Refraction—Astronomical Refraction and its Laws—Formation of Tables of
Refraction—Terrestrial Refraction—Its Quantity—Instances of
extraordinary Refraction—Reflection—Instances of extraordinary
Reflection—Loss of Light by the Absorbing Power of the
Atmosphere—Apparent Magnitude of Sun and Moon in the Horizon.
NOT only everything we hear but all we see is through the medium of the
atmosphere. Without some knowledge of its action upon light, it would be
impossible to ascertain the position of the heavenly bodies, or even to
determine the exact place of very distant objects upon the surface of
the earth; for, in consequence of the refractive power of the air, no
distant object is seen in its true position.
All the celestial bodies appear to be more elevated than they really
are; because the rays of light, instead of moving through the atmosphere
in straight lines, are continually inflected towards the earth. Light
passing obliquely out of a rare into a denser medium, as from vacuum
into air, or from air into water, is bent or refracted from its course
towards a perpendicular to that point of the denser surface where the
light enters it (N. 189). In the same medium, the sine of the angle
contained between the incident ray and the perpendicular is in a
constant ratio to the sine of the angle contained by the refracted ray
and the same perpendicular; but this ratio varies with the refracting
medium. The denser the medium, the more the ray is bent. The barometer
shows that the density of the atmosphere decreases as the height above
the earth increases. Direct experiments prove that the refractive power
of the air increases with its density. It follows therefore that, if the
temperature be uniform, the refractive power of the air is greatest at
the earth’s surface, and diminishes upwards.
A ray of light from a celestial object falling obliquely on this
variable atmosphere, instead of being refracted at once from its course,
is gradually more and more bent during its passage through it so as to
move in a vertical curved line, in the same manner as if the atmosphere
consisted of an infinite number of strata of different densities. The
object is seen in the direction of a tangent to that part of the curve
which meets the eye; consequently the apparent altitude (N. 190) of the
heavenly bodies is always greater than their true altitude. Owing to
this circumstance, the stars are seen above the horizon after they are
set, and the day is lengthened from a part of the sun being visible,
though he really is behind the rotundity of the earth. It would be easy
to determine the direction of a ray of light through the atmosphere if
the law of the density were known; but, as this law is perpetually
varying with the temperature, the case is very complicated. When rays
pass perpendicularly from one medium into another, they are not bent;
and experience shows, that in the same surface, though the sines of the
angles of incidence and refraction retain the same ratio, the refraction
increases with the obliquity of incidence (N. 189). Hence it appears
that the refraction is greatest at the horizon, and at the zenith there
is none. But it is proved that, at all heights above ten degrees,
refraction varies nearly as the tangent of the angular distance of the
object from the zenith, and wholly depends upon the heights of the
barometer and thermometer. For the quantity of refraction at the same
distance from the zenith varies nearly as the height of the barometer,
the temperature being constant; and the effect of the variation of
temperature is to diminish the quantity of refraction by about its 480th
part for every degree in the rise of Fahrenheit’s thermometer. Not much
reliance can be placed on celestial observations, within less than ten
or twelve degrees of the horizon, on account of irregular variations in
the density of the air near the surface of the earth, which are
sometimes the cause of very singular phenomena. The humidity of the air
produces no sensible effect on its refractive power; and it has been
proved that the amount of refraction is the same whatever be the
velocity of the incident light, that is whether the light comes from a
star in that part of the heavens towards which the earth is going, or
from one in that part of the sky whence it is receding.
Bodies, whether luminous or not, are only visible by the rays which
proceed from them. As the rays must pass through strata of different
densities in coming to us, it follows that, with the exception of stars
in the zenith, no object either in or beyond our atmosphere is seen in
its true place. But the deviation is so small in ordinary cases that it
causes no inconvenience, though in astronomical and trigonometrical
observations due allowance must be made for the effects of refraction.
Dr. Bradley’s tables of refraction were formed by observing the zenith
distances of the sun at his greatest declinations, and the zenith
distances of the pole-star above and below the pole. The sum of these
four quantities is equal to 180°, diminished by the sum of the four
refractions, whence the sum of the four refractions was obtained; and,
from the law of the variation of refraction determined by theory, he
assigned the quantity due to each altitude (N. 191). The mean horizontal
refraction is about 35ʹ 6ʺ, and at the height of forty-five degrees it
is 58ʺ·36. The effect of refraction upon the same star above and below
the pole was noticed by Alhazen, a Saracen astronomer of Spain, in the
ninth century; but its existence was known to Ptolemy in the second,
though he was ignorant of its quantity.
The refraction of a terrestrial object is estimated differently from
that of a celestial body. It is measured by the angle contained between
the tangent to the curvilineal path of the ray where it meets the eye,
and the straight line joining the eye and the object (N. 192). Near the
earth’s surface the path of the ray may be supposed to be circular; and
the angle at the centre of the earth corresponding to this path is
called the horizontal angle. The quantity of terrestrial refraction is
obtained by measuring contemporaneously the elevation of the top of a
mountain above a point in the plain at its base, and the depression of
that point below the top of the mountain. The distance between these two
stations is the chord of the horizontal angle; and it is easy to prove
that double the refraction is equal to the horizontal angle, increased
by the difference between the apparent elevation and the apparent
depression. Whence it appears that, in the mean state of the atmosphere,
the refraction is about the fourteenth part of the horizontal angle.
Some very singular appearances occur from the accidental expansion or
condensation of the strata of the atmosphere contiguous to the surface
of the earth, by which distant objects, instead of being elevated, are
depressed. Sometimes, being at once both elevated and depressed, they
appear double, one of the images being direct, and the other inverted.
In consequence of the upper edges of the sun and moon being less
refracted than the lower, they often appear to be oval when near the
horizon. The looming also or elevation of coasts, mountains, and ships,
when viewed across the sea, arises from unusual refraction. A friend of
the author’s, while standing on the plains of Hindostan, saw the whole
upper chain of the Himalaya Mountains start into view, from a sudden
change in the density of the air, occasioned by a heavy shower after a
very long course of dry and hot weather. Single and double images of
objects at sea, arising from sudden changes of temperature which are not
so soon communicated to the water on account of its density as to the
air, occur more rarely and are of shorter duration than similar
appearances on land. In 1818 Captain Scoresby, whose observations on the
phenomena of the polar seas are so valuable, recognised his father’s
ship by its inverted image in the air, although the vessel itself was
below the horizon. He afterwards found that she was seventeen miles
beyond the horizon, and thirty miles distant. Two images are sometimes
seen suspended in the air over a ship, one direct and the other
inverted, with their topmasts or their hulls meeting, according as the
inverted image is above or below the direct image (N. 193). Dr.
Wollaston has proved that these appearances are owing to the refraction
of the rays through media of different densities, by the very simple
experiment of looking along a red-hot poker at a distant object. Two
images are seen, one direct and another inverted, in consequence of the
change induced by the heat in the density of the adjacent air. He
produced the same effect by a saline or saccharine solution with water
and spirit of wine floating upon it (N. 194).
Many of the phenomena that have been ascribed to extraordinary
refraction seem to be occasioned by a partial or total reflection of the
rays of light at the surfaces of strata of different densities (N. 189).
It is well known that, when light falls obliquely upon the external
surface of a transparent medium, as on a plate of glass or a stratum of
air, one portion is reflected and the other transmitted. But, when light
falls very obliquely upon the internal surface, the whole is reflected,
and not a ray is transmitted. In all cases the angles made by the
incident and reflected rays with a perpendicular to the surface being
equal, as the brightness of the reflected image depends on the quantity
of light, those arising from total reflection must be by far the most
vivid. The delusive appearance of water, so well known to African
travellers and to the Arab of the desert as the Lake of the Gazelles, is
ascribed to the reflection which takes place between strata of air of
different densities, owing to radiation of heat from the arid sandy
plains. The mirage described by Captain Mundy in his Journal of a Tour
in India probably arises from this cause. “A deep precipitous valley
below us, at the bottom of which I had seen one or two miserable
villages in the morning, bore in the evening a complete resemblance to a
beautiful lake; the vapour which played the part of water ascending
nearly half way up the sides of the vale, and on its bright surface
trees and rocks being distinctly reflected. I had not been long
contemplating this phenomenon, before a sudden storm came on and dropped
a curtain of clouds over the scene.”
An occurrence which happened on the 18th of November, 1804, was probably
produced by reflection. Dr. Buchan, while watching the rising sun from
the cliff about a mile to the east of Brighton, at the instant the solar
disc emerged from the surface of the ocean, saw the cliff on which he
was standing, a windmill, his own figure and that of a friend, depicted
immediately opposite to him on the sea. This appearance lasted about ten
minutes, till the sun had risen nearly his own diameter above the
surface of the waves. The whole then seemed to be elevated into the air,
and successively vanished. The rays of the sun fell upon the cliff at an
incidence of 73° from the perpendicular, and the sea was covered with a
dense fog many yards in height, which gradually receded before the
rising sun. When extraordinary refraction takes place laterally, the
strata of variable density are perpendicular to the horizon, and, if
combined with vertical refraction, the objects are magnified as when
seen through a telescope. From this cause, on the 26th of July, 1798,
the cliffs of France, fifty miles off, were seen as distinctly from
Hastings as if they had been close at hand; and even Dieppe was said to
have been visible in the afternoon.
The stratum of air in the horizon is so much thicker and more dense than
the stratum in the vertical, that the sun’s light is diminished 1300
times in passing through it, which enables us to look at him when
setting without being dazzled. The loss of light, and consequently of
heat, by the absorbing power of the atmosphere, increases with the
obliquity of incidence. Of ten thousand rays falling on its surface,
8123 arrive at a given point of the earth if they fall perpendicularly;
7024 arrive if the angle of direction be fifty degrees; 2831, if it be
seven degrees; and only five rays will arrive through a horizontal
stratum. Since so great a quantity of light is lost in passing through
the atmosphere, many celestial objects are altogether invisible from the
plain, which may be seen from elevated situations. Diminished splendour,
and the false estimate we make of distance from the number of
intervening objects, lead us to suppose the sun and moon to be much
larger when in the horizon than at any other altitude, though their
apparent diameters are then somewhat less. Instead of the sudden
transitions of light and darkness, the reflective power of the air
adorns nature with the rosy and golden hues of the Aurora and twilight.
Even when the sun is eighteen degrees below the horizon, a sufficient
portion of light remains to show that at the height of thirty miles it
is still dense enough to reflect light. The atmosphere scatters the
sun’s rays, and gives all the beautiful tints and cheerfulness of day.
It transmits the blue light in greatest abundance; the higher we ascend,
the sky assumes a deeper hue; but, in the expanse of space, the sun and
stars must appear like brilliant specks in profound blackness.