scholarly journals Note on total reflexion of electric waves at the interface between two media

1928 ◽  
Vol 119 (783) ◽  
pp. 523-525
Keyword(s):  
Wave Front ◽  
Electric Force ◽  
Present Communication ◽  
Reflected Waves ◽  
Magnetic Forces ◽  
Previous Communication ◽  
Total Reflexion ◽  
Incident Waves ◽  
Electric Waves

In a previous communication it was assumed that, when total reflexion takes place at the interface between two media, the electric force in the disturbance in the second medium is in the plane of the wave-front; it may be shown that it is impossible in this case to satisfy the conditions that the electric and magnetic forces are both in the wave-front in the second medium. The object of the present communication is to investigate the disturbance in the second medium, and to obtain the changes of phase in the reflected waves in the first medium. Taking the plane z = 0 as the interface between the two media, let the components of the electric force in the incident waves, z > 0, be given by (A, B, C) cos K ( lx + my + nz + V t )

scholarly journals The reflexion and transmission of electric waves at the interface between two transparent media

1929 ◽  
Vol 123 (791) ◽  
pp. 1-27
Keyword(s):  
Electric Current ◽  
Plane Surface ◽  
Plane Waves ◽  
Present Communication ◽  
Important Paper ◽  
Reflected Waves ◽  
Magnetic Forces ◽  
Transparent Media ◽  
Approximate Expressions ◽  
Electric Waves

The effect of a transparent sphere on a train of plane waves has been fully investigated by Lorentz in an important paper. The object of the present communication is to obtain approximate expressions for the electric and magnetic forces in the transmitted and in the reflected waves, where electric waves are incident on the interface between two media, the surface of separation being any surface. In a former paper the writer investigated in particular the case of a perfectly conducting obstacle, and the method adopted for that purpose will be applied in the present case. The assumption is that the most important parts of the electric and magnetic forces in the transmitted and reflected waves are due to the magnetic and electric distributions at any point on the separating surface which would produce the electric and magnetic forces in the immediate neighbourhood of the point if the surface were a plane surface. The equations which express the magnetic and electric forces at a point in terms of the magnetic and electric current distributions are:—

scholarly journals The condition that the ratio of the intensities of the transmitted and reflected electric waves at the interface between two media is independent of their plane of polarisation

1925 ◽  
Vol 108 (747) ◽  
pp. 386-392
Keyword(s):  
Steady State ◽  
Magnetic Permeability ◽  
Outer Boundary ◽  
Electric Force ◽  
Present Communication ◽  
Dielectric Media ◽  
Set Up ◽  
Short Time ◽  
Incident Waves ◽  
Electric Waves

It has been shown that the condition that a steady state of electrical oscillations can be set up in a comparatively short time in a space, whose outer boundary separates two dielectric media with different electric constants, is that the ratio of the specific inductive capacities of the two media is approximately equal to the ratio of the magnetic permeabilities. This suggests that, when the ratios are equal, the ratios of the incident, transmitted, and reflected disturbances are independent of the direction of the plane of polarisation of the incident disturbance, and this can be readily verified. The object of the present communication is to prove that the condition is necessary, that is, the condition that the ratios of the intensities of the incident, transmitted, and reflected electric waves at the interface between two media is independent of the direction of the plane of polarisation of the incident waves is that the ratio of the specific inductive capacities of the two media is equal to the ratio of the magnetic permeabilities of the two media. Taking the plane of separation of the two media to be the plane z = 0, let K, μ be the specific inductive capacity and the magnetic permeability respectively of the medium for which z > 0, and let K', μ' be the specific inductive capacity and the magnetic permeability of the medium for which z ˂ 0, and let the electric force in the incident waves be given by (A, B, C) e tk ( lx+my+nz +V t ) , where A l + B m + C n = 0, KμV 2 = 1;

scholarly journals Integrals of the equations of electrodynamics with to the electric constants of a transparent medium

1926 ◽  
Vol 113 (764) ◽  
pp. 237-253 ◽  
Keyword(s):  
Electric Current ◽  
Current Distribution ◽  
Magnetic Force ◽  
Small Radius ◽  
Transparent Medium ◽  
Electric Force ◽  
Present Communication ◽  
Magnetic Current ◽  
Magnetic Forces ◽  
Equations Of Electrodynamics

Integrals of the equations of propagation of electrical disturbances have been given by the present writer which express the electric and magnetic forces at any point outside a surface enclosing all the sources in terms of an electric current distribution and a magnetic current distribution over the surface. The result for a source at a point can be obtained by taking as the surface a sphere of very small radius with its centre at the point. This suggests that the equations representing Faraday’s laws can be written 1/V 2 ∂X/∂ t +4π i x = ∂ϒ/∂ y – ∂β/∂ z , 1/V 2 ∂X/∂ t + 4π i v =∂∝/∂ z – ∂ϒ/∂ x , 1/V 2 ∂z/∂ t – 4π i z = ∂β/∂ x – ∂∝/∂ y (1) – ∂∝/∂ t + 4π m x = ∂z/∂ y – ∂Y/∂y, – ∂β/∂t + 4π my = ∂X/∂ z – ∂Z/∂ x , – ∂ϒ/∂ t + 4π mz ∂Y/∂ x – ∂X/∂ y , (2) where X, Y, Z are the components of the electric force, α, β, γ are the components of the magnetic force, i x , i y , i z are the components of an electric current distribution, and m x , m y , m z are the components of a magnetic current distribution throughout the space. The object of the present communication is to express X, Y, Z, α, β, γ in terms of the electric current and magnetic current distributions and to apply the result to the discussion of the electric constants of a transparent medium. It is convenient to take instead of equations (1) and (2) the following equations, which include (1) and (2) as a particular case

scholarly journals The transmission of electric waves around the Earth's surface

1916 ◽  
Vol 92 (643) ◽  
pp. 493-500 ◽  
Keyword(s):  
General Formula ◽  
Magnetic Force ◽  
Wave Length ◽  
Angular Distance ◽  
Electric Force ◽  
Present Communication ◽  
The Earth ◽  
Perfect Conduction ◽  
Electric Waves

The value of the magnetic force at a point on the earth's surface, due to a simple oscillator placed on the surface with its axis normal to the surface, has been recently calculated by Love for a wave-length of 5 kilom. at certain distances from the oscillator. His results for the case of perfect conduction are the same as the corresponding series when the surface of the earth is supposed to be imperfectly conducting, The object of the present communication is to obtain the general formula for the case of imperfect conduction. Let r, θ, ϕ be the polar co-ordinates of a point, where r is its distance from the centre of the earth, θ its angular distance from the oscillator, E r , E θ , E ϕ the components of the electric force, and α, β, γ , the corresponding components of the magnetic force. Then, Since there is symmetry round the axis of the oscillator, α =0, β =0, γ =0; and throughout space outside the surface

scholarly journals The total reflexion of electric waves the interface between two media

1929 ◽  
Vol 123 (792) ◽  
pp. 391-400
Keyword(s):  
Plane Surface ◽  
Plane Waves ◽  
Reflected Waves ◽  
Total Reflexion ◽  
The Media ◽  
Velocity Of Propagation ◽  
Shadow It ◽  
The Waves ◽  
Finite Extent ◽  
Electric Waves

The theory of total reflexion has been treated usually by considering a train of plane waves incident on a plane surface separating two different media. It has been observed by Schuster that there is the difficulty of seeing how the disturbance in the second medium is maintained, and he has discussed the problem of a parallel beam of waves of finite extent incident on the plane surface separating the media. It may be noticed that there is a similar difficulty in the case where there are both transmitted and reflected waves, as there is a transfer of energy in the second medium parallel to the interface at a rate which is in the ratio σ' tan θ'/σ tan θ to the rate of transfer of energy in the first medium parallel to the interface. If the source of the electric waves in the first medium is a simple oscillator, and the velocity of propagation in the second medium is greater than the velocity of propagation in the first medium, then the rays which are bounded by the cone, whose vertex is at the oscillator, and whose semi-vertical angle is the critical angle, are transmitted into the second medium, where their boun­dary is the position of the plane interface outside the base of the cone, and there is no portion of the space in shadow. To obtain a shadow it is necessary that the interface is concave towards the oscillator. It is proposed in the following to discuss the problem of the transmission and reflexion of electric waves, when the surface separating the media is a sphere, and the source of the waves is a simple oscillator inside the sphere, whose axis passes through the centre of the sphere.

scholarly journals Observations on the formation of bi-nuclear cells

1924 ◽  
Vol 96 (676) ◽  
pp. 291-293 ◽  
Keyword(s):  
X Rays ◽  
Present Communication ◽  
Normal Cells ◽  
Previous Communication

In a previous communication the changes observed during the growth and division of normal cells growing in vitro were described. The present communication deals with certain modifications of the normal processes of mitosis resulting in the formation of cells containing two nuclei. Bi-nucleate cells are frequently seen in cultures of tissues grown in vitro and are generally supposed to be formed by amitotic division of the nucleus. They can be produced experimentally by the use of a slightly unfavourable medium or by subjecting the culture to the influence of some agent such as X-Rays.

scholarly journals On the periodicity in the electric touch of chemical elements. Preliminary notice

1900 ◽  
Vol 66 (424-433) ◽  
pp. 450-451 ◽  
Keyword(s):  
Contact Resistance ◽  
Sensitive Element ◽  
Chemical Elements ◽  
Previous Communication ◽  
The Impact ◽  
Electric Waves

In my previous communication an account was given of the contact sensitiveness of elementary substances to electric radiation. It was shown that though many substances exhibit a diminution of contact resistance, there are others, of which potassium may be taken as an example, which show an increase of resistance—an increase which, in some cases, lasts during the impact of electric waves, the sensitive element quickly recovering on the cessation of radiation.

Instability of a stratified boundary layer and its coupling with internal gravity waves. Part 2. Coupling with internal gravity waves via topography

2008 ◽  
Vol 595 ◽  
pp. 409-433 ◽  
Author(s):  
XUESONG WU ◽  
JING ZHANG
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Shear Instability ◽  
Acoustic Analogy ◽  
Physical Processes ◽  
Reflected Waves ◽  
Instability Modes ◽  
Viscous Shear ◽  
Incident Waves

The aim of this paper is to show that the viscous shear instability identified in Part 1 is intrinsically coupled with internal gravity waves when a localized surface topography is present within a boundary layer. The coupling involves two aspects: receptivity and radiation. The former refers to excitation of shear instability modes by gravity waves, and the latter to emission of gravity waves by instability modes. Both physical processes are studied using triple-deck theory. In particular, the radiated gravity waves are found to produce a leading-order back action on the source, and this feedback effect, completely ignored in the acoustic analogy type of approach, is naturally taken into account by the triple-deck formalism. A by-product is that for certain incident angles, gravity waves are over-reflected by the boundary layer, i.e. the reflected waves are stronger than the incident waves.

scholarly journals Energy Exchanges between Density Fronts and Near-Inertial Waves Reflecting off the Ocean Surface

2016 ◽  
Vol 46 (2) ◽  
pp. 501-516 ◽  
Author(s):  
Nicolas Grisouard ◽  
Leif N. Thomas
Keyword(s):  
Analytical Model ◽  
Internal Waves ◽  
Energy Exchange ◽  
Viscous Friction ◽  
Nonlinear Effects ◽  
Ocean Surface ◽  
Inertial Waves ◽  
Viscous Effects ◽  
Reflected Waves ◽  
Incident Waves

AbstractInertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.

scholarly journals COMPARISON OF MODEL AND BEACH SCOUR PATTERNS

1970 ◽  
Vol 1 (12) ◽  
pp. 80
Author(s):  
John B. Herbich
Keyword(s):  
Gulf Coast ◽  
Wave Length ◽  
Laboratory Studies ◽  
Intermediate Type ◽  
Characteristic Parameters ◽  
Reflected Waves ◽  
Texas Gulf Coast ◽  
Laboratory Conditions ◽  
Set Up ◽  
Incident Waves

Artificial or natural barriers may be divided into two classes, those from which waves are reflected and those on which waves break In general, any intermediate type that gives a combination of reflection and breaking may set up severe erosive action of the beach m front of barriers When the reflected waves are superimposed on the incident waves a stationary spatial envelope of the combined incident and reflected waves is produced Previous laboratory studies indicated that the crests of the sand bed appear fairly closely under the nodes of the envelope and troughs of the scoured sand bed under the loops of the envelope The predominant scouring pattern had a spacing between crests equal to one-half the wave length Other studies by Keulegan and Shepard established characteristic parameters for bar and trough depth for laboratory conditions and for several field locations Their studies were compared with beach profiles taken along the Texas Gulf Coast.

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