Scattered Light--Sunset Colours--Law of the Scattering by Fine
Particles--Sunset Clouds--Luminosities of Sunlight at different
Altitudes of the Sun.
It is probable that we should be able to ascertain approximately the
true colour of sunlight (if we may talk of the colour of white light) if
we could collect all the light from a cloudless sky, and condense it on
a patch of sunlight thrown on a screen. For skylight is, after all, only
a portion of the light of the sun, scattered from small particles in the
atmosphere, part of the light being scattered into space, and part to
our earth. The small particles of water and dust--and when we say small
we mean small when measured on the same scale as we measure the lengths
of waves of light--differentiate between waves of different lengths, and
scatter the blue rays more than the green, and the green than the red;
consequently what the sun lacks in blue and green is to be found in the
light of the sky. The effect that small water particles have upon light
passing through them can be very well seen in the streets of London at
night, when the atmosphere is at all foggy. Gaslights at the far end of
a street appear to become ruby red and dim, and half-way down only
orange, but brighter, whilst close to they are of the ordinary yellow
colour, and of normal brightness. When no fog is present the gas-lights
in the distance and close to are of the same colour and brightness,
showing that their change in appearance is simply due to the misty
atmosphere intervening between them and the observer. We can imitate the
light from the sun, after its passage through various thicknesses of
atmosphere, in a very perfect manner in the lecture-room, using the
electric light as a source. A condensing lens is put in front of the
lamp, and in front of that a circular aperture in a plate. Beyond that
again is a lens which throws an enlarged image of the aperture on the
screen, which we may call our mock sun. If we place a trough of glass,
in which is a dilute solution of hyposulphite of soda, carefully
filtered from motes as far as possible, in front of the aperture, we
have an image of the aperture unaffected by the insertion of the
solution. The white disc on the screen will, as we have said before, be
a close approximation to sunlight on a May-day about noon, when the sky
is clear. By dropping into the trough a little dilute hydrochloric
acid, a change will be found to come over the light of the mock sun; a
pale yellow colour will spread over its surface, and this will give way
to an orange tint, and at the same time its brightness will diminish.
Gradually the orange will give place to red, the luminosity will be very
small, being of the same hue as that seen in the sun when viewed through
a London fog. Finally the last trace of red will so mingle with the
scattered white light that the image will disappear, and then the
experiment is over.
If we track the cause of this change of colour in our artificial sun, we
shall find that it is due to minute particles of sulphur separating out
from the solution of hyposulphite, and the longer the time that elapses
the more turbid the dilute solution will become. This experiment
exemplifies the action of small particles on light. Examining the trough
it will be found that whilst the light which passes _through the
solution_ principally loses blue rays, the light which is scattered from
the sides is almost cerulean in blue, and can well be compared with the
light from the sky. We can analyze the transmitted light very readily by
focusing the beam from the positive pole of the electric light on to the
slit of our colour apparatus, and placing the lens L6(Fig. 6) in
position to form the large spectrum on the screen. We can also show the
colour of the light which goes to form the spectrum, by sending the
patch of light reflected from the first surface of the first prism just
above it. We thus have the spectrum and the light forming the spectrum
to compare with one another. Using this apparatus and inserting the
trough of dilute hyposulphite in the beam, the spectrum is of the
character usually seen with the electric light; but on dropping the
dilute hydrochloric acid into the solution the same hues fall on the
slit of the spectroscope which fell upon the screen to form the mock
sun, and the spectrum is seen to change as the light changes from white
to yellow, and from yellow to red. First the violet will disappear, the
blue and the green being dimmed, the former most however; then the blue
will vanish to the eye, the green becoming still less luminous, and the
yellow also fading; the green and yellow will successively disappear,
leaving finally on the screen a red band alone, which will be a near
match to the colour of the unanalyzed light, as may be seen by comparing
it with the adjacent patch formed from the reflected beam.
We have here a proof that the succession of phenomena is caused by a
scattering of the shorter wave-lengths of light, and that the shorter
the waves are the more they are scattered. It has been found
theoretically by Lord Rayleigh that the scattering takes place in
inverse proportion to the fourth power of the wave-length; thus, if two
wave-lengths, which may be waves in the green and violet, are in the
proportion of three to four, the former will be scattered as 1/(3^4) to
1/(4^4), or as 256 to 81, which is approximately as three to one.
Consequently if the green in passing through a certain thickness of a
turbid medium loses one-half the violet in passing through the same
thickness will lose five-sixths of its luminosity. The inverse fourth
powers of the following wave-lengths, which are within the limits of the
whole visible spectrum, are shown below.
+-----------+------+------+------+------+
| [Lamda] | 7000 | 6000 | 5000 | 4000 |
+-----------+------+------+------+------+
|1/[Lamda]^4| 1 | ·504 | ·260 | ·107 |
+-----------+------+------+------+------+
Supposing [Lamda]7000 by the scattering of small particles loses one-tenth
of its luminosity, then [Lamda]6000 would have ·454 of its original
brightness; [Lamda]5000, ·234; and [Lamda]4000, ·095; that is, whilst [Lamda]7000
would lose one-tenth only of its luminosity, [Lamda]4000 in the violet
would retain not quite one-hundredth of its brightness.
During the years 1885, 1886, and 1887, the writer measured the
luminosity of the solar spectrum at different times of the year, and at
different hours of the day (see _Phil. Trans._ 1887: "Transmission of
Sunlight through the Earth's Atmosphere"), and from the results he found
that the smallest coefficient of scattering for one atmosphere at
sea-level for each wave-length was ·0013, when [Lamda]^-4 was for
convenience sake multiplied by 10^17 (thus [Lamda]6000^-4 on this scale
was 77·2), and that the mean was ·0017.
The following table shows the loss of light for the rays denoted by the
principal lines given at page 26, using this last coefficient for
different air thicknesses. This is equivalent to giving the intensity of
the rays of sunlight when the sun is at different altitudes.
+---+------+------------+--------------------------------------------+
| | | 1 | Light after passing through atmospheres of |
Line| Wave-| - | the following thicknesses. |
| |length|[Lamda]^-4+-+----+----+----+----+----+----+----+----+----+
| | | x10^17 |0| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 32 |
+---+------+----------+-+----+----+----+----+----+----+----+----+----+
| A | 7594 | 30 |1|·955|·908|·857|·815|·775|·736|·707|·665|·107|
| B | 6867 | 45 |1|·926|·858|·795|·735|·684|·632|·583|·542|·086|
| C | 6562 | 54 |1|·912|·832|·759|·693|·632|·576|·526|·480|·019|
| D | 5892 | 83 |1|·868|·754|·655|·569|·494|·428|·372|·323|·001|
| E | 5269 | 129 |1|·803|·644|·518|·427|·334|·268|·216|·173| -- |
| F | 4861 | 179 |1|·738|·544|·402|·296|·219|·161|·119|·088| -- |
| G | 4307 | 291 |1|·609|·367|·220|·137|·084|·051|·031|·019| -- |
| H | 3968 | 403 |1|·506|·254|·128|·071|·033|·016|·008|·004| -- |
+---+------+----------+-+----+----+----+----+----+----+----+----+----+
The sun traverses the following thicknesses of atmosphere when it is at
the angles shown above the horizon.
1 atmosphere 90°
2 " 30°
3 " 19·30
4 " 14·30
5 " 11·30
6 " 9·30
7 " 8·30
8 " 7·30
Fig. 10.--Absorption of Rays by the Atmosphere.
It traverses thirty-two atmospheres when it is very nearly setting.
Bougier and Forbes have calculated that the extreme thickness of the
atmosphere, traversed by its light when the sun is on the horizon, is
approximately 35-1/2 atmospheres. The absorption shown by 32 atmospheres
will therefore be very close to that which would be observed at sunset
on an ordinary day, and it will be seen that practically all rays have
been scattered from the light, except the red, and a little bit of the
orange.
As to the luminosity of the sun at these different altitudes, we can
easily find it by reducing the luminosity curve of the sun at some known
altitude by the factors in the table just given, for as many
wave-lengths as we please, and thus construct another curve. The area of
the figure thus obtained would be a measure of the total luminosity on
the same scale as the area of the luminosity curve from which it was
derived.
The following are the approximate luminosities of the sun when the light
shines
through 0 atmospheres 1
" 1 " ·840
" 2 " ·705
" 3 " ·594
" 4 " ·496
" 5 " ·417
" 6 " ·303
" 7 " ·256
" 8 " ·215
" 32 " ·002
It will thus be seen that the sun is 420 times less bright just at
sunset than it is if it were to shine directly overhead, and about 350
times brighter than it is for a winter sun in a cloudless and mistless
sky at twelve o'clock, for the altitude of the sun in our latitude is
about 30° at that time, and corresponds with a thickness of two
atmospheres, through which the sun has to shine. We all know that to
look at the sun at any time near noon in a cloudless sky dazzles the
eyes, but that near sunset it may be looked at with impunity. The
reduction in luminosity explains this fact.
The distribution of the scattering particles in the atmosphere is very
far from regular. As we ascend, the particles get more sparse, as is
shown by the less scattering that takes place of the blue rays compared
with the red. Thus at an altitude of some 8000 feet the mean coefficient
of scattering is about ·0003, instead of ·0017, which it is at
sea-level. It must be recollected that there is only about three-fourths
of the air above us at 8000 feet, and it is less dense. There will
therefore be a diminution of particles not only because there is less
air, but because the air itself is less capable of keeping them in
suspension. Up to 3000 or 4000 feet there is no very great marked
difference in the scattering of light, as observations carried on during
five years have shown; but above that the scattering rapidly
diminishes, and at 20,000 feet it must be very small indeed, if the
diminution increases as rapidly as has been found it does at the
altitude of 8000 feet.
We must repeat once more that the blue of the sky is principally if not
entirely due to the presence of these particles, the rays scattered by
them, which are principally the blue rays, being reflected back from
them, giving the sensation of blue which we know as sky-blue. The
greater the number of these fine particles that are encountered by
sunlight, the greater the scattering will be, and the bluer the sky. It
is more than probable that the blue sky of Italy, so proverbial for
being beautiful, is due to this cause, since from its geographical
position the small particles of water must be very abundant there.
Carrying this argument further, we should expect that as we mount higher
the blue would become more fully mixed with the darkness of space, and
this Alpine travellers will tell you is the case. At heights of 12,000
feet or more, on a clear day, the sky seems almost black, and it is no
uncommon thing to see this admirably rendered in photographs of Alpine
scenery when taken at a height. Many of the late Mr. Donkin's
photographs show this in great perfection, as also Signor Sella's.
Before quitting this subject we may call attention not only to the
colour of the sun itself at sunset, but also to the colouring of the sky
which accompanies the sun as it sinks. This colouring is often different
to the colour that the sun itself assumes; but we can easily show that
the effects so wonderfully beautiful are entirely dependent on this
scattering of light by these small intervening particles in the air. We
often see a ruddy sun, and perhaps nearly in the zenith, or even further
away from the sun, clouds of a beautiful crimson hue, lying on a sky
which appears almost pea-green, whilst nearer to the sun the sky is a
brilliant orange, which artists imitate with cadmium yellow. Let us fix
our attention first on the crimson cloud. The clouds of which the
colouring is so gorgeous are often not 1000 feet above us, and were we
to be at that altitude we should see the sun not quite so ruddy as we
see it from the earth, and the cloud would consequently be illuminated
by the sun with a more orange tint; but the light reflected from the
cloud to our eyes has to pass through, say 1000 feet of dense
atmosphere, and thus the total atmosphere that the light traverses in
the latter case is always greater than the air thickness through which
the direct light from the sun has to pass; hence more orange is cut off,
and the light reflected from the cloud is redder. This red, however,
will not account for the brilliant crimson and purples which we so
often see. It has to be remembered that not sunlight alone illumines the
cloud, but also the blue light of the sky. The feebler the intensity of
the red, the more will the blue of the sky be felt in the mixture of
light which reaches our eyes, and consequently we may have any tint
ranging from crimson to purple, since red and blue make these hues,
according to the proportions in which they are mixed.
Now let us see how we get the brilliant orange of the sky itself. When
the evening is perfectly clear and free from mist and cloud, the orange
in the sky is very feeble, showing that the intensity depends upon their
presence. Now a look at the table will show that the sun is very close
to the horizon when it becomes ruddy under normal conditions; but that
when the light traverses a thickness of eight atmospheres, the blue and
violet, and most of the green, are absent, leaving a light of yellowish
colour. To traverse eight atmospheres the light has only to come from a
point some eight degrees above the horizon. When the sun is near the
horizon, it sends its rays not only to us and over us, but in every
direction; and an eye placed some few thousand feet above the earth
would see the sun almost of its midday colour, for sunset colours of the
gorgeous character that we see at sea-level are almost absent at high
altitudes. If a cloud or mist were at such an altitude the sunlight
would strike it, and whilst only a small portion would be selectively
scattered, owing to the general grossness of the particles, the major
part would be reflected back to our eyes, and come from an altitude of
over eight to ten degrees, and would therefore, after traversing the
intervening atmosphere, reach us as the orange-coloured light of which
we have just spoken. The clouds which are orange when near the sun, are
usually higher than those which are simultaneously red or purple. The
pea-green colour of the sky is often due to contrast, for the contrast
colour to red is green, and this would make the blue of the sky appear
decidedly greener. Sometimes, however, it is due to an absolute mixture
of the blue of the sky and the orange light which illuminates the same
haze. In the high Alps it is no uncommon occurrence for the snow-clad
mountains to be tipped with the same crimson we have described as
colouring the clouds, and this is usually just after sunset, when the
sun has sunk so low beneath the horizon that the light has to traverse a
greater thickness of dense air, and consequently to pass through a
larger number of small particles than it has when just above the
horizon. In this case the red of the sunlight mixes with blue light of
the sky, and gives us the crimson tints. The deeper and richer tints of
the clouds just after sunset are also due to the same cause, the
thickness of air traversed being greater.
It is worth while to pause a moment and think what extraordinary sensual
pleasure the presence of the small scattering particles floating in the
air causes us; that without them the colouring which impresses itself
upon us so strongly would have been a blank, and that artists would have
to rely upon form principally to convey their feelings of art. Indeed
without these particles there would probably be no sky, and objects
would appear of the same hard definition as do the mountains in the
atmosphereless moon. They would be only directly illuminated by
sunlight, and their shadows by the light reflected from the surrounding
bright surfaces.