◽  
Vol 11 (13) ◽  
pp. 6179
Author(s):  
Felix Lehmkühler ◽  
Wojciech Roseker ◽  
Gerhard Grübel
Keyword(s):  
Time Scales ◽  
Free Electron Laser ◽  
Photon Correlation Spectroscopy ◽  
Signal To Noise Ratio ◽  
Coherent Scattering ◽  
Correlation Spectroscopy ◽  
X Rays ◽  
Photon Correlation ◽  
X Ray ◽  
Scattering Technique

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

scholarly journals The SEXTANTS beamline at SOLEIL: a new facility for elastic, inelastic and coherent scattering of soft X-rays

2013 ◽  
Vol 425 (7) ◽  
pp. 072018 ◽  
Author(s):  
M Sacchi ◽  
N Jaouen ◽  
H Popescu ◽  
R Gaudemer ◽  
J M Tonnerre ◽  
...  
Keyword(s):  
Coherent Scattering ◽  
X Rays ◽  
New Facility

Orientational Movements of the Foot of Littorina Species in Relation to the Plane of Vibration of Polarized Light

1961 ◽  
Vol 38 (1) ◽  
pp. 213-224
Author(s):  
G. H. CHARLES
Keyword(s):  
Polarized Light ◽  
Angle Of Incidence ◽  
Virtual Absence ◽  
Lens Aperture ◽  
Light Rays ◽  
Stimulation Of

1. Littorina littoralis (L.), L. saxatilis (L.), L. neritoides (L.) and L. littorea (L.) responded to the plane of vibration (e vector) of polarized light directly incident upon their eyes in the virtual absence of any substrate reflexions. Photonegative winkles orientated parallel with the plane of vibration and photopositive individuals at right angles to this plane. 2. Decrease of the angle of incidence towards zero of polarized light rays incident upon the lens aperture of Littorina littoralis completely destroyed the ability to orientate to the plane of vibration. This can be explained on the basis of a Fresnel reflexion/refraction mechanism of orientation. 3. Unilaterally blinded Littorina littoralis gave just as good an orientation to vertical rays of polarized light as winkles with intact vision. 4. It is concluded that the eyes of Littorina species are capable of detecting the plane of vibration of polarized light directly incident from above by means of a Fresnel reflexion/refraction mechanism, and that orientation does not depend on balanced stimulation of the two eyes.

Wechselwirkung kondensierter Molekularstrahlen mit festen Oberflächen

1968 ◽  
Vol 23 (2) ◽  
pp. 274-279 ◽  
Author(s):  
E. W. Becker ◽  
R. Klingelhöfer ◽  
H. Mayer
Keyword(s):  
Steel Surface ◽  
Tangential Velocity ◽  
Incident Beam ◽  
Stainless Steel Surface ◽  
Angle Of Incidence ◽  
Mean Velocity ◽  
Tangential Velocity Component ◽  
Polished Stainless Steel ◽  
The Mean ◽  
Angle Of Reflection

The reflection of a beam of nitrogen clusters from a polished stainless steel surface is investigated. The scattered flux shows a strong maximum at an angle of reflection almost 90°, independent of angle of incidence. The mean velocity of the reflected beam is about equal to the tangential velocity component of the incident beam. Measurements with increased background pressure demonstrate that the reflected beam still consists essentially of clusters.

Quantitative Determination of Carbon in Solid Hydrocarbons Using the Intensity Ratio of Incoherent to Coherent Scattering of X-Rays

1964 ◽  
Vol 18 (6) ◽  
pp. 171-174 ◽  
Author(s):  
C. J. Toussaint ◽  
G. Vos
Keyword(s):  
Intensity Ratio ◽  
Coherent Scattering ◽  
X Rays ◽  
Ray Method ◽  
Sample Weight ◽  
X Ray ◽  
Carbon Determination ◽  
Solid Hydrocarbons ◽  
Good Agreement

A method is presented for the determination of carbon in solid hydrocarbons using the intensity ratio of incoherent to coherent scattering of x-rays. The method is very rapid with precision at the 95% confidence level of about ±0.3%. The minimum sample weight necessary is 0 2 g. Analysis of samples by the x-ray method shows good agreement with values obtained by microcombustion. Finally a general comparison between different methods for carbon determination in solid hydrocarbons is discussed.

scholarly journals The reflection and diffraction of X-rays

1931 ◽  
Vol 133 (821) ◽  
pp. 274-291 ◽  
Keyword(s):  
Critical Angle ◽  
Close Agreement ◽  
Wave Length ◽  
Length Distribution ◽  
Incident Beam ◽  
Electromagnetic Theory ◽  
Spherical Mirror ◽  
Angle Of Incidence ◽  
X Rays ◽  
Carbon Target

The agreement between the theories of the reflection of X-rays by solids and observations is discussed. Generally the observations so far obtained are not in close agreement with each other or with theory. The writers find that X-rays of wave-lengths 13·3 Å. (Cu Lα) and 44·7 Å. (C Kα) are reflected by glass, quartz and stainless steel at angles considerably greater than the calculated critical angles. The radiation from carbon has been focussed by a spherical mirror for an angle of incidence of 45°. The ratio of the intensity of the reflected to the incident beam, when X-rays from a carbon target are incident on a glass mirror, has been determined approximately by a photographic method and is found to agree with the Fresnel electromagnetic theory provided a higher absorption of the X-rays occurs than has been previously supposed. This evidence of reflection for angles of incidence greater than the critical angle, which is 6° for glass at a wave-length of λ = 44·7 Å., is confirmed by observations with a glass diffraction grating with which the λ = 44·7 Å. line has been observed for angles of incidence on a plane grating up to 19°. A new plane ruled grating spectrometer is described by means of which the C Kα line has been obtained with short exposures in all orders from the 18th negative to the 13th positive. Microphotometer curves of the wave-length distribution of the energy in the grating spectrum of carbon radiation are given, and these indicate that it consists almost entirely of the Kα line, λ = 44·7 Å. Using Rowland’s method of coincidences the wave-length λ C kα is found to be 44·7 5 Å. relative to λ Cu Lα = 13·32 Å.

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