THE WONDERS OF THE REFRACTION OF LIGHT.
Our young hero was still too weak to leave the house, for the wound in
his leg was of so dangerous a description that Mr. Borlase had strictly
enjoined him to take as little exercise as possible; consequently, while
Humphry’s evenings were passed in conversation with young Mr. Watt, and
occasionally the Wedgwoods, his mornings were spent in his chamber alone,
so that he was glad to resort to study as a means of enlivening his
solitude.
Still the lad wanted some incentive to stir him to enter upon a fresh
branch of science. This, however, he had now found in the wonderful
photographic impressions Mr. Wedgwood had shown him, and he was eager
to make himself acquainted with the laws of the mysterious principle by
which they had been obtained.
The contemplation of the sun-pictures naturally led Humphry to think of
the more transient pictures formed in the _camera obscura_ by the light;
and he passed from the fixing of the images to the consideration of the
conditions by which the images themselves are produced.
“How comes it,” he mentally inquired, “that a piece of glass, merely
because it is rounded on one or both sides, is able to copy the forms
and colours of external objects? And why do several of such glasses, in
combination, bring the images of even the most distant things so close to
us, that we are enabled to make out their minutest parts?”
Humphry knew that the effect could arise only from some alteration in the
direction of the rays of light as they passed through the glass itself;
and, accordingly, he determined to set to work and discover the precise
change that a luminous ray undergoes on traversing different substances.
In the first place, however, it was necessary to determine what was the
_natural_ direction of a ray of light emitted by a luminous body.
For this purpose Humphry—who was still unable to undergo the exertion
of arranging his own experiments—had to avail himself of the assistance
of his sister Kitty; and so pleased was the girl with the office, that
she readily gave up to her brother every moment she could spare from her
household duties.
Kitty Davy was some two years younger than Humphry himself, so that they
had been infant playmates together, sharing the same toys and taking
parts in the same childish gambols. It was to Kitty, too, that the boy
had first recounted the fairy stories he loved to invent; and when, in
his after-youth, Humphry compounded his celebrated “thunder-powder,”
Kitty invariably aided him in the manufacture of the composition: so that
each year had served to increase the love which, from the remembrance of
the pleasures they had enjoyed together, had been begotten almost with
the dawn of memory itself.
Kitty was now budding into womanhood. She had grown so tall within the
last year, that her figure was spare, and not particularly comely; while
the curls, which once fell, with childish beauty, in tortuous profusion
about her neck, had now been displaced, and her hair twisted into the
more womanly, but less gainly, protuberance at the back. This style of
head-dress had long been a point of ambition with the young lady, and now
that she had risen to the dignity of wearing her hair like her mother,
Miss Kitty had grown to fancy that she was no longer a child.
Nor was she. The increasing strength of her affection for her brother
showed that her woman’s nature was developing, and she seemed to cling to
Humphry and her mother with a new tenderness, as if she needed some one
to heap her strengthened love upon. The doll upon which she had, until
the last year or so, bestowed her caresses, had been given to one of her
younger sisters; and now she appeared to take almost a mother’s pride in
tending little Johnny, her brother, instead.
Humphry during his illness had been constantly “nursed” by her, and
now that she was allowed to officiate in the kitchen, the girl loved
to surprise him each day with some new posset or jelly which she had
prepared for his gratification. She had read to him, too, so long by his
bed-side from the scientific books which her brother loved to listen
to, that, aided by his explanations of the more difficult parts of the
subject, she herself had acquired a slight knowledge of the phenomena of
the universe: so that, while assisting him in his experiments, she felt
almost the same taste for the work as Humphry did, and was not a little
delighted when the hour came for her to take her accustomed post in her
brother’s sick chamber.
* * * * *
Humphry, as we said, was intent upon discovering the natural direction
of a ray of light proceeding from a luminous body. With this view he got
Kitty to close the shutters so as to completely darken the room, and then
to pierce a fine hole through them. This being done, Humphry pointed
out to the girl that the beam was in a perfectly straight line—for the
course of it was rendered plain by the little particles of dust that
floated in the atmosphere, flashing, as they danced in the ray, like so
many tiny fire-flies. Then as Kitty wheeled her brother’s chair so that
the light fell directly upon his eye, the boy could see the sun itself
shining through the hole; thus proving that the beam proceeded in a
direct straight line from the orb of light to him.
The next step was to procure a flexible tube, and with this held
_straight_ before the eye, Humphry could still distinguish the sun
through the hole in the shutter, though when the tube was _curved_ the
effect was totally different, for then no light at all could be perceived.
Kitty was not a little delighted with the demonstration that a ray of
light proceeds in a straight line; and Humphry, to make her understand,
as well as to prove to himself experimentally, that all luminous
bodies _projected an infinity of such straight rays in every possible
direction_, bade the willing girl fetch him the rushlight and shade from
below.
While the shutters were still closed the candle was lighted, and then
Humphry pointed out to his sister how the little luminous circles that
were spattered over the wall all round the room, as the light passed
through the holes in the shade, showed that the rays proceeded from it in
every direction; and that they travelled in a straight course was easily
proved, by covering with the finger any one of the holes in the shade,
when the luminous circle on the wall, which was in a direct line with the
hole, and the flame became immediately obscured.
[Illustration]
It was plain, then, that a ray of light travelled naturally in a straight
line. Still, as a further proof of this phenomenon, Humphry threw the
shadow of an opaque body, of a certain size, upon a white screen, and
there measured its dimensions. Having cut a piece of millboard, exactly a
foot square, he placed it 1 foot distant from the flame of a candle, and
then arranging the screen at double the distance, or two feet from the
light, he found upon measuring the shadow of the millboard that it was
exactly (2 × 2) 4 times larger than the millboard. When the screen was
three feet distant from the candle, or 3 times as far from the light as
the millboard, the shadow was ascertained to be (3 × 3) 9 times larger
than the surface from which it was projected; while at the distance of
4 feet, the dark space upon the screen was discovered to be (4 × 4) 16
times greater than the millboard itself.
[Illustration]
[Illustration]
This effect could arise solely from the rays of the candle proceeding
in a straight direction, as will be rendered evident by the preceding
diagrams; where it will be seen that the opaque body, interposed between
the light and the screen, prevents the rays which fall upon it reaching
the screen itself, so that a dark space appears upon the latter, as
many times larger than the opaque body, as the distance of the screen
from the candle is greater than the body projecting the shadow; for
it is manifest, that if a series of right lines be drawn from the
luminous point to the edges of the opaque body, and thence to the screen
itself, they will exactly circumscribe a space whose dimensions will be
proportional to the distance of the one to the other.
“Well,” said Humphry to his sister, “we now see that luminous bodies
_emit_ rays of light _in all directions_, and that each ray from them
proceeds in a _straight_ line, while those substances which are called
opaque prevent, when placed before the light, the rays from reaching
other substances behind them—the rays, in such cases, being _stopped_
or intercepted. Some bodies, however,” added the boy, “are capable of
_transmitting_ the rays of light: that is to say, they allow the beams to
pass through them, and these are, therefore, termed transparent; since,
unlike opaque bodies, they project no shadows when placed between the
light and other bodies. Let us now see what occurs when a ray of light
passes through a transparent body.”
Accordingly, Humphry procured a small open vessel, in one of the sides of
which there was a hole near the top, large enough to admit the light from
a candle. The lad then proceeded to ascertain the exact place where the
ray of light from the flame fell at the bottom of the vessel; and found
that, when the vessel was empty and the candle placed at a short distance
from the hole, there was a small circle of light formed at the bottom,
which was, of course, in a direct line with the hole and the flame, as
here shown.
[Illustration]
Having then set a mark at A, where the circle of light appeared, he
directed Kitty to pour water into the vessel until it was half full; and
when she had done so, he noticed that the ray of light from the candle
no longer fell upon the same spot as it did when the vessel was empty,
but at a little distance nearer the candle, so that it was plain that the
ray, instead of proceeding in a straight line as before, had, in passing
through the water, _been bent down out of its visual course_, in the
manner indicated at B.
[Illustration]
“You see, then,” remarked Humphry, “that a ray of light, when it falls
in a _slanting_ direction upon a transparent body, _no longer travels on
in a straight line, but is refracted_,” as it is called, “_or bent out
of its previous course, at a certain angle_. Consequently, if the spot B
was a fish lying at the bottom of a river, it would be seen by a person
on the shore in the direction of the point A; and thus it would appear
out of its true place, and, in order to strike it with a spear, we should
have to direct the weapon at a spot _nearer_ to us than where the fish
_seemed_ to be lying.”
Then her brother told her that it was for the same reason that a straight
stick appeared to be crooked when half immersed in a pool of water, and
a crooked stick a straight one under the same circumstances; “for,” said
he, “if instead of the straight ray of light we imagine a straight stick
to be passed through the hole, so that the point of it may be at the spot
A, it is plain that in the water the end of the stick will appear at
B, since the part of it which is immersed will seem to be bent in that
direction; whereas if the stick itself be bent, so that the end of it is
at B, it will, for the same reason, appear when in the water at A, and,
consequently, seem to be perfectly straight.”
The next step was to try and measure the _degree_ of refraction, or, in
other words, to find out how much a ray of light was bent out of its
usual course on passing through different transparent substances.
Accordingly, Humphry procured his old school-slate, and having managed,
with Kitty’s assistance, to mount this on a heavy pedestal, he described
upon the slate a circle with two diameters, each perpendicular to the
other; then having bored a hole in the centre, he fitted into it a large
cork; this had a straight tube afterwards let into it, so that the tube,
by means of the cork in the middle, could be moved freely round the
circle, turning, as it did, upon the centre of it. The whole apparatus
was then inserted in a vessel of water, so that the fluid reached exactly
to the level of the horizontal diameter—thus, without touching the end of
the tube.
[Illustration]
The youth then found, that when the tube A was directly perpendicular to
the surface of the water, a ray of light, on passing down it, suffered
no change at all in its direction; and that on placing a sixpence in the
water, exactly in a line with the perpendicular diameter, B, it could
be seen distinctly through the tube, so that the rays from the coin, on
quitting the water, proceeded in the same straight course as they had
pursued while passing through the fluid.
Hence it was evident that a ray of light, on _entering or quitting a
refracting surface in a PERPENDICULAR LINE, is not refracted or bent out
of its course_.
[Illustration]
It was different, however, when the tube was _slanted_, instead of being
placed _straight_ above the surface of the water, for when a ray of light
passed down it in that direction, the ray was found to be refracted, or
bent out of a straight course, as shown in the above diagram.
Now the precise direction of the refracted ray having been marked upon
the slate, the apparatus was removed from the water, and the distance
of the tube A from B, the vertical diameter, measured, as well as the
distance of the refracted ray, a, from the same perpendicular line,
_b_, and it was then found that the refracted ray, _a_, was as near as
possible 3 inches from the diameter, _b_, while the ray A, which passed
down the tube, was as much as 4 inches distant from B, the same line.
The tube A was then set at about 1⅓ inches from the diameter B, and the
apparatus replaced in the water, when it was discovered that a ray of
light, _a_, on passing down it, fell exactly at 1 inch from _b_, the
perpendicular line.
Several other positions of the tube were afterwards tried, and invariably
with the same result: let the tube be slanted as it might, the distance A
... B of the ray which passed down it, when compared with the distance
_a ... b_ of the refracted ray from the perpendicular line, was _always
ascertained to be in the same proportion_—viz. very nearly as 1⅓ to 1;
or, more correctly speaking, when A ... B, the sine of the angle at which
the ray entered the water, was 1⅓, then _a ... b_, the sine of the angle
formed by the refracted ray, was exactly 1.
On referring to his books, Humphry found that the number 1³³⁶⁄₁₀₀₀
constituted what was termed the _index of refraction_ for water.
On performing the same experiment with oil of turpentine the lad
discovered, that when the ray which passed down the tube was almost as
much as 1½ inch distant from the perpendicular, the refracted ray was 1
inch distant from the same line; whereas with sulphuret of carbon (though
with this the experiment was performed on a smaller scale), when the ray
passing down the tube was 1⅔ inch removed from the perpendicular—the
refracted ray was still only 1 inch away from the same line.
Humphry then consulted a table of the refractive power of different
bodies, and learned that hydrogen gas is the least refractive of all
known substances (that is to say, a ray of light passing through this gas
is bent down by it out of its previous course, less than by any other
known body), and that the diamond has very nearly the greatest refractive
power of all, while the refraction of the air in its ordinary state is
only 294 millionths greater than that of a _vacuum_.
This, however, is the refractive power of the atmosphere at its average
density near the earth’s surface. But we learn from the barometer that
the density of the air diminishes as we mount above the earth, and it
has been found by experiment that the refractive power of the atmosphere
decreases in proportion as it becomes more and more rarified; so that the
atmospheric refraction is greatest at the earth’s surface, and gradually
diminishes upwards, till the air becomes so rare as to be able to produce
scarcely any effect at all upon the rays of light.
[Illustration]
“In order to understand this,” said Humphry to his sister, “we must
consider the earth to be encased in a series of shells, as it were,
of atmosphere, each of a less density than the one below it, and,
consequently, of a less refractive power—thus.
“Let us suppose,” the lad continued, “the round ball in the centre here
to represent the earth, and the ring of atmosphere immediately next to it
to have a refractive power nearly 300 millionths greater than a vacuum;
and the refractive power of the ring, or shell of atmosphere immediately
above this, to be equal to only 200 millionths compared with the same
standard, while the power of the third ring decreases to 100 millionths,
and that of the outer one to 50 millionths, whereas beyond this no
refraction whatever exists, so that the rays moving through free space
will continue in the same line as that in which they are emitted from
the sun. What, then, will be the effect of such a series of atmospheric
shells upon a ray of light passing through them?”
To illustrate this Humphry drew the lines here shown through the
following diagram.
[Illustration]
“The orb S, outside the earth,” continued Humphry, “represents the sun
below the horizon, emitting, let us suppose, his rays in all directions.
These, passing through free space, proceed onwards in a perfectly
straight line; and one of them is here made to fall upon the outer ring
of the earth’s atmosphere, where it is slightly refracted, or bent down
out of its former course, so that, instead of continuing in the direction
of the dotted line _a_, it proceeds through the upper portion of our
atmosphere in the direction of the unbroken line, until it reaches a
part of the atmosphere of greater density—as in the second ring; when,
instead of going on in the direction of the second dotted line _b_, it
is again refracted, or bent down, in a greater degree than before. Then
travelling onwards, it reaches the third ring, where the atmosphere,
being of a still greater density, and, consequently, having a greater
refractive power, it is once more bent out of its course _c_, and that to
a still greater extent than before. In this manner it ultimately arrives
at a stratum of atmosphere which immediately envelopes the surface of the
earth, and which, having the greatest density of all, has the greatest
refractive power; so that the ray, instead of continuing in the direction
_d_, is here bent down more than ever, and finally reaches the eye in
the direction _e_, which is in a direct line with the orb _s_. The
consequence is, that as _every object is seen in the direction that the
ray has at the instant of arriving at the eye_, the sun itself appears to
be above the horizon when it is positively _below_ it, as at S; so that,
by the refraction of the atmosphere, the sun is seen by us before he
rises in the morning, and for a short time after he sets in the evening.”
Kitty was so astonished at the above conclusion, that, though she
understood the explanation, she told her brother that she could hardly
help doubting the fact; saying, “it was almost the same as asserting that
we could see a thing that was out of sight.”
Humphry undertook to prove to his sister, by experiment, that such a
result was quite possible by refraction.
Accordingly, he bade Kitty place the wash-hand basin upon the table,
and then having deposited a shilling at the bottom of it, he told the
girl herself to recede from the table until the edge of the basin
obscured the shilling from her sight; and when Kitty assured him that
she could no longer see the coin, he poured some water into the vessel,
and immediately the girl exclaimed—“Dear, dear, how odd! I can see the
shilling quite plainly now.”
“You perceive, then, Miss Kitty,” cried the boy, triumphantly, “it is
quite possible by refraction to see things that are out of sight, for the
ray from the shilling, A, on passing out of the water into the air, is
bent out of its course, and you behold it in the direction of the line in
which it enters your eye—thus, at _a_.
[Illustration]
“But far more wonderful things than this have been brought to pass by the
same means, Kitty,” said her brother, delighted to impart the knowledge
he had obtained from his books on this subject, “and these are what
are called _mirages_, or optical illusions, produced by extraordinary
refractions in the atmosphere. For instance, the cliffs on the French
coast are 50 miles distant from Hastings, on the coast of Sussex, and
they are actually hidden from the eye by the convexity of the earth; that
is to say, a straight line drawn from Hastings to Calais or Boulogne
would pass through the sea. A year or two ago, however, Mr. Latham, a
Fellow of the Royal Society, who was residing at Hastings, was surprised
to see a crowd of people running to the sea-side. Upon inquiry into the
cause of this, he was informed that the coast of France could be seen
by the naked eye. He immediately went down to the shore to witness so
singular a sight, and there discovered distinctly the French cliffs
extending for some leagues along the horizon, and so vividly that they
appeared to be only a few miles off. The sailors and fishermen, with whom
Mr. Latham walked along the water’s edge, could hardly, at first, be
persuaded of the reality of the appearance; but as the cliffs gradually
became more elevated, they were so convinced that they pointed out to
Mr. Latham the different places they had been accustomed to visit: such
as the bay and the windmill at Boulogne, St. Vallery, and other places
on the coast of Picardy, even as far as Dieppe, all the French shores
appearing to the English sailors as if they were sailing at a short
distance from them towards the harbours. With the aid of a telescope
the French fishing-boats were plainly seen at anchor, and the different
colours of the land upon the heights, together with the buildings, were
perfectly discernible. The day when this occurred is said to have been
extremely hot, without a breath of wind stirring, and the phenomenon
continued visible in the highest splendour until past 8 o’clock in the
evening, having been seen for three hours continuously.”
Some few years after the date of the above, a no-less-marvellous optical
illusion was seen by Professor Vince of Cambridge, in company with
another gentleman, at Ramsgate. Between this town and Dover there is a
hill, on the farther side of which stands Dover Castle, the summits of
whose four turrets can, in ordinary states of the atmosphere, be just
seen projecting above the brow, while the body of the castle itself is
usually hidden from view by the rising earth between it and Ramsgate. On
the evening of the 6th of August, 1806, however, when the air was very
still, and a little hazy, not only were the tops of the four towers of
the castle visible above the brow of the hill in the distance, but the
_whole_ of the castle itself appeared transferred to the side of the
hill next Ramsgate, as if it had been really built there, instead of
on the other side of the eminence. This phenomenon was so singular and
unexpected that Dr. Vince, at first sight, thought it an illusion. On
continuing his observations, however, he became satisfied that what he
saw was a real image of the castle. To assure himself that it was no
deception, he gave the telescope to a gentleman who was with him at the
time, and who also saw the same clear image of the entire castle, situate
on the near side of the hill, as the Doctor himself had witnessed. The
view of the castle was very strong, and well defined; and though the
rays from the farther side of the hill must, undoubtedly, have reached
the eye at the same time, still the strength of the image of the castle
itself so far obscured the background that it made no sensible impression
on the spectators. Dr. Vince continued to observe the image for about
20 minutes, during which time the appearance remained precisely the
same, but rain then came on, and he was prevented making any further
observations.
* * * * *
Humphry now began to study how, by means of extraordinary refraction,
inverted images of objects might be seen in the atmosphere.
[Illustration]
With this view he drew the subjoined diagram. “There, Kitty,” said the
lad, as he laid down his pencil and compasses, “the drawing represents
a ship below the horizon, and concealed from the eye of an observer by
the convexity of the earth. Well, if we suppose the refractive power of
the air at a little above the earth’s surface to be less than it is at
the surface itself, then the rays which proceed upward from the ship, and
which never could, in the ordinary state of the atmosphere, reach the eye
in the position here shown, will be refracted into curved lines, so that
they will cross one another; while the ray which came from the masthead,
instead of being uppermost, will change places with that coming from the
hull, and becoming the undermost of the two, will enter the eye in that
position: consequently, as every object is seen, as I said before, _in
the direction of the rays at the moment of their arriving at the eye,
without reference to their previous course_, an inverted image of the
ship will be perceived in the air, in the direction of the dotted lines,
and thus appear elevated above the horizon.”
Kitty said she could hardly follow the explanation, and wished to know
whether her brother could not devise some experiment in proof of it.
After a few moments’ consideration, Humphry requested his sister to
fetch him a square phial, and to make him a little clear syrup with some
lump-sugar and water. When this was prepared, the boy poured a small
quantity of the syrup into the phial, and upon this again he poured
very carefully an equal quantity of pure water, so that it might float
upon the syrup. Now the syrup, being a fluid of greater density than the
water, had a proportionately greater refractive power, and as the two
combined with each other they formed strata, having different refractive
powers, the same as those which had been supposed to exist in the
atmosphere at certain times, at a little distance above the surface of
the earth. Then having printed the word SYRUP upon a card, Humphry held
this behind the bottle, and the letters were seen _erect_ through the
stratum of syrup at the bottom, but _upside down_ at the part where the
syrup was mixing with the water, and _erect_ again through the layer of
water itself at the top.
After this the lad poured the same quantity of spirits of wine carefully
over the water itself, so that the spirit being lighter than this might
float above this again; and then having printed the word SPIRIT on the
upper part of the same card, the letters of this were seen _erect_
through the layer of water, but _topsy-turvy_ at the part where the
spirit and water were mingling, and in their _proper form_ through the
uppermost stratum of spirit itself.
Humphry afterwards produced the same effect by holding a heated iron
above a tumbler of water, so that the upper surface of it became warmed
while the lower remained cold, and the portion in the middle became
tepid. The heat, therefore, expanded, and so rendered rarer the upper
portions of the liquid; and as it forced its way downwards, produced
strata of different densities, and, consequently, of different refractive
powers. The result was, that on looking through the glass vessel three
images were seen as before; the upper and the lower ones—which arose from
the rays passing through the colder and the warmer strata—being erect,
and the middle one, or that which proceeded from the rays passing through
the portion in the middle, being inverted—as previously observed. The
same effect may be produced by looking along the side of a red-hot poker,
at an object 10 or 12 feet off, when an inverted image will be seen at
the distance of about ⅜ths of an inch from the line of the poker, and an
erect image within and without this.
The youth, having now demonstrated to his sister how it was possible to
produce three distinct images, and one of these inverted, from the same
object, when seen through strata of different densities, proceeded to
recount to Kitty stories of similar phenomena observed at sea. He told
her how Dr. Vince had seen at Ramsgate a ship whose top-masts only were
visible above the horizon, while over this, in the air, two images of the
complete ship were observed, the uppermost being _erect_, and the under
one _inverted_, with the pennant from the masthead of the inverted image
nearly touching that from the real ship, seen peeping above the horizon.
This was distinctly visible through the telescope; the sea appearing
between the two ships in the air, as here represented:
[Illustration]
“As the ship rose to the horizon,” said Humphry, “the upper image
gradually disappeared, and while this was going on the lower and inverted
image as gradually descended; but the mastheads of the real and the
spectral inverted ship never exactly touched. On the real ship becoming
entirely visible, the aërial images were found to have been perfect
representations of it, even though the whole of the vessel at the time
must have been concealed below the horizon.”
There is, however, it may here be added, a still more marvellous story
in connexion with this part of the subject, though it occurred at a more
recent date than that recounted by Humphry. During a voyage to the coast
of Greenland in the year 1822, Captain Scoresby, having seen an image
of an inverted ship in the air, directed his telescope to it, and was
able to discover that it was _his father’s vessel, which was at the time
below the horizon, and cruising in a neighbouring inlet_. “The image,”
says the captain, “was so well defined that I could distinguish by a
telescope every sail, the general ‘rig of the ship,’ and its particular
character, insomuch that I confidently pronounced it to be my father’s
ship the ‘FAME,’ which it afterwards proved to be; though, on comparing
notes with my father, I found that our relative position at the time gave
our distance from one another 30 miles, which is about 17 miles beyond
the horizon, and some leagues beyond the limit of direct vision. I was so
much struck by the peculiarity of the circumstance,” adds the captain,
“that I mentioned it to the officer of the watch, stating my full
conviction that the ‘Fame’ was then cruising in the neighbouring inlet.”
The same officer, while navigating the Greenland sea in 1820, saw the
images of several ships in the air. Some of these were double, and
inverted, while along with them there appeared aërial images of the ice,
in two strata; the highest of which had an altitude of a quarter of a
degree.
The representation of ships in the air by unequal refraction has, no
doubt, given rise in early time to the superstitions of phantom-ships,
which are always said to sail in the eye of the wind, and to plough
their way through the sea when there is not a breath of wind to ruffle
its surface. The story of the “Flying Dutchman” had, probably, a similar
origin; and the legend of the wizard beacon-keeper of the Isle of France,
who saw in the air the vessels bound to the island long before they were
visible in the horizon, doubtlessly arose from the man’s observation of
some such phenomena.