Emergence Angle Research Articles

Optical Studies of Injected Carriers. II. Recombination Radiation in Germanium

The radiation produced by the direct recombination of electrons and holes in germanium is studied. The observed spectral distribution is in fair agreement with theory. For injection into high resistivity, as well as into doped material, the radiation is observed to be a linear function of injection current. Possible explanations for this are discussed. Magnetic concentration of carriers produced changes in the radiation intensity. Polarization of the radiation at oblique angles of emergence is observed.

ELASTIC WAVES THROUGH A PACKING OF SPHERES

Based on a theory of porous solids previously developed by the author, the elasticity of a hexagonal close packing of equal spheres is treated. The packing is anisotropic and because of the weight of the spheres, also inhomogeneous. The velocities of propagation of elastic waves have been calculated for evacuated interspaces and for interspaces filled with a liquid or gas. In the case of evacuated or air‐filled interspaces, the wave rays and travel times have been computed. The packing which has been treated may be of use as a model for a dry or wet loose material such as gravel or sand. Though the model is very simplified, the results obtained show some typical effects such as anisotropy, in homogeneity, and a 90° angle of emergence.

The limiting polarization of medium waves reflected from the ionosphere

A method is described of measuring the polarization of a downcoming wireless wave which has been reflected obliquely from the ionosphere. Two rotatable crossed loops are adjusted to be in quadrature by dephasing one forwards and the other backwards 45° from resonance. With the usual goniometer technique the search coil gives zero pick-up when the tangent of the angle at which it is set is equal to the ratio of the axes of the projected polarization ellipse, and the frames are turned so that their planes are along the axes of this ellipse. Results obtained on medium-wave broadcasting stations are compared with ellipses calculated on the magnetoionic theory for an assumed angle of emergence and direction of the earth's magnetic field. The comparison shows that, within the present accuracy of the apparatus, the absorption due to electronic collisions does not appreciably affect the limiting polarization of the emergent wave, and sets an upper limit of 106 per sec. to the collisional frequency in the region where the polarization assumes its limiting value. The experiments also suggest that the ratio of the number of ions to the number of electrons in this region is not greater than 10,000, and further work with increased accuracy should give valuable information relevant to the inclusion of the Lorentz term in the magnetoionic theory for the E layer.

Local earthquakes in New England*

Summary During 1934 and 1935, records of approximately 150 definitely local disturbances were obtained on the Benioff seismographs at the Harvard Seismograph Station. Because of a curious concentration in the daytime hours and the few earthquakes reported felt during this interval, an attempt was made to establish criteria by which records of blasts and of local earthquakes might be distinguished from each other. Three, the ratio of the maximum P to the maximum S, the character of the surface waves, and the angle of emergence are discussed. The records of 32 of these disturbances, well recorded on all three Benioff components, are described. It is concluded that, although some of New England's seismic activity is artificial, there is, nevertheless, a greater amount of natural activity than is ordinarily attributed to this region.

Motion of the surface of the Earth in the compressions phase of a deep‐focus earthquake, and the effects of a layered crust

The early portion of the compressional phase on 28 seismograms of the deep‐focus earthquake of November 13, 1932, are integrated to obtain the motion of the surface of the Earth. Comparisons are offered between the observed and actual azimuths of the epicenter at all stations for which two horizontal‐component seismograms were available, and between the observed and theoretical apparent angles of emergence for all stations for which three components of motion were available. A test is made of the usual methods of reducing trace‐amplitudes, which are based on the assumption that the Earth‐motion is sinusoidal. The results of this test indicate that satisfactory estimates of the displacement of the ground corresponding to an impulse on a seismogram can be obtained from the simple harmonic ground‐motion assumption, provided the free period of the seismograph is somewhat longer than the duration of the impulse, and provided that the transients in the solution of the equation of motion of the seismograph are retained. Sources of error encountered in any attempt to secure the detailed ground‐motion from seismograms are discussed.

Study of Emergence Angle and Propagation Paths of Seismic Waves

Travel-time curves are given for elastic waves through the earth in a region in which the velocity increases continuously with depth. These time-distance curves have been approximated by an equation of the form X=aT2+bT from which the velocity depth relation has been deduced. A new method for measurement of the emergence angle has been used and the values obtained agree reasonably well with those deduced from theoretical treatment of the time-distance curve. Formulas for the travel-time between any two points in the medium under consideration are derived. These formulas agree closely with two sets of direct measurements. In one of these the seismograph was placed at various distances directly beneath the explosion. In the second case it was placed at a fixed depth beneath the surface and the explosion was located on the surface at various distances. The approximate depth to bed rock is obtained from the time-distance curves by use of the formulas mentioned above.

X-Ray Line Intensities and Cathode-Ray Retardation in Thick Targets of Silver

$K$-line intensities from thick silver targets have been measured in arbitrary units for voltages up to 180 kv, with emergence angles from 1 to 25\ifmmode^\circ\else\textdegree\fi{}. A practical use of these data is the determination of the voltage which will give the maximum efficiency of line emission at any emergence angle. At 1\ifmmode^\circ\else\textdegree\fi{} the best voltage is 70 kv but at 25\ifmmode^\circ\else\textdegree\fi{} it is well above 180 kv. These data are also used in conjunction with data on thin targets to get information as to the retardation of cathode rays in silver. For this purpose the thick-target data are corrected to eliminate the effects of target absorption, indirect production of line rays through fluorescence and loss of cathode rays by rediffusion. The loss of energy per unit distance along the path of a cathode ray varies as the -1.4 power of the speed, just as it does in light elements according to more direct evidence collected by E. J. Williams.

The Prism with an Index of Refraction Less than Unity

The general expressions for the deviation, for the relative widths of the refracted and incident beams, and for the relation between errors in the measured quantities and the index of refraction have been derived for radiation in a principal section of a prism whose index of refraction is less than unity. It is shown that the maximum deviation that can be produced by refraction is equal to the deviation at the critical angle of reflection. It develops that for angles of incidence in the neighborhood of the critical angle of reflection the refracted beam is very broad. With the direction of the light reversed, that is, for large glancing angles of incidence and for values of glancing angles of emergence with the second surface in the region of the critical angle, the refracted beam is very sharp. Diagrams are given to show the relationships in the case of a prism whose index of refraction is 1−10−5. It is pointed out that, assuming ideal conditions, the best experimental arrangement would be one using a right-angled prism with a glancing angle of incidence equal to 90° (angle of incidence equal to zero).

Deviation from Lambert’s Law and Polarization of Light Emitted by Incandescent Tungsten, Tantalum and Molybdenum and Changes in the Optical Constants of Tungsten with Temperature*

Deviations from Lambert’s cosine law for the light emitted by W, Mo, and Ta. The deviations for all three metals is very much of the same order. The brightness in each instance increases from the normal value at normal emergence gradually with increase in emergence angle to about 75° by about 20 per cent. From there on the brightness decreases rapidly to zero at grazing emergence. Straight filaments of circular cross-section have average brightnesses viewed normal to their axes which are about 3 per cent greater than the normal brightnesses (W 2.8 per cent, Mo 3.6 per cent, Ta 2.7 per cent). The average brightness of a filament, considering all directions, is about 5 per cent greater than the normal brightness (W 4.4 per cent, Mo 6.2 per cent, Ta 4.3 per cent).Polarization of light emitted by W, Mo, and Ta. The light emitted by these materials starting with zero polarization for normal emergence increases with the angle of emergence, at first slowly, to about 95 per cent at grazing emergence. The polarizations of the light from straight filaments of circular cross-section viewed normal to their axes amount to about 20 per cent (W 19.3 per cent, Mo 20.8 per cent, Ta 18.5 per cent).Change in optical constants of tungsten with temperature. Values obtained have depended on the variations of the emissivity and the reflectivity for the two polarized components. At room temperature 3.86 and.81 were obtained for n and k, at 1900°K 3.85 and.89 were obtained. This difference checks well with observed values of emissivity for normal emergence.

The Depth of Origin of Earthquakes

It is a peculiarity of the present state of seismology that it is necessary to define the meaning which one attaches to the word. earthquake. Up to the end of the last century this was hardly necessary, the word was still used in its old-fashioned sense of a quaking, or shaking, of the earth which could be felt and, when violent enough, caused damage. When it was found that, with suitable instruments, disturbances could be detected, which could not be felt, and it was observed that some of these were evidently connected with great earthquakes, it was too readily assumed that this was true of all, and a new connotation of the word arose. This newer branch of seismology has been more and more extensively followed up, until it has almost ousted the older seismology, and some of its devotees are inclined to refuse the right, of the Disturbance which can be felt, to the name of earthquake, unless it is accompanied by long-distance records. In what follows the word is used in the old-fashioned sense, and the earthquakes dealt with are the disturbances which can be felt, which are essentially phenomena of the outer crust, and as such belong to the domain of geology. In the study of these, one of the first objects is a determination of the depth of origin, and several distinct principles are involved in the methods which have been proposed. Robert Mallet believed that that angle of emergence could be determined from the measurement

Further Note on the Depth of Xarthquake Foci.

SUMMARY 1. Galitzin's direct observations of the “angle of emergence” at Pulkovo led him to specify three new “critical surfaces” at the moderate depths 106 km., 232 km., and 492 km. below the surface, in addition to the surface much lower already indicated by Wiechert. 2. Results obtained for the relative depth of earthquake foci suggest that they also collect about three chief values, without, however, giving any indication as to the absolute depth of any. 3. If we identify the three corresponding depths of focus with those of Galitzin's three surfaces and revise the calculated velocities near the surface accordingly, we (a) can get a value for the surface velocity of P agreeing with that observed at the Oppau explosion; (b) can get the value 207 km. for the depth of the average focus corresponding to the adopted tables. The depths of the three principal seats of earthquakes are of course those given above from Galitzin; (c) The destructive earthquakes are probably those originating in the uppermost layer, at a depth of 106 km. = 66 miles.

The Depth of Earthquake Focus

IN the Philosophical Transactions of the Royal Society, Series A, vol. 222, pp. 45–56 (1921), Mr. G. W. Walker, relying on certain observations of the emergence-angle of P waves at Pulkovo, makes the somewhat startling suggestion that the depth of focus is of the order one-fifth of the earth's radius, or about 1250 km. This is a much larger estimate of depth than that hitherto suggested, viz. of order less than 100 km. Mr. Walker's estimate of depth is a consequence of accepting the Pulkovo numbers as correct. It appears that the values of the apparent angle of emergence calculated from Zöppritz's curve do not agree with its value directly measured at Pulkovo. This discrepancy is so marked that either the time-curve or the Pulkovo values must be seriously in error, and Mr. Walker proceeds on the assumption that within the limits of possible error in the time-curve we can modify it so as to agree with the direct measure of the apparent angle of emergence.

Societies and Academies

LONDON. Royal Society, May 13.—Prof. C. S. Sherrington, president, in the chair.—G. W. Walker: The problem of finite focal depth revealed by seismometers. Observations of the emergence angle of P waves at Pulkovo suggest that the depth of focus is of order one-fifth of the earth's radius. Important modifications are necessary in the interpretation of seismo-grams and in the attempt to determine how speed of propagation depends on depth. A test of the accuracy of the Pulkovo values can be made by a scrutiny of seismograms for distances >11,000 kilometres. Corresponding measures of the angle of emergence of S waves by means of three component seismometers are required.—E. A. Griffiths: A liquid oxygen vaporiser. The liquid oxygen is contained in a metal vacuum vessel. The emission of gas is governed by bringing a flexible portion of the outer wall into contact with the inner; the degree of contact determines the rate of transmission of heat. An desired rate of gas evolution can be obtained up to 10 litres per minute, and the delivery remains constant.—Dorothy M. Palmer and W. G. Palmer: Some experiments on the catalytic reduction of ethylene to ethane. The hydrogenation of ethylene in the presence of nickel has been quantitatively examined. The mixture of ethylene and hydrogen was brought into contact with nickel in motion in an electrically heated tube. The rate of hydrogenation was measured by the rate at which a mixture of ethylene and hydrogen in equal proportions by volume had to be passed into the tube to maintain the gas therein at constant pressure. The effects of varying conditions were studied. The curves showing rate of reaction against time display “induction” periods during which no hydrogenation took place, varying in duration from a few seconds to many hours, according to the conditions of the experiment. Then the rate of reaction increases rapidly to a sharp maximum, and decreases less rapidly to a lower value, which decreases slowly. A theory is advanced to account for these effects.—W. G. Palmer: The catalytic activity of copper. Part ii. The activity of copper when prepared from oxide by reduction with carbon monoxide and methyl alcohol vapour is discussed. Constant-boiling mixtures of several alcohols with water were used as reacltants. Water acts as a positive, and hydrogen as a negative, auxiliary catalyst when adsorbed on the copper. The activity-temperature curves for a catalyst prepared by carbon monoxide obey a simple exponential law. Between 270° and 280° C. the activity curves generally undergo a sudden change of direction corresponding to a great reduction of the temperature coefficient. This is attributed to the diminution in the thickness of the adsorbed alcohol layer to at most two molecular diameters. The activity of the catalyst does not increase continuously, as the temperature of its preparation from oxide is lowered.—Prof. C. F. Jenkin and D. N. Shorthose: The total heat of liquid carbonic acid. The total heat of carbonic acid between temperatures of +10° C. and +100° C. and between pressures of 900 Ib, and 1800 Ib. per square inch was measured. The values hitherto accepted, based on the assumption that the specific heat at constant volume does not change over this range, require slight correction.—Dr. A. O. Rankine: The viscosity and molecular dimensions of gaseous cyanogen. The viscosity of gaseous cyanogen has been measured at 15° C. and 100° C., the values obtained being, respectively, 0.986 × 10- 4 and 1.264 × 10- 4 C.G.S. units. Assuming Sutherland's law of temperature variation, the data have been used to calculate Sutherland's constant (C. =280) and the viscosity at 0° C. (η0.–0.935 × 10- 4 C.G.S. units). The mean collision area of the molecule of cyanogen deduced, –1.31 × 10- 15 cm.2, proves to be practically the same as that of a bromine molecule, 1.28 × 10- 15 cm.2 This is consistent with the evidence from crystal examination, for the molecular volumes of KBr and KCN are nearly equal. If X-ray crystal examination should prove that KCN and KBr are strictly isomorphous, the results here obtained are consistent with the Lewis-Langmuir view that the cyanogen molecule has a size and shape nearly the same as those of two nitrogen molecules linked together by sharing one pair of outer electrons.

On the Accuracy Attainable with Critical Angle Refractometers

The three factors controlling the determination of a refractive index by means of a critical angle refractometer are, so far as the prism system is concerned, (i.) the angle of the prism, (ii.) its refractive index, and (iii.) the angle of emergence of the critical ray from the second prism face. Expressions are obtained for the variation of the required refractive index with each of these factors separately and curves are given connecting these variations with the angle of emergence from the second prism face for various prism angles.

A Study of the Polarization of the Light emitted by Incandescent Solid and Liquid Surfaces. II

In spite of the prodigious activity of physicists during the first three quarters of this century in attacking the problems of reflection, refraction, and polarization in all their different phases, both from the side of experiment and that of mathematical theory, the problem of polarization of light by emission seems to have received comparatively little attention. Although the fact that incandescent solids and liquids emit, at oblique angles of emergence, partially polarized light, was discovered more than seventy years ago, it does not appear even to-day to be very generally known. Few, even of the more complete text-books on physics, make any mention of the fact.

A Study of the Polarization of the Light emitted by Incandescent Solid and Liquid Surfaces

In spite of the prodigious activity of physicists during the first three quarters of this century in attacking the problems of reflection, refraction, and polarization in all their different phases, both from the side of experiment and that of mathematical theory, the problem of polarization of light by emission seems to have received comparatively little attention. Although the fact that incandescent solids and liquids emit, at oblique angles of emergence, partially polarized light, was discovered more than seventy years ago, it does not appear even to-day to be very generally known. Few, even of the more complete text-books on physics, make any mention of the fact.

XI. Double refraction and dispersion in Iceland Spar: an experimental investigation, with a comparison with Huyghen’s construction for the extraordinary wave

In a paper read before the Royal Society, June 20, 1878, the results of an investigation into the truth of Fresnel’s theory of double refraction in a biaxal crystal were stated. The comparison between theory and experiment was made by a method suggested by Professor Stokes (British Association Report, 1862), according to which the reciprocal of the velocity of wave propagation was determined by experiment and also on Fresnel’s theory. The greatest difference between the two amounted to ·0009, and there appeared to be some connexion between the differences and the wave length of the light used. In the endeavour to follow up this connexion I undertook a series of similar experiments with light of different wave lengths, using three lines of the hydrogen spectrum and the sodium line. The extreme smallness of the arragonite prisms I had previously worked with led me to use, at first at least, Iceland spar, which could be obtained in large pieces with ease, and for which the theoretical calculations were greatly more simple. Professor Stokes had already made a series of experiments by the same method with this substance (Proceedings of the Royal Society, vol. 20, p. 443) and arrived at results confirming Huyghen’s construction. The details of his experiments are as yet unpublished, and I venture to think it might be useful to have arranged in tabular form a series of results, to serve in the future as a test of any theory of double refraction which might be proposed. The method of the experiments, as suggested by Professor Stokes (British Association Report, 1862), is as follows: A prism is cut from a piece of spar, and the position of its faces with reference to the cleavage faces carefully determined. The prism is mounted on a spectrometer, and the collimator adjusted so that the rays of a definite wave length falling on the prism are parallel, the edge of the prism being parallel to the axis of revolution of the reading telescope. The deviation of the light passing through the prism in any position is observed, also the position of the image of the slit formed by reflexion at the face of incidence. From this and the known direction of the incident light we can calculate the angle of incidence. Let this be Ф . Let the deviation be D and the angle of the prism i . Let V be velocity of the light in air, v in the crystal. Let ψ be the angle of emergence, Ф′ ψ′ the angles which the wave normal in the crystal makes with the faces of the prism.

III. On the magnifying-power of the half-prism as a means of obtaining great dispersion, and on the general theory of the 'half-prism spectroscope.'

On account of the oblique incidence of the rays on the isosceles prism and the consequent diminution of the aperture of the collimator, a “ half-prism,” formed by dividing an isosceles prism by a plane perpendicular to the base, has frequently been employed for the commencement of the train of prisms, and also for the end, though apparently, without due consideration of the effect of the “half-prism” on the dispersion of the other prisms preceding in the train. This is a matter of some importance; for it will be found that when the angles of incidence and emergence are unequal (as in the half-prism), the angular separation between two pencils of parallel rays is increased or diminished according as the angle of emergence is greater or less than the angle of incidence. In consequence of this the angle between the pencils corresponding to any two lines in the spectrum, e. g . the two D lines, will be increased by passing through a half-prism (independently of the effect of ordinary dispersion) if the perpendicular face be turned towards the slit. At the same time the angle between the pencils coming from the two edges of the slit will, for any monochromatic light, also be increased in nearly the same ratio, and thus the lines in any spectrum become broader as they are further separated by virtue of this property, and the purity of the spectrum remains unaltered. In fact the half-prism is from this point of view equivalent to a cylindrical magnifier, a property which may prove most useful in the construction of the spectroscope, leading to the substitution of three or, at the most, four half-prisms for the long train of fifteen or twenty isosceles prisms now used. For this purpose direct-vision prisms will be most suitable; but I propose to begin by considering the simpler case of a half-prism of flint. The expression“ Magnifying-power” may be conveniently extended to the property in question, which, as will be seen presently, is strictly analogous to that of a lens; for it will be found that the same law holds with combinations of prisms as with other optical combinations, viz. the magnifying-power is the ratio of the breadth of the incident to the breadth of the emergent pencil. In consequence of the property of the half-prism stated above, it becomes necessary to distinguish between separation accompanied by increased breadth of the lines and separation in terms of this breadth. If the sense of the term “dispersion” had not been fixed by usage, it might very well be applied to the latter effect, retaining “separation” for the other; but it will undoubtedly be more in conformity with received ideas to define “dispersion” as the angular length of the spectrum, whilst the term “purity” may be used for the ratio of this angular length to the angular breadth of the spectrum lines (expressed in terms of the angular width of the slit). In the case of an isosceles prism, for which the magnifying-power is 1, the dispersion and purity are equal.