LIGHT WAVES AND THE SPECTRUM
The Wave Theory of Light.
There have been several theories about the nature of light. The
great English physicist, Isaac Newton (1642-1727), who was a pioneer
in the study of light as well as in that of mechanics, favoured
an atomic explanation of light; _i.e._, he thought that it
consisted of particles or light corpuscules which were emitted from
luminous bodies like projectiles from a cannon. In contrast to this
“emission” theory was the wave theory of Newton’s contemporary, the
Dutch scientist, Huygens. According to him, light was a wave motion
passing from luminous bodies into a substance called the ether,
which filled the otherwise empty universe and permeated all bodies,
at least all transparent ones. In the nineteenth century the wave
theory, particularly through the work of the Englishman, Young, and the
Frenchman, Fresnel, came to prevail over the emission theory. Since
the wave theory plays an important part in the following chapters,
a discussion of the general characteristics of all wave motions is
appropriate here. The examples will include water waves on the surface
of a body of water, and sound waves in air.
[Illustration: FIG. 4.—Photograph of the interference between two
similar wave systems.]
[Illustration: FIG. 5.—A section of the same picture enlarged.
(From Grimsehl, _Lehrbuch der Physik_.)]
Let us suppose that we are in a boat which is anchored on a body of
water and let us watch the regular waves which pass us. If there is
neither wind nor current, a light body like a cork, lying on the
surface, rises with the wave crests and sinks with the troughs, going
forward slightly with the former and backward with the latter, but
remaining, on the whole, in the same spot. Since the cork follows the
surrounding water particles, it shows their movements, and we thus see
that the individual particles are in oscillation, or more accurately,
in circulation, one circulation being completed during the time in
which the wave motion advances a _wave-length_, _i.e._, the distance
from one crest to the next. This interval of time is called the _time
of oscillation_, or the _period_. If the number of crests passed in a
given time is counted, the oscillations of the individual particles
in the same time can be determined. The number of oscillations in
the unit of time, which we here may take to be one minute, is called
the _frequency_. If the frequency is forty and the wave-length is
three metres, the wave progresses 3 × 40 = 120 metres in one minute.
The velocity with which the wave motion advances, or in other words
its _velocity of propagation_, is then 120 metres per minute. We thus
have the rule that _velocity of propagation is equal to the product of
frequency and wave-length_ (cf. Fig. 8).
On the surface of a body of water there may exist at the same time
several wave systems; large waves created by winds which have
themselves perhaps died down, small ripples produced by breezes and
running over the larger waves, and waves from ships, etc. The form of
the surface and the changes of form may thus be very complicated; but
the problem is simplified by combining the motions of the individual
wave systems at any given point. If one system at a given time gives
a crest and another at the same instant also gives a crest at the
same point, the two together produce a higher crest. Similarly, the
resultant of two simultaneous troughs is a deeper trough; a crest from
one system and a simultaneous trough from the other partially destroy
or neutralize each other. A very interesting yet simple case of such
“interference” of two wave systems is obtained when the systems have
equal wave-lengths and equal amplitudes. Such an interference can be
produced by throwing two stones, as much alike as possible, into the
water at the same time, at a short distance from each other. When
the two sets of wave rings meet there is created a network of crests
and troughs. Figs. 4 and 5 show photographs of such an interference,
produced by setting in oscillation two spheres which were suspended
over a body of water.
[Illustration: FIG. 6.—Schematic representation of an interference.]
In Fig. 6 there is a schematic representation of an interference of the
same nature. Let us examine the situation at points along the lower
boundary line. At 0, which is equidistant from the two wave centres,
there is evidently a wave crest in each system; therefore there is a
resultant crest of double the amplitude of a single crest if the two
systems have the same amplitude. Half a period later there is a trough
in each system with a resultant trough of twice the amplitude of a
single trough. Thus higher crests and deeper troughs alternate. The
same situation is found at point 2, a wave-length farther from the left
than from the right wave centre; in fact, these results are found at
all points such as 2, 2′, 4 and 4′, where the difference in distance
from the two wave centres is an even number of wave-lengths. At the
point 1, on the other hand, where the difference between the distance
from the centres is one-half a wave-length, a crest from one system
meets a trough from the other, and the resultant is neither crest nor
trough but zero. There is the same result at points 1′, 3, 3′, 5, 5′,
etc., where the difference between the distances from the two wave
centres is an odd number of half wave-lengths. By throwing a stone
into the water in front of a smooth wall an interference is obtained,
similar to the one described above. The waves are reflected from the
wall as if they came from a centre at a point behind the wall and
symmetrically placed with respect to the point where the stone actually
falls.
[Illustration: FIG. 7.—Waves which are reflected by a board and pass
through a hole in it.]
When a wave system meets a wall in which there is a small hole, this
opening acts as a new wave centre, from which, on the other side
of the wall, there spread half-rings of crests and troughs. But if
the waves are small and the opening is large in proportion to the
wave-length, the case is essentially different. Let us suppose that
wave rings originate at every point of the opening. As a result of the
co-operation of all these wave systems the crests and troughs will
advance, just as before, in the original direction of propagation,
_i.e._, along straight lines drawn from the original wave centre
through the opening; lines of radiation, we may call them. It can be
shown, however, that as these lines of radiation deviate more and more
from the normal to the wall, the interference between wave systems
weakens the resultant wave motion. If the deviation from the normal to
the wall is increased, the weakening varies in magnitude, provided that
the waves are sufficiently small; but even if the wave motions at times
may thus “flare up” somewhat, still on the whole they will decrease as
the deviation from the normal to the wall is increased. The smaller the
waves in comparison to the opening, the more marked is the decrease
of the wave motions as the distance from the normal to the wall is
increased, and the more nearly the waves will move on in straight
lines. That light moves in straight lines, so that opaque objects cast
sharp shadows, is therefore consistent with the wave theory, provided
the light waves are very small; though it is reasonable to expect
that on the passage of light through narrow openings there will be
produced an appreciable bending in the direction of the rays. This
supposition agrees entirely with experiment. As early as the middle
of the seventeenth century, the Italian Grimaldi discovered such a
_diffraction_ of light which passes through a narrow opening into
a dark room.
[Illustration: FIG. 8.—Schematic representation of a wave.
A and B denote crests; C denotes a trough.
λ = wave-length. α = amplitude of wave.
If T denotes the time the wave takes to travel from A to B, and ν = 1/T
the frequency, the wave velocity _v_ will be equal to λ/T = λν.
Points P and P′ are points in the same phase.]
In both light and sound the use of such terms as wave and wave motion
is figurative, for crests and troughs are lacking. But this choice of
terms is commendable, because sound and light possess an essential
property similar to one possessed by water waves. What happens when
a tuning-fork emits sound waves into the surrounding air, is that
the air particles are set in oscillation in the direction of the
propagation of sound. All the particles of air have the same period as
the tuning-fork, and the number of oscillations per second determines
the pitch of the note produced; but the air particles at different
distances from the tuning-fork are not all simultaneously in the same
_phase_ or condition of oscillation. If one particle, at a certain
distance from the source of sound and at a given time, is moving most
rapidly away from the source, then at the same time there is another
particle, somewhat farther along the direction of propagation, which is
moving towards the source most rapidly. This alternation of direction
will exist all along the path of the sound. Where the particles
are approaching each other, the air is in a state of condensation,
and where the particles are drawing apart, the air is in a state
of rarefaction. While the individual particles are oscillating in
approximately the same place, the condensations and rarefactions, like
troughs and crests in water, advance with a velocity which is called
the velocity of sound. If we call the distance between two consecutive
points in the same phase a wave-length, and the number of oscillations
in a period of time the frequency, then, as in the case of water waves,
the velocity of propagation will be equal to the product of frequency
and wave-length.
Light, like sound, is a periodic change of the conditions in the
different points of space. These changes which emanate from the
source of light, in the course of one period advance one wave-length,
_i.e._, the distance between two successive points in the same
phase and lying in the direction of propagation. As in the cases of
sound and water waves, the velocity of propagation or the velocity of
light is equal to the product of frequency and wave-length. If this
velocity is indicated by the letter _c_, the frequency by ν and
the wave-length by λ, then
_c_ _c_
_c_ = νλ or ν = ---- or λ = ---- .
λ ν
The velocity of light in free space is a constant, the same for all
wave-lengths. It was first determined by the Danish astronomer Ole
Rømer (1676) by observations of the moons of Jupiter. According to
the measurements of the present day the velocity of light is about
1,000,000,000 feet or 300,000 kilometres per second. In centimetres it is
thus about 3 × 10¹⁰.
Efforts have been made to consider light waves, like sound waves, as
produced by the oscillations of particles, not of the air, but of a
particular substance, the “ether,” filling and permeating everything;
but all attempts to form definite representations of the material
properties of the ether and of the movements of its particles have been
unsuccessful. The _electromagnetic theory of light_, enunciated
about fifty years ago by the Scottish physicist, Maxwell, has
furnished information of an essentially different character concerning
the nature of light waves.
Let us suppose that electricity is oscillating in a conductor
connecting two metal spheres, for instance. The spheres, therefore,
have, alternately, positive and negative charges. Then according to
Maxwell’s theory we shall expect that in the surrounding space there
will spread a kind of _electromagnetic wave_ with a velocity
equal to that of light. Wherever these waves are, there should arise
electric and magnetic forces at right angles to each other and to
the direction of propagation of the waves; the forces should change
direction in rhythm with the movements of electricity in the emitting
conductor. By way of illustration let us assume that we have somewhere
in space an immensely small and light body or particle with an electric
charge. If, in the region in question, an electromagnetic wave motion
takes place, then the charged particle will oscillate as a result of
the periodically changing electrical forces. The particle here plays
the same rôle as the cork on the surface of the water (cf. p. 35);
the charged body thus makes the electrical oscillations in space
apparent just as the cork shows the oscillations of the water. In
addition to the electrical forces there are also magnetic forces in an
electromagnetic wave. We can imagine that they are made apparent by
using a very small steel magnet instead of the charged body. According
to Maxwell’s theory, the magnet exposed to the electromagnetic wave
will perform rapid oscillations. Maxwell came to the conclusion that
light consisted of electromagnetic waves of a similar nature, but much
more delicate than could possibly be produced and made visible directly
by electrical means.
In the latter part of the nineteenth century the German physicist, H.
Hertz, succeeded in producing electromagnetic waves with oscillations
of the order of magnitude of 100,000,000 per second, corresponding to
wave-lengths of the order of magnitude of several metres.
_c_ 3 × 10¹⁰
(λ = ---- = -------- = 300 cm.).
ν 10⁸
Moreover, he proved the existence of the oscillating electric forces
by producing electric sparks in a circle of wire held in the path
of the waves. He showed also that these electromagnetic waves were
reflected and interfered with each other according to the same laws
as in the case of light waves. After these discoveries there could be
no reasonable doubt that light waves were actually electromagnetic
waves, but so small that it would be totally impossible to examine the
oscillations directly with the assistance of electric instruments.
But there was in this work of Hertz no solution of the problems about
the nature of ether and the processes underlying the oscillations. More
and more, scientists have been inclined to rest satisfied with the
electromagnetic description of light waves and to give up speculation
on the nature of the ether. Indeed, within the last few years,
specially through the influence of Einstein’s theory of relativity,
many doubts have arisen as to the actual existence of the ether.
The disagreement about its existence is, however, more a matter of
definition than of reality. We can still talk about light as consisting
of ether waves if we abandon the old conception of the ether as a
rigid elastic body with definite material properties, such as specific
gravity, hardness and elasticity.
The Dispersion of Light.
It has been said that the wave-length of light is much shorter than
that of the Hertzian waves. This does not mean that all light waves
have the same wave-length and frequency. The light which comes to us
from the sun is composed of waves of many different wave-lengths and
frequencies, to each of which corresponds a particular colour.
In this respect also light may be compared with sound. In whatever way
a sound is produced, it is in general of a complicated nature, composed
of many distinct notes, each with its characteristic wave-length and
frequency. Naturally the air particles cannot oscillate in several
different ways simultaneously. At a given time, however, we can think
of the condensation and rarefactions of the air or the oscillations
of the particles corresponding to different tones, as compounded with
each other in a way similar to that in which the resultant crests and
troughs are produced on a body of water with several coexistent wave
systems. When we say that the complicated wave-movement emitted from
some sound-producing instrument consists of different tones, this
does not only mean that we may imagine it purely mathematically as
resolved into a series of simpler wave systems. The resolution may
also take place in a more physical way. Let us assume that we have a
collection of strings each of which will produce a note of particular
pitch. Now, if sound waves meet this collection of strings, each
string is set in oscillation by the one wave in the compound sound
wave which corresponds to it. Each string is then said to act as a
_resonator_ for the note in question. The notes which set the
resonator strings in oscillation sound more loudly in the neighbourhood
of the resonators; but, as the wave train continues on its journey the
tones taken out by the strings will become weak in contrast to those
notes which found no corresponding strings. The resonator is said to
_absorb_ the notes with which it is in pitch.
Light which is composed of different colours, _i.e._, of wave
systems with different wave-lengths, can also be resolved or dispersed,
but by a method different from that in the case of sound.
When light passes from one medium to another, as from air to glass
or _vice versa_, it is refracted, _i.e._, the direction of
the light rays is changed; but if the light is composed of different
colours the refraction is accompanied by a “spreading” of the colours
which is called dispersion. If we look through a glass prism so that
the light from the object examined must pass in and out through two
faces of the prism which make not too great an angle with each other,
the light-producing object is not only displaced by the refraction,
but has coloured edges. Newton was the first to explain the relation
of the production of the colours to refraction. He made an experiment
with sunlight, which he sent through a narrow opening into a dark room.
The sunlight was then by a glass prism transformed or dispersed into a
band of colour, a _spectrum_ consisting of all the colours of the
rainbow, red, yellow, green, blue and violet, in the order named, and
with continuous transition stages between neighbouring colours.
[Illustration: FIG. 9.—Prism spectroscope. To the right is
seen the collimator, to the left the telescope, in the foreground a
scheme for illuminating the cross-wire.
(From an old print.)]
In Newton’s original experiment the different wave-lengths were but
imperfectly separated. A spectrum with pure wave-lengths can be
obtained with a _spectroscope_ (cf. Fig. 9). The light to be
investigated illuminates an adjustable vertical slit in one end of a
long tube, called the collimator, with a lens in the other end. If the
slit is in the focal plane of the lens, the light at any point in the
slit goes in parallel rays after meeting the lens. It then meets a
prism, with vertical edges, placed on a little revolving platform. The
rays, refracted by the prism, go in a new direction into a telescope
whose objective lens gives in its focal plane, for every colour, a
clear vertical image of the slit. These images can be examined through
the ocular of the telescope; but since the different colours are not
refracted equally, each coloured image of the slit has its own place.
The totality of the slit images then forms a horizontal spectrum of
the same height as the individual images. By revolving the collimator
different parts of the spectrum can be put in the middle of the field
of view. To facilitate measurements in the spectrum there is in the
focal plane of the collimator a sliding cross-wire with an adjusting
screw or a vertical strand of spider web.
[Illustration: FIG. 10.—The mode of operation of a grating.
_A_, grating; _C, D, E_ ... _H_, slits; _M M_, incident rays. When _D
D′, E E′_ ... are a whole number of wave-lengths, the light waves which
move in the direction indicated by _C N_ and are collected by a lens,
at the focal point will all be in the same phase and therefore will
reinforce each other. In other directions the light action from one
slit is compensated by that from another.]
Instead of using the refraction of light in a prism to separate the
wave-lengths, we can use the interference which arises when a bundle of
parallel light waves passes through a ruled _grating_, consisting
of a great many very fine parallel lines, equidistant from each other;
such a grating can be made by ruling lines with a diamond point on the
metal coating of a silvered plate of glass. From each line there are
sent out light waves in all directions; but if we are considering
light of one definite colour (a given wave-length, _monochromatic
light_), the interference among the waves from all the slits
practically destroys all waves except in the direction of the original
rays and in the directions making certain angles with the former,
dependent upon the wave-length and the distance between two successive
lines (the grating space). Monochromatic light can be obtained by
using as the source of light a spirit flame, coloured yellow with
common salt (sodium chloride). If the slit in a spectroscope is lighted
with a yellow light from such a flame, and if a grating normal to
the direction of the rays is substituted for the prism, then in the
telescope there is seen a yellow image of the slit, and on each side
of it one, two, three or more yellow images. If sunlight is used the
central image is white, since all the colours are here assembled. The
other images become spectra because the different colours are unequally
refracted. In these _grating spectra_, which according to their
distance from the central line are called spectra of the first, second
or third order, the violet part lies nearest to the central line, the
red part farthest away. Since the deflection is the greater the greater
the wave-length, then violet light must have the shortest wave-length
and red the greatest. From the amount of the refraction and the size of
the grating space the wave-length of the light under investigation can
be calculated.
For the yellow light from our spirit flame the wave-length is about
0·000589 mm. or 0·589 μ or 589 μμ. In centimetres the wave-length is
0·0000589 cm.; from the formula ν = _c_/λ, ν = 526 × 10¹². The
frequency is thus almost inconceivably large. For the most distant
red and violet in the spectrum the wave-lengths are respectively
about 800 μμ and 400 μμ, and the frequencies 375 × 10¹² and 750 × 10¹²
oscillations per second.
In scientific experiments a grating of specular metal with parallel
rulings is substituted for the transparent grating. The spectrum is
then given by the reflected light from the parts between the rulings.
Specular gratings can be made by ruling on a concave mirror, which
focuses the rays so that a glass lens is unnecessary. Gratings with
several hundred lines or rulings to the millimetre give excellent
spectra, with strength of light and marked dispersion. The preparation
of the first really good gratings is due to the experimental skill
of the American, Rowland, who in 1870 built a dividing engine from
which the greater part of the good gratings now in use originate. The
contribution which Rowland thereby made to physical science can hardly
be over-estimated.
Spectral Lines.
In the early part of the nineteenth century Wollaston, in England,
and later Fraunhofer in Germany, discovered dark lines in the solar
spectrum, a discovery which meant that certain colours were missing.
The most noticeable of these so-called “Fraunhofer Lines” were named
with the letters A, B, C, D, E, F, G, H, from red to violet. It was
later discovered that some of the lines were double, that the D-line,
for instance, can be resolved into D₁ and D₂; other letters, such
as _b_ and _h_, were introduced to denote new lines. With
improvements in the methods of experiment and research the number
of lines has increased to hundreds and even thousands. The light
from a glowing solid or liquid element forms, on the other hand, a
continuous spectrum, _i.e._ a spectrum which has no dark lines. An
illustration of the solar spectrum with the strongest Fraunhofer lines
is given at the end of the book.
In contrast to the solar spectrum with dark lines on a bright
background are the so-called _line spectra_, which consist of
bright lines on a dark background. The first known line spectrum was
the one given by light from the spirit flame coloured with common
salt, mentioned in connection with monochromatic light. As has been
said, this spectrum had just one yellow line which was later found to
consist of two lines close to each other. It is sodium chloride which
colours the flame yellow. The colour is due, not to the chlorine, but
to the sodium, for the same double yellow line can be produced by using
other sodium salts not compounded with chlorine. The yellow light is
therefore called sodium light. No. 7 in the table of spectra at the end
of the book shows the spectrum produced by sodium vapour in a flame.
(On account of the small scale in the figure it is not shown that the
yellow line is double.)
Another interesting discovery was soon made, namely, that the sodium
line has exactly the same wave-length as the light lacking in the solar
spectrum, where the double D-line is located. About 1860 Kirchhoff and
Bunsen explained this remarkable coincidence as well as others of the
same nature. They showed by direct experiment that if sodium vapour is
at a high temperature it can not only send out the yellow light, but
also absorb light of the same wave-length when rays from a still warmer
glowing body pass through the vapour. This phenomenon is something like
that in the case of sound waves where a resonator absorbs the pitch
which it can emit itself. The existence of the dark D-line in the solar
spectrum must then mean that in the outer layer of the sun there is
sodium vapour present of lower temperature than the white-hot interior
of the sun, and that the light corresponding to the D-line is absorbed
by the vapour. Several ingenious experiments, which cannot be described
here, have given further evidence in favour of this explanation.
In the other line spectra, just as in that from the common salt flame,
definite lines correspond to definite elements and not to chemical
compounds. The emission of these lines is then not a molecular
characteristic, but an atomic one. The line spectra of metals can often
be produced by vaporizing a metallic salt in a spirit flame or in a
hot, colourless gas flame (from a Bunsen burner). It is even better to
use an electric arc or strong electric sparks. The atoms from which
gaseous molecules are formed can also be made to emit light which by
means of the spectroscope is shown to consist of a line spectrum. These
results are obtained by means of electric discharges of various kinds,
arcs, and spark discharges through tubes where the gas is in a rarefied
state.
The other Fraunhofer lines in the solar spectrum correspond to bright
lines in the line spectra of certain elements which exist here on
earth. These Fraunhofer lines must then be assumed to be caused by the
absorption of light by the elements in question. This may be explained
by the presence of these elements as gases in the solar atmosphere,
through which passes the light from the inner layer. This inner surface
would in itself emit a continuous spectrum.
The work of Kirchhoff and Bunsen put at the disposal of science
became a new tool of incalculable scope. First and foremost, spectrum
examinations were taken into the service of chemistry as _spectrum
analysis_. It has thus become possible to analyse quantities of
matter so small that the general methods of chemistry would be quite
powerless to detect them. It is also possible by spectrum analysis
to detect minute traces of an element; several elements were in this
way first discovered by the spectroscope. Moreover, chemical analysis
has been extended to the study of the sun and stars. The spectral
lines have given us answers to many problems of physics—problems which
formerly seemed insoluble. Last but not least spectrum analysis has
given us a key to the deepest secrets of the atom, a key which Niels
Bohr has taught us how to use.
In the discussion of the spectrum we have hitherto restricted ourselves
to the visible spectrum limited on the one side by red and on the other
by violet. But these boundaries are in reality fortuitous, determined
by the human eye. The spectrum can be studied by other methods than
those of direct observation. The more indirect methods include the
effect of the rays on photographic plates and their heating effect on
fine conducting wires for electricity, held in various parts of the
spectrum. It has thus been discovered that beyond the visible violet
end of the spectrum there is an _ultra-violet_ region with strong
photographic activity and an _infra-red_ region producing marked
heat effects. There are both dark and light spectral lines in these
new parts of the spectrum. The fact that glass is not transparent to
ultra-violet or infra-red rays has been an obstacle in the experiments,
but the difficulty can be overcome by using other substances, such as
quartz or rock salt, for the prisms and lenses, or by substituting
concave gratings. By special means it has been possible to detect rays
with wave-lengths as great as 300 μ and as small as about 0·02 μ,
corresponding to frequencies between 10¹², and 15 × 10¹⁵ vibrations per
second, while the wave-lengths of the luminous rays lie between 0·8 and
0·4 μ. The term “light wave” is often used to refer to the ultra-violet
and infra-red rays which can be shown in the spectra produced by prisms
or gratings.
[Illustration: FIG. 11.—Photographic effect of X-rays, which
are passed through the atom grating in a magnesia crystal.]
The electrically produced electromagnetic waves, as already mentioned,
have wave-lengths much greater than 300 μ. In wireless telegraphy
there are generally used wave-lengths of one kilometre or more,
corresponding to frequencies of 300,000 vibrations per second or less.
By direct electrical methods it has, however, not been possible to
obtain wave-lengths less than about one-half a centimetre, a length
differing considerably from the 0·3 millimetre wave of the longest
infra-red rays. Wave-lengths much less than 0·02 μ or 20 μμ exist in
the so-called _Röntgen rays_ or _X-rays_ with wave-lengths
as small as 0·01 μμ corresponding to a frequency of 30 × 10¹⁸. These
rays cannot possibly be studied even with the finest artificially made
gratings, but crystals, on account of the regular arrangement of the
atoms, give a kind of natural grating of extraordinary fineness. With
the use of crystal gratings success has been attained in decomposing
the Röntgen rays into a kind of spectrum, in measuring the wave-lengths
of the X-rays and in studying the interior structure of the crystals.
The German Laue, the discoverer of the peculiar action of crystals on
X-rays (1912), let the X-rays beams pass through the crystal, obtaining
thereby photographs of the kind illustrated in Fig. 11. Later on
essential progress was due to the Englishmen, W. H. and W. L. Bragg,
who worked out a method of investigation by which beams of X-rays are
reflected from crystal faces. The greatest wave-length which it has
been possible to measure for X-rays is about 1·5 μμ, which is still a
long way from the 20 μμ of the furthermost ultra-violet rays.
It may be said that the spectrum since Fraunhofer has been made not
only longer but also finer, for the accuracy of measuring wave-lengths
has been much increased. It is now possible to determine the
wave-length of a line in the spectrum to about 0·001 μμ or even less,
and to measure extraordinarily small changes in wave-lengths, caused by
different physical influences.
In addition to the continuous spectra emitted by glowing solids
or liquids, and to the line spectra emitted by gases, and to the
absorption spectra with dark lines, there are spectra of still another
kind. These are the absorption spectra which are produced by the
passage of white light through coloured glass or coloured fluids. Here
instead of fine dark lines there are broader dark absorption bands,
the spectrum being limited to the individual bright parts. There are
also the band spectra proper, which, like the line spectra, are purely
emission spectra, given by the light from gases under particular
conditions; these seem to consist of a series of bright bands which
follow each other with a certain regularity (cf. Fig. 12). With
stronger dispersion the bands are shown to consist of groups of bright
lines.
[Illustration:
FIG. 12.—Spectra produced by discharges of different character
through a glass tube containing nitrogen at a pressure of ¹/₂₀ that of
the atmosphere. Above, a band spectrum; below, a line spectrum.]
Since the line spectra are most important in the atomic theory, we
shall examine them here more carefully.
The line spectra of the various elements differ very much from each
other with respect to their complexity. While many metals give a great
number of lines (iron, for instance, gives more than five thousand),
others give only a few, at least in a simple spectroscope. With a more
powerful spectroscope the simplicity of structure is lost, since weaker
lines appear and other lines which had seemed single are now seen to
be double or triple. Moreover, the number of lines is increased by
extending the investigation to the ultra-violet and infra-red regions
of the spectrum. The sodium spectrum, at first, seemed to consist of
one single yellow line, but later this was shown to be a double line,
and still later several pairs of weaker double lines were discovered.
The kind and number of lines obtained depends not only upon the
efficiency of the spectroscope, but also upon the physical conditions
under which the spectrum is obtained.
The eager attempts of the physicists to find laws governing the
distribution of the lines have been successful in some spectra. For
instance, the line spectra of lithium, sodium, potassium and other
metals can be arranged into three rows, each consisting of double
lines. The difference between the frequencies of the two “components”
of the double lines was found to be exactly the same for most of
the lines in one of these spectra, and for the spectra of different
elements there was discovered a simple relationship between this
difference in frequency and the atomic weight of the element in
question. But this regularity was but a scrap, so to speak; scientists
were still very far from a law which could exactly account for the
distribution of lines in a single series, not to mention the lines in
an entire spectrum or in all the spectra.
The first important step in this direction was made about 1885 by
the Swiss physicist, Balmer, in his investigations with the hydrogen
spectrum, the simplest of all the spectra. In the visible part
there are just three lines, one red, one green-blue and one violet,
corresponding to the Fraunhofer lines C, F and _h_. These
hydrogen lines are now generally known by the letters Hα, Hᵦ and Hᵧ.
In the ultra-violet region there are many lines also.
Balmer discovered that wave-lengths of the red and of the green
hydrogen line are to each other exactly as two integers, namely, as 27
to 20, and that the wave-lengths of the green and violet lines are to
each other as 28 to 25. Continued reflection on this correspondence led
him to enunciate a rule which can be expressed by a simple formula.
When frequency is substituted for wave-length Balmer’s formula is
written as
( 1 1 )
ν = K(--- - -------),
( 4 _n_² )
where ν is the frequency of a hydrogen line, K a constant equal to 3·29
× 10¹⁵ and _n_ an integer. If _n_ takes on different values,
ν becomes the frequency for the different hydrogen lines. If _n_ =
1 ν is negative, for _n_ = 2 ν is zero. These values of _n_
therefore have no meaning with regard to ν. But if _n_ = 3, then
ν gives the frequency for the red hydrogen line Hα; _n_ = 4 gives
the frequency of the green line Hᵦ and _n_ = 5 that of the violet
line Hᵧ. Gradually more than thirty hydrogen lines have been found,
agreeing accurately with the formula for different values of _n_.
Some of these lines were not found in experiment, but were discovered
in the spectrum of certain stars; the exact agreement of these lines
with Balmer’s formula was strong evidence for the belief that they are
due to hydrogen. The formula thus proved itself valuable in revealing
the secrets of the heavens.
As _n_ increases 1/_n_² approaches zero, and can be made as
close to zero as desired by letting _n_ increase indefinitely. In
mathematical terminology, as _n_ = ∞, 1/_n_² = 0 and ν =
K/4 = 823 × 10¹², corresponding to a wave-length of 365 μμ. Physically
this means that the line spectrum of hydrogen in the ultra-violet is
limited by a line corresponding to that frequency. Near this limit the
hydrogen lines corresponding to Balmer’s formula are tightly packed
together. For _n_ = 20 ν differs but little from K/4, and the
distance between two successive lines corresponding to an increase of
1 in _n_ becomes more and more insignificant. Fig. 13, where the
numbers indicate the wave-lengths in the Ångström unit (0·1 μμ), shows
the crowding of the hydrogen lines towards a definite boundary. The
following table, where K has the accurate value of 3·290364 × 10¹⁵,
shows how exactly the values calculated from the formula agree with
experiment.
[Illustration: FIG. 13.—Lines in the hydrogen spectrum corresponding to
the Balmer series.]
TABLE OF SOME OF THE LINES OF THE BALMER SERIES
---------+----------------------------+-------------+-------------+
| ν = K(¹⁄₄ - 1/_n_²) = ν | | |
| (calculated). | ν (found). | λ (found). |
--------+----------------------------+-------------+-------------+
_n_ = 3|K(¼ - ¹/₉ ) = 456,995 bills|456,996 bills|656·460 μμ Hα|
_n_ = 4|K(¼ - ¹/₁₆ ) = 616,943 “ |616,943 “ |486·268 “ Hᵦ|
_n_ = 5|K(¼ - ¹/₂₅ ) = 690,976 “ |690,976 “ |434·168 “ Hᵧ|
_n_ = 6|K(¼ - ¹/₃₆ ) = 731,192 “ |731,193 “ |410·288 “ Hδ|
_n_ = 7|K(¼ - ¹/₄₉ ) = 755,440 “ |755,441 “ |397·119 “ Hε|
--------+----------------------------+-------------+-------------+
_n_ = 20|K(¼ - ¹/₄₀₀) = 814,365 “ |814,361 “ |368·307 “ |
--------+----------------------------+-------------+-------------+
From arguments in connection with the work of the Swedish scientist,
Rydberg, in the spectra of other elements, Ritz, a fellow countryman of
Balmer’s, has made it seem probable that the hydrogen spectrum contains
other lines besides those corresponding to Balmer’s formula. He assumed
that the hydrogen spectrum, like other spectra, contains several series
of lines and that Balmer’s formula corresponds to only one series. Ritz
then enunciated a more comprehensive formula, the Balmer-Ritz formula:
( 1 1 )
ν = K( ------- - -----),
( _n″_² _n′_²)
where K has the same value as before, and both _n′_ and _n″_
are integers which can pass through a series of different values.
For _n″_ = 2, the Balmer series is given; to _n″_ = 1, and
_n′_ = 2, 3 ... ∞ there corresponds a second series which lies
entirely in the ultra-violet region, and to _n″_ = 3, _n′_
= 4, 5 ... ∞ a series lying entirely in the infra-red. Lines have
actually been found belonging to these series.
Formulæ, similar to the Ritz one, have been set up for the line spectra
of other elements, and represent pretty accurately the distribution
of the lines. The frequencies are each represented by the difference
between two terms, each of which contains an integer, which can pass
through a series of values. But while the hydrogen formula, except for
the _n_′s, depends only upon one constant quantity K and its terms
have the simple form K/_n_², the formula is more complicated with
the other elements. The term can often be written, with a high degree
of exactness, as K/(_n_ + α)², where K is, with considerable
accuracy, the same constant as in the hydrogen formula. For a given
element α can assume several different values; therefore the number of
series is greater and the spectrum is even more complicated than that
of hydrogen.
All these formulæ are, however, purely empirical, derived from the
values of wave-lengths and frequencies found in spectrum measurements.
They represent certain more or less simple bookkeeping rules, by which
we can register both old and new lines, enter them in rows, arrange
them according to a definite system. But from the beginning there could
be no doubt that these rules had a deeper physical meaning which it was
not yet possible to know. There was no visible correspondence between
the spectral line formulæ and the other physical characteristics of
the elements which emitted the spectra; not even in their form did the
formulæ show any resemblance to formulæ obtained in other physical
branches.