The decrease in the illumination within the geometrical shadow is continuous, that is, there are no maxima and minima. The reason is that,

EDCBN

M

supposing the edge to occupy the position shown in Fig. 364, then, starting from N, we may divide the remainder of the wave-front into half-period zones NB, BC, CD, &c. Of these zones, each will produce a greater effect than the next, but adjacent ones will send to P waves in opposite phase. Thus the illumination sent to P will be practically the difference of the effects of the first two zones, or at any rate of the first three or P four. As the distance NA is increased, that is, as P is taken further and further inside the geometrical shadow, the difference between the effect produced by the first two zones will decrease, just as in § 379 we found that consecutive zones, after about the tenth from the pole, had equal and opposite effects.

A

M'

FIG. 36.

Thus the wave theory indicates that the shadow cast by a sharp edge when illuminated by parallel light, or, what comes to the same thing, light from a point, source, or narrow slit at a considerable distance, is not quite sharp. Outside the geometrical shadow will be a series of light and dark bands, and inside the light will not cease suddenly, but will fall off rapidly.

The intensity of the illumination on a screen placed at a distance of one metre from a diffracting edge, and illuminated by a parallel beam of light, is shown by means of a curve in Fig. 365. It will be seen that the

illumination at the edge of the geometrical shadow is a quarter of the illumination at some distance from the edge, that is, of the illumination which would occur if the diffracting obstacle were removed.

If we have parallel light falling on a slit, then, as before, we may divide the incident wave into half wave-length zones with reference to a point P. If the slit is at a considerable distance from the pole of P, it will include many zones, for at this distance from the pole the zones are very narrow, and the total effect of these zones will be zero. As the slit is moved nearer to the pole, the number of zones included in the portion of the wave which can pass through the slit decreases, and when there is an even number the zones very nearly neutralise each other's effect, and there is a minimum of illumination at P, while when the slit includes an odd number of zones, the illumination is a maximum. The illumination will, of course, be a maximum at a point immediately opposite the slit. On either side will be formed a number of alternate dark and bright lines, the intensity of the maxima rapidly decreasing as we go away from the central band.

CHAPTER VIII

EMISSION AND ABSORPTION OF LIGHT

381. Nature of the Light emitted by a Luminous Body-Spectra. -In § 368 we have referred to the spectrum obtained when sunlight is passed through a prism, we now have to examine the constitution of the light given out by other sources.

If a solid body, such as a piece of lime or of metal, is heated, it begins to glow with a dull red colour at a temperature of about 600° C., and if the light emitted is examined in a spectroscope only the red end of the spectrum will be seen. At a temperature of about 1000° the yellow will appear as well as the red, while at about 1600°, the solid will glow with a white light, and the spectrum will stretch from the red to the violet.

The spectrum thus obtained with a glowing solid will differ from the solar spectrum in that there will be no dark bands, the spectrum being continuous from one end to the other.

The same character of spectrum is given by incandescent fluids, such as molten platinum.

When, however, the light given out by glowing gases or vapours is examined, the spectrum produced is of an entirely different character.

Thus, if a salt of either of the metals sodium, calcium, strontium, lithium, &c., is held in a colourless flame, such as that of a Bunsen burner, and the light is examined in a spectroscope, the spectrum will be found to be no longer continuous, but to consist of a number of bright lines in various parts of the spectrum. The position and number of these lines varies for the different metals, but does not depend either on the salt of the metal used (chloride, bromide, sulphate, &c.) or on the nature of the flame into which the salt is introduced. The number of lines visible with any given metal depends, to a certain extent, on the temperature of the flame, but although new lines may make their appearance as the temperature is raised, the position of the lines already present does not vary. FIG. 366. In the case of gases, the spectrum is obtained by passing the spark from an induction coil (§ 524) through the gas which is contained in a rarefied condition in a tube of the shape shown in Fig. 366. In addition to line spectra, under certain conditions of pressure and temperature, the spectra of some gases exhibit bands of light,

which with a small dispersion are generally sharply defined on one side, but shade off gradually on the other. With a high dispersion, these bands are seen to be composed of numerous lines packed close together. When, however, the temperature is raised, the band spectrum becomes changed into a line spectrum.

The character of the lines in the spectrum of a gas depends very much on the pressure to which the gas is subjected. Thus in the case of hydrogen, at low pressures, say below I mm. of mercury, the spectrum consists of three narrow lines, one in the violet, one in the blue, and one in the red, which are generally indicated by H1, Hß, and Ha. As the pressure is increased, first the line Hy, then Hs, and finally also Ha becomes wider, while under a pressure of about 36 cm. of mercury the spectrum is practically continuous. The explanation of these changes, if we accept the kinetic theory of gases, is comparatively easy. When a gas is under a low pressure, the mean free path ($141) of the molecules is great, so that the interval between successive impacts of a molecule with another is comparatively great. Thus although during the impact the atoms will be set into all kinds of forced vibrations, yet all these vibrations, except those which correspond to the natural period of vibration of the atoms, will very rapidly die out, and for the greater part of the time the atoms will be vibrating in their own natural period. Hence, if we suppose that in a glowing gas the light emitted is due to the vibrations of the atoms, it is evident that at low pressures the gas will give out light of certain definite wavelengths, corresponding to the natural periods of the atoms. As the pressure increases the mean free path of the molecules decreases, and hence the impacts become more frequent. Under these circumstances the forced vibrations will begin to tell, and at first it will be those vibrations which are nearly of the same period as the natural period that will be most noticeable, so that the bands will widen out. When the pressure is further increased, the encounters between the molecules are so frequent that the forced vibrations persist from one encounter to the next, and hence vibrations of all periods will be taking place in the different molecules, and a continuous spectrum will be obtained.

382. Series of Spectral Lines.-If we assume that the frequency of the light vibrations given out by a luminous body is the same as the frequency of the vibrations set up within the molecules of the substance, we are led to the conclusion that the motion of even a gaseous molecule must be very complicated, for the spectrum of most substances contains quite a large number of bright lines, each line corresponding, on the above hypothesis, to a different mode of vibration.

Although at first sight the arrangement of the lines in the spectrum of a gas or vapour appears in general quite irregular, yet a study of this subject has shown that in many cases certain relations are found to hold between the frequencies of the various lines.

The first relation of this kind observed is due to Balmer, who noticed that the wave-lengths, A, of the lines in the hydrogen spectrum can be represented with great accuracy by the general expression

in which is in succession given the values 3, 4, 5, &c., up to 16. The kind of agreement obtained between the observed values and those calculated from Balmer's formula is shown in the following table :

Another curious fact is that when there exists in the spectrum of an element a doublet or triplet, that is, two or three lines close together, there are also, in general, a number of other doublets or triplets, and the difference between the frequencies of the components of these doublets and triplets is the same for all those which occur in the spectrum of any one element. Thus, in the case of thallium, Kayser and Runge have found the following values for the reciprocals of the wavelengths of the components of the doublets. The reciprocal of the wave-length being proportional to the frequency of the vibrations, the differences will also be proportional to the differences of the frequencies.