1911 Encyclopædia Britannica/Absorption of Light

by Joseph Rogerson Cotter

ABSORPTION OF LIGHT. The term “absorption” (from Lat. absorbere) means literally “sucking up” or “swallowing,” and thus a total incorporation in something, literally or figuratively; it is technically used in animal physiology for the function of certain vessels which suck up fluids; and in light and optics absorption spectrum and absorption band are terms used in the discussion of the transformation of rays in various media.

If a luminous body is surrounded by empty space, the light which it emits suffers no loss of energy as it travels outwards. The intensity of the light diminishes merely because the total energy, though unaltered, is distributed over a wider and wider surface as the rays diverge from the source. To prove this, it will be sufficient to mention that an exceedingly small deficiency in the transparency of the free aether would be sufficient to prevent the light of the fixed stars from reaching the earth, since their distances are so immense. But when light is transmitted through a material medium, it always suffers some loss, the light energy being absorbed by the medium, that is, converted partially or wholly into other forms of energy such as heat, a portion of which transformed energy may be re-emitted as radiant energy of a lower frequency. Even the most transparent bodies known absorb an appreciable portion of the light transmitted through them. Thus the atmosphere absorbs a part of the sun’s rays, and the greater the distance which the rays have to traverse the greater is the proportion which is absorbed, so that on this account the sun appears less bright towards sunset. On the other hand, light can penetrate some distance into all substances, even the most opaque, the absorption being, however, extremely rapid in the latter case.

The nature of the surface of a body has considerable influence on its power of absorbing light. Platinum black, for instance, in which the metal is in a state of fine division, absorbs nearly all the light incident on it, while polished platinum reflects the greater part. In the former case the light penetrating between the particles is unable to escape by reflexion, and is finally absorbed.

The question of absorption may be considered from either of two points of view. We may treat it as a superficial effect, especially in the case of bodies which are opaque enough or thick enough to prevent all transmission of light, and we may investigate how much is reflected at the surface and how much is absorbed; or, on the other hand, we may confine our attention to the light which enters the body and inquire into the relation between the decay of intensity and the depth of penetration. We shall take these two cases separately.

Absorptive Power.—When none of the radiations which fall on a body penetrates through its substance, then the ratio of the amount of radiation of a given wave-length which is absorbed to the total amount received is called the “absorptive power” of the body for that wave-length. Thus if the body absorbed half the incident radiation its absorptive power would be 1/2, and if it absorbed all the incident radiation its absorptive power would be 1. A body which absorbs all radiations of all wave-lengths would be called a “perfectly black body.” No such body actually exists, but such substances as lamp-black and platinum-black approximately fulfil the condition. The fraction of the incident radiation which is not absorbed by a body gives a measure of its reflecting power, with which we are not here concerned. Most bodies exhibit a selective action on light, that is to say, they readily absorb light of particular wave-lengths, light of other wave-lengths not being largely absorbed. All bodies when heated emit the same kind of radiations which they absorb—an important principle known as the principle of the equality of radiating and absorbing powers. Thus black substances such as charcoal are very luminous when heated. A tile of white porcelain with a black pattern on it will, if heated red-hot, show the pattern bright on a darker ground. On the other hand, those substances which either are good reflectors or good transmitters, are not so luminous at the same temperature; for instance, melted silver, which reflects well, is not so luminous as carbon at the same temperature, and common salt, which is very transparent for most kinds of radiation, when poured in a fused condition out of a bright red-hot crucible, looks almost like water, showing only a faint red glow for a moment or two. But all such bodies appear to lose their distinctive properties when heated in a vessel which nearly encloses them, for in that case those radiations which they do not emit are either transmitted through them from the walls of the vessel behind, or else reflected from their surface. This fact may be expressed by saying that the radiation within a heated enclosure is the same as that of a perfectly black body.

Coefficient of Absorption, and Law of Absorption.—The law which governs the rate of decay of light intensity in passing through any medium may be readily obtained. If I₀ represents the intensity of the light which enters the surface, I₁ the intensity after passing through 1 centimetre, I₂ the intensity after passing through 2 centimetres, and so on; then we should expect that whatever fraction of I₀ is absorbed in the first centimetre, the same fraction of I₁ will be absorbed in the second. That is, if an amount j I₀ is absorbed in the first centimetre, j I₁ is absorbed in the second, and so on. We have then

${\mbox{I}}_{1}={\mbox{I}}_{0}\left(1-j\right)$

${\mbox{I}}_{2}={\mbox{I}}_{1}\left(1-j\right)={\mbox{I}}_{0}\left(1-j\right)^{2}$

${\mbox{I}}_{3}={\mbox{I}}_{2}\left(1-j\right)={\mbox{I}}_{0}\left(1-j\right)^{3}$

and so on, so that if I is the intensity after passing through a thickness t in centimetres

${\mbox{I}}={\mbox{I}}_{0}\left(1-j\right)^{t}$

(1).

We might call j, which is the proportion absorbed in one centimetre, the “coefficient of absorption” of the medium. It would, however, not then apply to the case of a body for which the whole light is absorbed in less than one centimetre. It is better then to define the coefficient of absorption as a quantity k such that k/n of the light is absorbed in 1/n th part of a centimetre, where n may be taken to be a very large number. The formula (1) then becomes

${\mbox{I}}={\mbox{I}}_{0}\,e^{-k\,t}$

(2)

where e is the base of Napierian logarithms, and k is a constant which is practically the same as j for bodies which do not absorb very rapidly.

There is another coefficient of absorption (κ) which occurs in Helmholtz’s theory of dispersion (see Dispersion). It is closely related to the coefficient k which we have just defined, the equation connecting the two being k＝4πκ/λ, λ being the wave-length of the incident light.

The law of absorption expressed by the formula (2) has been verified by experiments for various solids, liquids and gases. The method consists in comparing the intensity after transmission through a layer of known thickness of the absorbent with the intensity of light from the same source which has not passed through the medium, k being thus obtained for various thicknesses and found to be constant. In the case of solutions, if the absorption of the solvent is negligible, the effect of increasing the concentration of the absorbing solute is the same as that of increasing the thickness in the same ratio. In a similar way the absorption of light in the coloured gas chlorine is found to be unaltered if the thickness is reduced by compression, because the density is increased in the same ratio that the thickness is reduced. This is not strictly the case, however, for such gases and vapours as exhibit well-defined bands of absorption in the spectrum, as these bands are altered in character by compression.

If white light is allowed to fall on some coloured solutions, the transmitted light is of one colour when the thickness of the solution is small, and of quite another colour if the thickness is great. This curious phenomenon is known as dichromatism (from δι-, two, and χρῶμα, colour). Thus, when a strong light is viewed through a solution of chlorophyll, the light seen is a brilliant green if the thickness is small, but a deep blood-red for thicker layers. This effect can be explained as follows. The solution is moderately transparent for a large number of rays in the neighbourhood of the green part of the spectrum; it is, on the whole, much more opaque for red rays, but is readily penetrated by certain red rays belonging to a narrow region of the spectrum. The small amount of red transmitted is at first quite overpowered by the green, but having a smaller coefficient of absorption, it becomes finally predominant. The effect is complicated, in the case of chlorophyll and many other bodies, by selective reflexion and fluorescence.

For the molecular theory of absorption, see Spectroscopy.

References.—A. Schuster’s Theory of Optics (1904); P. K. L. Drude’s Theory of Optics (Eng. trans., 1902); F. H. Wüllner’s Lehrbuch der Experimentalphysik, Bd. iv. (1899).  (J. R. C.)