Showing papers on "Reflection (physics) published in 1968"
TL;DR: In this paper, it is shown that if the surface is flat and smooth, the nature of the reflection is called specular, i.e., mirror-like, and obeys the simple law that the angle of incidence equals the angles of reflection.
Abstract: Reflection of light is a surface phenomenon—it is strongly dependent on the nature of the surface and can therefore be used to study surfaces. If the surface is flat and smooth, the nature of the reflection is called specular, i.e., mirrorlike, and obeys the simple law that the angle of incidence equals the angle of reflection.
1,809 citations
TL;DR: In this article, a two-scale model of rough surfaces is considered which permits theoretical interpretation of the features of very high frequency (VHF) scattering from such surfaces (say, from a sea surface).
Abstract: A two-scale model of rough surfaces is considered which permits theoretical interpretation of the features of very high frequency (VHF) scattering from such surfaces (say, from a sea surface). The scattering surface is assumed to be a superposition of small-scale ripple and large waves (swell). Reflection from the latter may he considered by the Kirchhoff approximation. The spatial spectrum of corrugations is taken into consideration; the calculations based on this model help to give an explanation of the behavior of the scattered intensity as a function of the angle of incidence \psi , and to establish which factors affect this dependence at various values of \psi - Theoretically predicted dependence of the scattered intensity upon radio wavelength \lambda , depolarization of the scattered signal, and other features of the scattered radiation are in good agreement with the experimental data obtained from direct measurements. Frequency spectra of the backscattered signal were also investigated (experimental measurements were carried out at wavelengths 3.2 cm, 10 cm, 50 cm, 1.5 m, and 4 m). Observed shifts of the central frequency agree with results of other authors (for the range of \lambda = 3 cm to 200 m). The measured values of the spectrum width appeared approximately twice those theoretically calculated. This may be explained by the influence of dissipative processes and of fluctuations of the skin-deep layer drift velocities. Space correlation of the backscattered signal was also investigated (both theoretically and experimentally). 50 percent decorrelation occurs at distances compared with dimensions of a wave slope.
117 citations
TL;DR: In this article, a procedure for the numerical computation of synthetic seismo-grams of the reflected wave arising from the incidence of a spherical wave on an inhomogeneous transition zone with arbitrary depth-dependent variation of the elastic moduli and density is presented.
Abstract: A procedure has been presented for the numerical computation of synthetic seismo-grams of the reflected wave (including head waves and continuously refracted waves) arising from the incidence of a spherical wave on an inhomogeneous transition zone with arbitrary depth-dependent variation of the elastic moduli and density. The reflection phenomenon will be discussed in the frequency domain where the method of stationary phase gives a rapid estimate of the important features of the reflected wave field as a function of frequency, phase velocity and distance. Using this estimate synthetic seismograms are obtained by numerical integration with respect to wave number and by applying a fast Fourier transform technique. Synthetic seismogram sections for three typical examples of crust-mantle transition zones are discussed in detail. The procedure described in this paper provides a new means of placing more severe bounds on possible crustal and upper mantle models.
98 citations
01 Nov 1968
TL;DR: In this paper, it was shown that the existence, approximate angular location, and qualitative behavior of the element pattern null are determined by inspection of a simple infinite array representative of a class of structures which permit external resonances.
Abstract: In recent years, unusual dips or nulls have been observed in the element patterns of certain phased-array antennas at angles closer to broadside than that for which an endfire grating lobe exists. These nulls are known to bear a direct and simple relation to a total reflection condition which occurs when all elements of the array are excited. The purposes of this paper are to investigate the basic cause of these element pattern nulls, and to clarify the relationship between these nulls and possible guided waves which may be supported by the array face. It is shown herein that, for a certain class of arrays, these nulls (actually the total reflection condition) are caused by the forced resonance of a higher external mode in the vicinity of the array aperture. The nature of this resonance is demonstrated on a simple infinite array representative of a class of structures which permit external resonances. A detailed analysis of this array (of waveguide-fed slots covered by a dielectric layer) yields a simple equivalent network from which the existence, approximate angular location, and qualitative behavior of the element pattern null are determined by inspection. There are two types of guided waves which are of concern here, surface waves and leaky waves. It is shown that the actual array cannot support a true surface wave, and that the surface wave customarily associated with element pattern nulls is really a driven surface-wave-like field which appears on the array face only at precisely the total reflection condition, and which is indistinguishable in its properties from a true surface wave on a modified (corrugated) structure, not on the actual array. The leaky wave, whose role is explained here for the first time, is a true mode of the actual array and radiates at an angle close to that for the element pattern null. Its influence on the element pattern null is akin to the relation between free and forced resonances, and its attenuation constant yields the width of this null.
90 citations
29 Jan 1968
TL;DR: In this paper, the behavior of thin and rectangular solid submerged breakwaters is examined and a theoretical relationship for the reflection coefficient of a thin breakwater across the wave number spectrum is proposed.
Abstract: The behaviour of thin and rectangular solid submerged breakwaters is re-examined. Dean's theory is found to be correct for a thin barrier in infinitely deep water. An empirical and theoretical relationship for the reflection coefficient of a thin breakwater across the wave number spectrum is proposed. Rectangular solid breakwaters have a maximum reflection when the incident wave has the same period as a standing wave on top of the breakwater and with a wave length equal to the crest width. A submerged permeable breakwater for depths of submergence greater than 5% of the total depth transmits less wave energy than the solid over a certain frequency range. The minimum is transmitted when the criterion above for solid breakwaters is also met. Both permeable and solid rectangular breakwaters cause a substantial loss in wave energy and at least 501 of the incident energy is lost to turbulence. A substantial proportion, 30 to 601 of the energy transmitted is transferred to higher frequencies than the incident wave.
87 citations
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01 Aug 1968
TL;DR: In this paper, three models were examined to study the transmission of ocean waves through an ice field, where the effect of ice thickness, water depth, and the wavelength and angle of incidence of the incoming ocean wave was considered.
Abstract: Three models are examined to study the transmission of ocean waves through an ice-field. In each case the effect of ice thickness, water depth, and the wavelength and angle of incidence of the incoming ocean wave is considered. In Model 1 the ice is assumed to consist of floating non-interacting mass elements of varying thickness and the shallow-water approximation is utilized to simplify the equations. A simple cosine distribution varying in one direction only is assumed. In Model 11 the mass elements, of constant thickness, interact through a bending stiffness force so that the ice acts as a thin elastic plate. The mass elements are connected through a surface tension force in Model 111 so that the ice is simulated by a stretched membrane. In both Models 11 and 111 the full linearized equations are solved. Because of the complexity of the resulting analysis, calculations of the reflection and transmission coefficients, and the pressure under the ice, are made in Model 11 on the basis of the shallow water approximation.
76 citations
TL;DR: In this paper, it was shown that if a longitudinal wave is excited in a collision-free plasma and Landau-damps away, and later a second wave was excited and also damped away, then a third wave will spontaneously appear in the plasma.
Abstract: It is shown that, if a longitudinal wave is excited in a collision‐free plasma and Landau‐damps away, and later a second wave is excited and also damps away, then a third wave will spontaneously appear in the plasma. This wave appears long after the first two waves have damped away at a time proportional to the interval between the first two waves, and is in that sense an echo. It is also shown that, if a wave is continuously excited at one point in a plasma and a second wave is continuously excited many Landau damping lengths from the first point, then a third wave will spontaneously appear many Landau damping lengths from the second point. Fundamentally, plasma wave echoes are possible because of the reversible nature of Landau damping. However, small‐angle Coulomb collisions are very effective in destroying the echo.
73 citations
TL;DR: In this paper, the authors explored the effect of the level of detail in the description of the radiation properties of surfaces and showed that under some conditions the choice of the model for radiation surface characteristics can be very critical for both the local radiant heat flux and for overall radiant interchange calculations.
72 citations
69 citations
TL;DR: In this paper, an asymmetrically cut first crystal is used to increase the effective width of the incident wave and therefore approach the plane wave condition, which is in poor agreement with theory.
Abstract: Oscillations have been observed in the tails of the Darwin curve from thin specimens of silicon. Dynamical theory predicts such oscillations (Pendellosung) for plane wave incident conditions in which two wave points on the same branch of the dispersion surface interfere and produce beating in the diffracted intensity. The usual Pendellosung is observed in transmission in which beating occurs between wavefields on different branches of the dispersion surface related by spherical rather than plane wave conditions. The present experiment uses an asymmetrically cut first crystal to increase the effective width of the incident wave and therefore approach the plane wave condition. Quantitative fringe measurements versus thickness are in fair agreement with theory. The intensity and contrast of the fringes are in poor agreement with theory. Several of the more important factors which reduce the contrast are discussed. With a relatively simple assumption, the observed and expected intensity dislocations can be brought into good agreement.
58 citations
TL;DR: In this article, the authors applied matrix multiplication techniques to the treatment of multilayer ionosphere models, where the individual ionosphere layers are thin relative to the wavelength, and the approximate field representations give in the limits of horizontal and radial static magnetic field results identical to those obtained using more accurate treatments of curvature effects.
Abstract: Fields of cylindrically curved ionosphere layers are approximated by exponential functions that consider the increase of the phase velocity and decrease of the attenuation rate with the altitude of the layers. Matrix multiplication techniques are applied to the treatment of multilayer ionosphere models. The individual ionosphere layers are thin relative to the wavelength, and the approximate field representations give in the limits of horizontal and radial static magnetic field results identical to those obtained using more accurate treatments of curvature effects. TM modes in the space between the earth and the ionosphere excite coupled TM and TE modes in the ionospheric layers, the presence of which are considered in an iterative solution of the modal equation. In the ELF range, propagation parameters computed for the east-to-west (EW) and west-to-east (WE) directions differ most for dip angles of 15-30°. In the VLF range propagation parameters may exhibit discontinuities at nighttime for the EW direction, when the fields penetrate higher into the ionosphere. The interference distance D of the two lower wave guide modes is increased for propagation in the EW direction relative to propagation in WE direction provided that the electron concentration profiles exhibit sharp density gradients at heights in the range from 80 to 85 km. The desired propagation characteristics could not be produced in the presence of a nondipping static magnetic field or using smoothly varying electron concentration profiles.
TL;DR: In this paper, the reflection coefficient of parallel-plate waveguide apertures is analyzed by wedge diffraction theory for the TEM and TE 01 modes, and the results are compared with those obtained by other analyses for the normally truncated guide mounted in a ground plane and for that with thin walls.
Abstract: The reflection coefficient of parallel-plate waveguide apertures is analyzed by wedge diffraction theory for the TEM and TE 01 modes. Results are compared with those obtained by other analyses for the special case of the normally truncated guide mounted in a ground plane and for that with thin walls. Measured values of reflection coefficient are used as verification of results for other guide geometries. The method gives accurate results for guide widths as narrow as \lambda/4 .
Patent•
31 Dec 1968TL;DR: In this article, a light beam is deflected into a pattern represented by a synthesized sawtooth waveform by means of a light switch and a triangular wave generator, which is used for video display applications.
Abstract: A light beam is deflected into a pattern represented by a synthesized sawtooth waveform by means of a light switch and a triangular wave generator. In a video display application, a light switch directs an intensity modulated light beam along one of two paths. When directed along either path, the modulated light beam is incident upon one or the other of a mirror pair. One mirror of the pair reflects a light beam incident thereon from along a first path to the second mirror for reflection therefrom in a pattern approximated by a triangular wave, and the second mirror of the pair reflects a light beam incident thereon from along the second path to the first mirror for reflection therefrom in a pattern approximated by a triangular wave displaced 180* from the first pattern. To generate the approximated triangular waves, the first mirror of the pair oscillates at a frequency omega to deflect a light beam incident thereon in a pattern represented by the expression (sin omega t) and the second pair oscillates at a frequency 3 omega to deflect a light beam incident thereon in a pattern represented by the expression (sin 3 omega t), where omega equals the fundamental frequency. The mirrors oscillate in a manner such that the individual patterns produced are optically added. To generate the sawtooth function, only the positive going portion of the triangular wave is selected and the resultant scan patterns are interlaced on the screen.
TL;DR: Seismic waves reflected as many as four times within Earth's outer core are routinely recorded from large earthquakes, and minor adjustments to outer-core velocities may be necessary to account for certain of these arrivals that are not predicted by present core models.
Abstract: Seismic waves reflected as many as four times within Earth's outer core are routinely recorded from large earthquakes. Observations of these waves are confined to rays near grazing incidence on the core-mantle boundary, in agreement with theoretical expectation. Minor adjustments to outer-core velocities may be necessary to account for certain of these arrivals that are not predicted by present core models. A change of 10 kilometers or more in the currently accepted core radius, 3473 kilometers, is not corroborated by the new data.
TL;DR: In this article, the propagation of electromagnetic waves along the axis of a cholesteric material, using constitutive equations based on a theoretical model for the structure of this type of material, is studied.
Abstract: Equations are derived for the propagation of electromagnetic waves along the axis of a cholesteric material, using constitutive equations based on a theoretical model for the structure of this type of material The resulting time-independent equations are a pair of coupled equations for left- and right-hand circularly polarized waves Solutions are obtained for these equations and are shown to provide good agreement with experimental observations on the circular dichroism and reflection of circularly polarized light for cholesteric materials
TL;DR: In this article, a boundary condition is developed that generalizes the author's earlier results and embodies the effect of multiple scatter for acoustic reflection on a rough surface, where the size of the roughness is assumed to be sufficiently small in comparison with the wavelength.
Abstract: A boundary condition is developed that generalizes the author's earlier results and embodies the effect of multiple scatter for acoustic reflection on a rough surface. The size of the roughness is assumed to be sufficiently small in comparison with the wavelength. Both induced radiating dipoles and radiating sources are taken into account. The results are further generalized to take into account roughness of various shapes, nonuniform distribution, and anisotropic properties. The anisotropy represented by a two‐dimensional symmetric tensor of Rank 2. Results open the way to the analysis of combined coherent and incoherent reflection including the cooperative resonance due to multiple scatter.
TL;DR: In this paper, modal reflection and coupling coefficients for a semi-infinite flanged and unflanged hardwall circular tube excited by one of the propagating modes are calculated by a ray method wherein the incident mode is decomposed into local plane waves impinging on the rim.
Abstract: Modal reflection and coupling coefficients are calculated for a semi‐infinite flanged and unflanged hard‐wall circular tube excited by one of the propagating modes. The calculation is performed by a ray method wherein the incident mode is decomposed into local plane waves impinging on the rim. Consequent diffraction effects establish the reflected waves and are represented equivalently in terms of radiation from a nonisotropic ring source having a radiation pattern determined by the local scattering properties of the rim. The rays emitted by the nonisotropic ring source and reflected repeatedly from the tube wall are summed into modal form, the quality of the resulting asymptotic mode series being improved by comparison with the exact solution for an isotropic ring source. Reflection and coupling coefficients are provided by the modal amplitudes in this representation and are determined for primary diffraction due to the incident mode only and also for multiple diffraction due to interaction across the mouth of the tube. Comparison with exact computations for the thin‐walled tube shows that the multiple interaction ray‐acoustical calculation is capable of high accuracy not only at high frequencies but even in the dominant mode regime. Data are also presented for flanged terminations for which no exact solution is available.
TL;DR: In this paper, the phase angle between the fundamental and second-harmonic components in the distorted wave was measured by using a pulse technique and agreement between theory and experiment was established for the phase shift upon reflection from water copper, from water duralumin, and from water mica-glycerin interfaces when correction is made for finite-amplitude effects between the interface and the receiving transducer.
Abstract: When an ultrasonic wave is reflected from an interface, a phase shift that is dependent on the angle of incidence may occur. If the wave is nonsinusoidal, this phase shift causes relative spatial shifting of the Fourier harmonic components. The assumption of independent reflection of the Fourier harmonics allows the use of linear theory to calculate the change in the phase angle between the fundamental and the second‐harmonic components in the distorted wave. A pulse technique is used to measure this change in phase angle. Agreement between theory and experiment is good for the phase shift upon reflection from water‐copper, from water‐duralumin, and from water‐mica‐glycerin interfaces when correction is made for finite‐amplitude effects between the interface and the receiving transducer.
TL;DR: In this article, the reflection of ion acoustic waves from a negatively biased grid immersed in a plasma is observed only in the region where the plasma is “perturbed.”
Abstract: The experimental observation of the reflection of ion acoustic waves from a negatively biased grid immersed in a plasma is reported. Reflection is detected only in the region where the plasma is “perturbed.”
TL;DR: In this paper, a motor-driven ultrasonic goniometer consisting of a single transducer and a 90° reflector is described, which facilitates rapid investigation and automatic recording of reflection data.
Abstract: A motor‐driven ultrasonic goniometer is described consisting of a single transducer and a 90° reflector. This relatively simple device facilitates rapid investigation and automatic recording of reflection data. The reflectivity curves are interpreted in terms of reflector geometry and the physical properties of the specimen. Among other things, the technique has been used to determine surface‐wave velocities in the Y‐Z plane of quartz, and the results are shown to be in reasonable agreement with both theoretical and other experimental data.
TL;DR: The phase velocities of surface waves on low index surfaces of singlecrystal copper have been determined by an ultrasonic reflection technique and found to be in excellent agreement with theoretical values as mentioned in this paper.
Abstract: The phase velocities of surface waves on low index surfaces of single‐crystal copper have been determined by an ultrasonic reflection technique and found to be in excellent agreement with theoretical values. Variations in reflectivity have been related to both generalized surface waves and pseudo‐surface waves.
01 Jul 1968
TL;DR: In this paper, the effect of surface tension on the reflection of waves from a fixed vertical barrier immersed to a depth a into deep water is considered and the solution for the velocity potential may be determined uniquely when simple assumptions are made concerning the free surface near the barrier.
Abstract: In this paper the effect of surface tension is included in a well-known problem in the theory of two-dimensional infinitesimal water waves. The problem is that of the reflection of waves from a fixed vertical barrier immersed to a depth a into deep water. It is shown how the solution for the velocity potential may be determined uniquely when simple assumptions are made concerning the behaviour of the free surface near the barrier. In particular, expressions are derived for the reflection coefficient, defined as the ratio of the amplitude of the reflected wave to that of the incident wave, at infinity, and the transmission coefficient, defined similarly. It is shown how these coefficients, for small values of the surface tension force, tend to the values obtained by Ursell (4) when surface tension is ignored. The related problem of a completely immersed vertical barrier extending to a distance a from the surface may be solved in a similar manner. Expressions for the reflection and transmission coefficients for this case are given.
TL;DR: In this paper, the reflection and transmission of sound waves by a moving fluid layer are treated theoretically using the more proper boundary conditions, and the reflection coefficients are determined, and a specific numerical example is also given.
Abstract: The reflection and transmission of sound waves by a moving fluid layer are treated theoretically using the more proper boundary conditions, and the reflection and transmission coefficients are determined. A specific numerical example is also given.
TL;DR: The spectral composition of the short wave radiation transmitted and reflected by 16 contrasting vegetation types is given and it is shown that all green vegetation had low reflection and transmission of visible radiation and high of infra-red radiation.
Abstract: Summary The spectral composition of the short wave radiation (400–1,050 nanometres) transmitted and reflected by 16 contrasting vegetation types is given. The transmission and reflection spectra were similar for a particular vegetation. All green vegetation had low reflection and transmission of visible radiation and high of infra-red radiation. By contrast, dry and dead vegetation showed a continuons increase through the visible and infra-red. The infra-red transmission and reflection spectra of green vegetation tended towards three types: (1) Approximately uniform levels at all wavelengths. (2) Increasing transmission or reflection at the longer wavelengths. (3) In one case (sweet corn) decreasing reflection at the longer wavelengths. Reported single leaf studies show the first pattern only. In the visible radiation there were considerable differences in the proportion of green radiation transmitted or reflected by the different vegetations, some having a sharp peak and others having none. Transmission ...
TL;DR: A series of photoelastic tests were conducted to determine transmission and reflection coefficients associated with the stress and displacement of a Rayleigh wave propagating past a step change in elevation on the boundary of an elastic half plane as discussed by the authors.
Abstract: A series of photoelastic tests were conducted to determine transmission and reflection coefficients associated with the stress and displacement of a Rayleigh wave propagating past a step change in elevation on the boundary of an elastic half plane. The determinations were made on six different models with ratios of step height to wave length ( h /λ) ranging from 0 to 1.1. The stress transmission coefficient varied from 1 to about 1.5 as h /λ increased from 0 to 1.1. The stress reflection coefficient increased from 0 to 0.7 with increasing h /λ. The displacement transmission coefficient increased initially to a value of 1.4 for h /λ = 0.2 then decreased monotonically to about 1 as h /λ increased to 1.1. Finally, the displacement reflection coefficient increased monotonically from 0 to about 1.5 as h /λ increased over the range considered. The photoelastic method provides information over the entire region of interest which is very useful in the understanding and analysis of the complex wave interaction problems associated with Rayleigh wave propagation past boundary irregularities.
TL;DR: The pattern of reflection of solar radiation from clouds as a function of angle is obtained by statistical analysis of observations from the TIROS IV visible radiation channel (0.55-0.75 μ) as discussed by the authors.
Abstract: The pattern of reflection of solar radiation from clouds as a function of angle is obtained by statistical analysis of observations from the TIROS IV visible radiation channel (0.55–0.75 μ). Readings from the water-vapor window channel (8ndash;12 μ) were used to select cases in which clouds fill the field of view of the sensor. The results show a generally anisotropic reflection pattern, which varies with solar zenith angle. The anisotropy is greatest for large values of solar zenith angle, the main feature in these cases being high intensity values of the radiation reflected at azimuths close to 180° from the sun, and at large zenith angles.