ABSORPTION OF LIGHT AND HEAT RADIATION BY SMALL SPHERICAL PARTICLES: II. SCATTERING OF LIGHT BY SMALL CARBON SPHERES

1942 ◽  
Vol 20a (3) ◽  
pp. 25-32 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Scattered Radiation ◽  
Scattered Light ◽  
Wave Length ◽  
Spherical Particles ◽  
Heat Radiation ◽  
Fourth Power ◽  
Main Beam ◽  
Carbon Spheres ◽  
Absorption Of Light ◽  
Diffused Light

Spheres of carbon for which 2a/λ, the ratio between the diameter of the particle and the incident wave-length, is less than about [Formula: see text] scatter the light uniformly in all directions. The intensity of the scattered radiation for any angle is proportional to the square of the volume of the particle and inversely proportional to the fourth power of the wave-length. As the ratio 2a/λ increases from [Formula: see text] to [Formula: see text] and greater values, the diffused light collects more and more into a main beam that appears as a continuation of the incident ray and that decreases in width as 2a/λ increases. Blue light prevails in the scattered radiation. When the size of the particles is unknown, the intensity, distribution, and polarization of the scattered light give an at least approximate value for the radius.

ABSORPTION OF LIGHT AND HEAT RADIATION BY SMALL SPHERICAL PARTICLES: I. ABSORPTION OF LIGHT BY CARBON PARTICLES

1941 ◽  
Vol 19a (10) ◽  
pp. 117-125 ◽  
Author(s):  
R. Ruedy
Keyword(s):  
Classical Theory ◽  
Bessel Functions ◽  
Incident Light ◽  
Wave Length ◽  
Plane Waves ◽  
Spherical Particles ◽  
Heat Radiation ◽  
Carbon Particles ◽  
Absorption Of Light ◽  
Light Particles

From Mie's classical theory of the action of small spherical particles on plane waves of light, the expression giving the loss of light due to absorption and scattering is reduced to the formula involving only Bessel functions of orders given by half integral values. The result is used for calculating the absorption by small carbon particles whose diameter is comparable with the wave-length of the incident light, particles that can be measured only by interference methods. When the diameter is less than 0.2 μ the coefficient of absorption decreases toward the red end of the spectrum. The reverse is true for 0.3 and 0.4 μ particles.

scholarly journals The absorption of light by the coloured globules in the retina of the domestic hen

1929 ◽  
Vol 105 (738) ◽  
pp. 371-374 ◽  
Keyword(s):  
Scattered Light ◽  
Wave Length ◽  
Visible Spectrum ◽  
Short Wave ◽  
Alternative View ◽  
Short Wave Length ◽  
Full Explanation ◽  
Absorption Of Light ◽  
Specific Receptors ◽  
Domestic Hen

Schultze (1866) pointed out that the coloured globules in the retinæ of birds might afford a means wherby stimulation of the cones would be restricted to certain regions of the visible spectrum (7). A few other investigators have ascribed sensual discrimination of colour to retinal filters situate in front of the specific receptors fro light (1, 4 and 6). An alternative view (2, 3) regards the coloured globules as decreasing, merely generally and relatively unselectively, i. e. , quantitatively rather than qualitatively, the amount of light of short wave-length which reaches the sensitive (outer) limb of the cones. This might possibly be useful by reducing the amount of the more highly scattered light and so might improve the visibility of distant objects (2). This, however, can hardly be the full explanation, for if the function of the coloured globules be merely to reduce the amount of the more refrangible end of the spectrum the various globules need not be of more than one colour.

scholarly journals XII. On the scattering and absorption of light in gaseous media, with applications to the intensity of sky radiation

1913 ◽  
Vol 212 (484-496) ◽  
pp. 375-433 ◽  
Keyword(s):  
Scattered Radiation ◽  
Gaseous Medium ◽  
Wave Length ◽  
Incident Radiation ◽  
Continuous Change ◽  
Small Particles ◽  
Absorption Of Light ◽  
Original Direction ◽  
Gaseous Media ◽  
Parallel Radiation

1. On the Scattering of Parallel Radiation by Molecules and Small Particles . The effect of small particles in scattering incident radiation was first worked out by Lord Rayleigh. When a stream of parallel radiation falls on a particle whose dimensions are small compared with the wave-length the resulting secondary disturbance travels in all directions at the expense of the intensity in the original direction. In a later paper Lord Rayleigh gave reasons for believing that the molecules of a gas are themselves able to scatter radiation in this way. In a gaseous medium it is legitimate to sum up the intensities of the scattered radiation due to each molecule in an element of volume without a consideration of phase-difference in consequence of the continuous change in the relative positions of a molecule in a gas. The same remark applies to the case where the scattering is due to small particles of dust since these partake, to some extent at least, of the molecular agitation of the gas in which they are held in suspension.

scholarly journals On the scattering and absorption of light in gaseous media, with applications to the intensity of sky radiation

1913 ◽  
Vol 88 (601) ◽  
pp. 83-89 ◽  
Keyword(s):  
Refractive Index ◽  
Scattered Radiation ◽  
Unit Volume ◽  
Solid Angle ◽  
Wave Length ◽  
Incident Radiation ◽  
Small Particles ◽  
Absorption Of Light ◽  
Original Direction ◽  
Gaseous Media

Sections 1 and 2.—Lord Rayleigh showed, in 1871, that when radiation travels through a medium containing small particles whose dimensions are small compared with the wave-length, each of these sets up a secondary disturbance which travels in all directions at the expense of the energy in the original direction. Various hypotheses of the æther and of the molecule agree in giving for the scattered radiation near an element of volume an expression of the form I (0, θ ) - μ ( θ ) E = ½ π 2 ( n 2 ─ 1) 2 λ -4 (1+cos 2 θ ) E/N, (1) where ω I (0, θ ) is the intensity contained in a small solid angle ω in a direction θ with the direction of the original beam E; n is the refractive index of the gas, N the number of molecules per unit volume, and λ the wave-length of the incident radiation.

scholarly journals On the absorption of light by crystals

1938 ◽  
Vol 167 (930) ◽  
pp. 384-391 ◽  
Keyword(s):  
Absorption Spectrum ◽  
Wave Length ◽  
Short Wave ◽  
Point Of View ◽  
Theoretical Point ◽  
Lattice Vibrations ◽  
Short Wave Length ◽  
Continuous Absorption ◽  
Absorption Of Light ◽  
Positive Hole

The purpose of this paper is to discuss the absorption of light by non-metallic solids, and in particular the mechanism by which the energy of the light absorbed is converted into heat. If one considers from the theoretical point of view the absorption spectrum of an insulation crystal, one finds that it consists of a series of sharp lines leading up to a series limit, to the short wave-length side of which true continuous absorption sets in (Peierls 1932; Mott 1938). In practice the lattice vibrations will broaden the lines to a greater of less extent. When a quantum of radiation is absorbed in the region of true continuous absorption, a free electron in the conduction band and a "positive hole" are formed with enough energy to move away from one another and to take part in a photocurrent within the crystal. When, however, a quantum is absorbed in one of the absorption lines , the positive hole and electron formed do not have enough energy to separate, but move in one another's field in a quantized state. An electron in a crystal moving in the field of a positive hole has been termed by Frenkel (1936) an "exciton".

scholarly journals A new method of spectrophotometry in the visible and ultra­violet and the absorption of light by silver bromide

1920 ◽  
Vol 97 (683) ◽  
pp. 181-190 ◽  
Keyword(s):  
Light Intensity ◽  
Photographic Plate ◽  
Wave Length ◽  
New Method ◽  
Silver Bromide ◽  
Selective Absorption ◽  
Quantitative Investigation ◽  
Advantages And Disadvantages ◽  
Absorption Of Light

A quantitative investigation of the absorption of light by silver bromide has been undertaken as a preliminary to a photochemical investigation of the action of silver bromide in the photographic dry plate. A good summary of the advantages and disadvantages of the various methods which have been devised by different experimenters for the quantitative investigation of the absorption of light by substances is given by Ewest in a thesis entitled, “Beiträge zur quantitativen Spectralphotographie,” of which an abstract is given by F. F. Renwick. All the methods which have been used previously either depend upon Schwarzschild’s law of the relation between time of exposure and the photographic effect, or a so-called neutral wedge is used which is supposed to absorb equally in all wave-lengths or is calibrated for selective absorption. The method which we have used is in some ways similar to that used by Ewest, but the apparatus required is very much simpler and a wedge of the material under examination is used instead of the neutral wedge of Ewest. In our method all that is required of the photographic plate is that the exposure of two adjacent portions of the same plate to the same light intensity of the same wave-length or the same time gives the same density under identical conditions of development. This condition is easily satisfied. As will be seen in the sequel, errors are reduced to errors in measurements of length.

The continuous absorption of light in alkali-metal vapours

1953 ◽  
Vol 219 (1136) ◽  
pp. 89-101 ◽  
Keyword(s):  
Cross Section ◽  
Alkali Metals ◽  
Theoretical Calculations ◽  
Wave Length ◽  
Energy Difference ◽  
Continuous Absorption ◽  
Absorption Of Light ◽  
Sodium Vapour ◽  
Good Agreement ◽  
Dipole Length

The first section of this paper is an account of some experiments on the absorption of light in sodium vapour from the series limit at 2412 Å to about 1600 Å (an energy difference of 2·6 eV). The absorption cross-section at the limit is 11·6 ± 1·2 x 10 -20 cm 2 . The cross-section decreases giving a minimum of 1·3 ± 0·6 x 10 -20 cm 2 at 1900 Å and then increases to 1600 Å. A theoretical calculation by Seaton based on the dipole-length formula gives good agreement with the experiments at the series limit and also correctly predicts the wave-length for the minimum, but it predicts a significantly lower absorption at the minimum. The experiments described in the first section of the paper conclude a series on the absorption of light in the alkali metals. The second section consists of a general discussion of the results of these experiments and of their relation to theoretical calculations. There is good agreement between theory and experiment except in regard to the magnitude of the absorption at the minimum.

scholarly journals The absorption of hard monochromatic γ-radiation

1930 ◽  
Vol 128 (807) ◽  
pp. 345-359 ◽  
Keyword(s):  
Absorption Coefficient ◽  
High Frequency ◽  
Wave Length ◽  
Low Frequency ◽  
Photoelectric Effect ◽  
Fourth Power ◽  
X Rays ◽  
Photoelectric Absorption ◽  
Initial Direction ◽  
Γ Radiation

Energy may be removed from a beam of γ -rays traversing matter by two distinct mechanisms. A quantum of radiation may be scattered by an electron out of its initial direction with change of wave-length, or it may be absorbed completely by an atom and produce a photoelectron. The total absorption coefficient, μ, is defined by the equation d I/ dx = -μI, and is the sum of the coefficients σ and τ referring respectively to the scattering and to the photoelectric effect. For radiation of low frequency, such as X-rays, the photoelectric absorption is very much more important than the absorption due to scattering, and many experiments have shown that the photoelectric absorption per atom varies as the fourth power of the atomic number and approximately as the cube of the wave-length. For radiation of high frequency, such as the more penetrating γ -rays, the photoelectric effect is, even for the heavy elements, smaller than the scattering absorption; and, since the scattering from each electron is always assumed to be independent of the atom from which it is derived, it is most convenient to divide μ. defined above by the number of electrons per unit volume in the material and to obtain μ e the absorption coefficient per electron.

Bearing Pressures and Cracks: Bearing Pressures Through a Slightly Waved Surface or Through a Nearly Flat Part of a Cylinder, and Related Problems of Cracks

1939 ◽  
Vol 6 (2) ◽  
pp. A49-A53 ◽  
Author(s):  
H. M. Westergaard
Keyword(s):  
Horizontal Plane ◽  
Wave Length ◽  
Circular Cylinders ◽  
Fourth Power ◽  
Classical Study ◽  
Partial Contact ◽  
Initial Separation ◽  
Noncircular Cylinder ◽  
Contact Pressures ◽  
Initial Line

Abstract The task is undertaken of determining the bearing pressures, and the stresses and deformations created by them, in some cases that differ from those considered by Hertz in his classical study of contact. Thus two solids are examined which, before loading, are in contact along a row of evenly spaced lines in a horizontal plane, as indicated in Fig. 1(a). Between these lines the surfaces have a separation defined by a nearly flat cosine wave. A uniform pressure on top of the upper solid creates contact over an area consisting of a row of strips, reduces the separation of the solids between the strips, as suggested in Fig. 1(b), and creates contact pressures distributed as indicated in Fig. 1(c), with vertical rises in the diagram of pressure at the edges of the strips. At a greater load the width of the strip becomes equal to the wave length, and the contact is complete. At still greater loads the stresses increase as if the two solids were one. The procedure by which this problem is solved is demonstrated first by showing its easy application to some well-known cases, especially Hertz’s problem of circular cylinders in contact. Further applications are to a noncircular cylinder resting on a solid with a flat top, with an initial separation of the surfaces varying as the fourth power of the distance from the initial line of contact; to partial contact of two surfaces which are initially plane, except that one of them has a ridge or several parallel ridges; and to some related problems in which two parts of the same body are partially separated by the forming of one or more cracks.

Introduction to light absorption: visible and ultraviolet spectra

2000 ◽  
Author(s):  
Robert K. Poole ◽  
Uldis Kalnenieks
Keyword(s):  
Electromagnetic Radiation ◽  
Light Absorption ◽  
Energy State ◽  
Monochromatic Light ◽  
Heat Radiation ◽  
Infrared Light ◽  
Visible Radiation ◽  
Absorption Of Light ◽  
The Difference

Light is a form of electromagnetic radiation, usually a mixture of waves having different wavelengths. The wavelength of light, expressed by the symbol λ, is defined as the distance between two crests (or troughs) of a wave, measured in the direction of its progression. The unit used is the nanometre (nm, 10-9 m). Light that the human eye can sense is called visible light. Each colour that we perceive corresponds to a certain wavelength band in the 400-700 nm region. Spectrophotometry in its biochemical applications is generally concerned with the ultraviolet (UV, 185-400 nm), visible (400-700 nm) and infrared (700-15 000 nm) regions of the electromagnetic radiation spectrum, the former two being most common in laboratory practice. The wavelength of light is inversely related to its energy (E), according to the equation: . . . E = ch/ λ . . . where c denotes the speed of light, and h is Planck’s constant. UV radiation, therefore, has greater energy than the visible, and visible radiation has greater energy than the infrared. Light of certain wavelengths can be selectively absorbed by a substance according to its molecular structure. Absorption of light energy occurs when the incident photon carries energy equal to the difference in energy between two allowed states of the valency electrons, the photon promoting the transition of an electron from the lower to the higher energy state. Thus biochemical spectrophotometry may be referred to as electronic absorption spectroscopy. The excited electrons afterwards lose energy by the process of heat radiation, and return to the initial ground state. An absorption spectrum is obtained by successively changing the wavelength of monochromatic light falling on the substance, and recording the change of light absorption. Spectra are presented by plotting the wavelengths (generally nm or μm) on the abscissa and the degree of absorption (transmittance or absorbance) on the ordinate. For more information on the theory of light absorption, see Brown (1) and Chapters 2, 3 and 4. The most widespread use of UV and visible spectroscopy in biochemistry is in the quantitative determination of absorbing species (chromophores), known as spectrophotometry.

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