THE WONDERS OF THE REFRACTION OF LIGHT (_continued_).
Young Humphry now sought to discover the circumstances upon which the
formation of images, or pictorial representations of objects, depends.
“In the first place,” said he to his sister, “you must bear in mind that
all objects throw off from them, in all directions, rays of light, which
are of the _same colour_ as the objects themselves. The soldier’s coat
appears red to us, because it sends _red rays to the eye_; the fields are
green, because they emit rays of _green light_; and the summer clouds are
white, because the light they reflect to us is of _that colour_. Indeed
every flower, whatever may be its tint, is seen by us coloured as it is
merely because the rays of light proceeding from it are of the _same hue
as the flower itself appears in our eyes_.”
Kitty told Humphry that she could hardly comprehend this; saying, “that
the pattern of the paper on the wall was green and yellow, and yet, let
her look at it in whatever way she might, _she_ could see no green and
yellow rays coming from it.”
Her brother, however, assured her that, if _no rays_ from the paper
entered her pupil, she would not be able to see it at all; that is to
say, the wall would appear absolutely _black_ in her eyes; whereas, if
the rays it reflected were _colourless_, it would seem perfectly _white_
to her.
“In ancient times,” continued Humphry, “it was believed that the
eye itself had some peculiar power of emitting light, and thus of
distinguishing objects by its own agency; but now we know that no such
power resides in the organ of sight, the eye being almost _passive_
during vision, and seeing only those objects _which emit or reflect rays
of light to it_: for it is merely by such rays of light entering the
pupil, and forming a picture of the object at the back of the eye, that
we are enabled to distinguish the forms, as well as the colours, of the
things around us. So you must bear in mind, Kitty,” he added, “that the
figures and tints which you see _come to your eye, instead of your eye
sending out anything to them_; for, were it otherwise, you would be able
to see without any light at all.”
[Illustration: THE WONDERS OF THE REFRACTION OF LIGHT.—Page 371.]
Humphry then applied himself to prove, experimentally, that all objects
send off rays of light of the same colour as themselves.
Accordingly, he took an empty cigar-box, and having drilled a fine
pin-hole at one end of it, he bored another small hole in the lid—the
latter being for the purpose of looking through. Then, inside the box,
at the end opposite the pin-hole, he pasted a piece of white paper, and
placed a rose-tree at some short distance in front of the box itself, so
that the rays of light from the plant might pass through the pin-hole,
and be projected upon the white paper at the farther end of the dark box.
The arrangement being complete, he bade Kitty apply her eye to the hole
in the lid, and tell him what she saw.
“Dear, dear!” cried the astonished girl, “I declare if there isn’t a
little tiny picture of the rose-tree painted on the paper inside the box.
It isn’t very plain though, Humphry; but I can just see patches of red
for the roses, and patches of green for the leaves.”
“Yes,” said her brother, “and how could the colours come there, unless
the plant itself was giving off different tinted rays from its leaves and
flowers?”
“But, Humphry,” the girl exclaimed, as she continued gazing through the
hole, “I _do_ believe it’s upside down; for the patches of red that I
see are below the green, and in the rose-tree itself the flowers are up
above, and the leaves underneath. How very strange!”
The lad having had a peep himself at the image, proceeded to explain to
Kitty the reason of the picture appearing inverted.
With this view he drew the annexed diagram:
[Illustration]
“The rose-bush,” said he, “is sending off rays of light in all
directions. Well, let us suppose two of these rays to pass through the
pin-hole in front of the dark box, one coming from the top, and another
from the bottom of the plant. Now the consequence would be, that the two
rays, on passing through the pin-hole, would cross each other; so that
the one which was uppermost would be transferred to the lower part, and
that which was originally the bottom ray take the place of the top one.
Hence it is plain that the image, or picture, of the object must appear
upside down.”
Kitty was perfectly satisfied with the explanation, but, wishing to see
the picture of the rose more plainly upon the paper, she asked Humphry
whether he could not admit more light into the box.
The brother smiled at the simplicity of the request; but, to let the girl
see the result of enlarging the light-hole, he set to work to make a
greater aperture in front of the box. This done, he told Kitty once more
to peep through the hole in the lid.
“Why, what’s the matter with it, Humphry?” cried the sister; “I don’t see
anything at all now.”
Humphry smiled at his sister’s wonder, and proceeded to recount to her
the reason why the picture had become obliterated. He told her that when
the hole was a very small one, no two rays from different parts of the
object fell upon the same place; but that, now the hole was enlarged,
the rays that were being sent off in all directions from every part of
the rose-tree became confused with one another, so that those from the
green leaves fell upon the same part of the paper as those from the red
flowers, and the consequence was that the one colour obliterated the
other.
For the easier comprehension of this part of the subject, Humphry drew
the subjoined representation of the rays proceeding from one of the
flowers and one of the leaves; where it will be seen that, owing to the
enlargement of the aperture at the front of the box, the red ray from
the flower, and the green ray from the leaf, fall upon the same part of
the paper at the back; for as the leaf and the blossom each send off
rays in all directions, it is evident that—supposing only two of these,
for simplification’s sake, to pass through the aperture—one of the green
leaf-rays would fall upon the same spot with one of the red blossom-rays,
and one of the blossom-rays, on the other hand, become blended with one
of the leaf-rays.
[Illustration]
Kitty was not a little disappointed at the result which had followed the
enlargement of the light-hole; but Humphry, to console her, said that
it was possible, by means of a lens, to increase the light, and yet to
_prevent_ the rays from different points of the object falling upon the
same part of the paper at the end of the box.
For this purpose the lad placed a double convex lens, which he had
previously made out of two watch-glasses cemented together, into the
aperture at the front of the cigar-box, and then told his sister to look
once more through the hole in the lid.
Kitty no sooner applied her eye to the sight-hole than she cried aloud,
“O how beautiful! I declare it is much brighter than the first, and I can
now see every leaf and blossom perfectly made out. It’s the picture of a
little fairy rose—that it is. But tell me, Humphry,” said the girl, “how
could a little bit of rounded glass like that which you put into the box
produce so wonderful a change?”
“Well,” returned the brother, “you recollect I told you that every object
which we see is sending off rays of light from every part of it in all
directions. In the first case, when there was a mere pin-hole in front of
the box, the aperture was so small that only _one_ ray from each point
of the rose-tree passed through it, and, therefore, the image was so dim
you could scarcely make it out. With the convex lens, however, as many
more rays enter the box from every part of the plant, as the lens itself
is bigger than the small hole which we had in the box at first; and the
reason, again, why these rays are prevented from becoming confused one
with the other, and so obliterating the picture—as was the case when
we enlarged the light-hole in front of the box, without inserting any
lens in it—is because they are all duly refracted by the lens, so that
they severally fall in their proper places. But you will understand this
better by a drawing.” And, so saying, Humphry prepared the illustration
below given:
[Illustration]
“Here you see there are three rays,” continued the lad, “drawn from the
top, bottom, and centre of the object; three only are given for the sake
of simplicity, though every point of the plant is sending light from it
in the same manner as here indicated. Well, Kitty, the rays from the
flower at the top of the tree fall upon every part of the glass, and,
by the laws of refraction, are made to come together at a point on the
other side of it. Again, the rays from the leaves at the bottom of the
tree fall upon every part of the lens, and are so refracted that they all
meet at another point on the other side of the glass; while those from
the rosebud in the centre are likewise blended into a focus at the same
distance behind the lens. But you will perceive, that the rays which come
from the upper part of the object fall at the lower part of the image;
and those, on the other hand, which proceed from the top, fall at the
bottom. This is because the rays from these parts cross one another in
the centre of the lens, while those which are sent off from the rosebud
in the middle suffer no change of position, because _they_ proceed—as you
observe by the dotted lines in the drawing—directly through the glass,
rather than traversing it obliquely as the others do.”
“Oh, thank you, Humphry,” said Kitty; “I can make it out well now. The
image from the lens is so much brighter because it not only allows more
light to pass through the aperture, but prevents the rays from the
different parts of the object mingling one with the other. But, Humphry,”
ejaculated the girl, as a new thought struck her, “the image, as you call
it, is much smaller than the rose-tree itself: why is that?”
“To make you understand this, Kitty,” answered the boy, “I will place the
tree farther from the lens, and you shall tell me the effect.”
Humphry had no sooner removed the plant to a greater distance, than the
girl cried, “Oh, it’s much smaller than ever now!”
“And now that I bring it nearer the box, what do you see?” inquired the
youth.
“Why it seems to grow and grow, Humphry,” replied Kitty, as she continued
peeping through the hole in the lid, “so that I fancy it would get as big
as the tree itself. The picture, though, is not nearly so bright.”
“No,” returned her brother; “that is because it gets out of focus.
Now look you here, Kitty; I will do another drawing, to enable you to
comprehend how the size of the image depends upon the distance of the
object from the lens.
[Illustration]
“You must bear in mind,” proceeded Humphry, on the completion of the
diagram, “that _the rays which pass through the centre of a lens
never change their direction_. Well, I have drawn here, you see, one
ray from the tip of the arrow, and one from the bottom; and as these
rays necessarily form the extremes of the image, and so regulate its
size, you will readily comprehend that, when the object is, as here
represented, 4 yards, or feet—or, indeed, 4 measures of any kind—in front
of the lens, and the image falls, also, at 4 such measures behind it, as
at the arrow 4, the image itself must be exactly of the same size as the
object. If, however, the image fell at half the distance behind the lens
which the object was from the front of it, then the picture would be only
half the size of the body producing it—as here, at the arrow 2; whereas
if the image was at twice the distance of the object from the lens, as at
the arrow 8, then it would be exactly twice the size of it. Consequently,
the dimensions of the image produced by a lens bear always the same
proportion to the object _as the distance of the object from the lens
does to that of the image_: that is to say, if the object be 3 times as
far from the lens as the image is, then the image will be 3 times smaller
than the object itself, and _vice versâ_, if the object be 3 times nearer
the lens than the image, then the image will be 3 times larger than the
object.”
Kitty having informed her brother that she thoroughly understood the
matter now, Humphry went on to tell her that, in order to produce an
image, it was necessary that the picture should be received upon some
opaque or in-transparent substance, otherwise the rays of light would
pass _through_ the substance itself without being reflected from it or
sent back to the eye.
“The opaque body,” continued the youth, “upon which the image is thrown,
should be of a white colour, for this reflects the greatest amount of
light.”
To elucidate this part of the subject, Humphry removed the wooden end of
the cigar-box that he had previously employed, and substituted a piece of
ground glass in its stead; when Kitty, on placing her eye behind the box,
saw the picture of the rose-tree once more portrayed upon it.
“Now,” added her brother, “if I smear the ground glass over with any
grease, or even water, so as to increase its transparency, you will see
that the image immediately disappears.”
This done, Humphry explained to Kitty that the image might be received
upon smoke, or, indeed, any vapour that consisted of a number of opaque
white particles, and then he recounted to her the story of the “spectre
of the Brocken.”
“The Brocken,” said he, “is the name given to the loftiest of the Hartz
mountains, which is a picturesque chain of hills situate in the kingdom
of Hanover. The highest of these is elevated 3300 feet above the sea,
and commands the view of a plain upwards of 200 miles in extent. This
spot has been the seat of the marvellous from the earliest periods. One
of the accounts given of the ‘Spectre of the Brocken’ is that of M.
Haue. After having been on the summit of the mountain no less than thirty
times, he had, at last, the good fortune of witnessing the object of
his curiosity. The sun rose at about 4 o’clock in the morning through a
serene atmosphere. In the south-west, towards Achtermannshohe, a brisk
wind carried before it the transparent vapours which had not yet been
condensed into thick, heavy clouds. About a quarter past 4 M. Haue looked
round to see whether the atmosphere would afford him a free prospect
towards the south-west, when he observed, at a very great distance
towards Achtermannshohe, a human figure, of a monstrous size. At this
moment a violent gust of wind ensued, and M. Haue suddenly raised his
hand to his head, to prevent his hat being carried away, when, to his
great astonishment, he beheld the colossal figure in the distance do
the same. He immediately made another movement by bending his body, and
this action, too, was instantly repeated by the spectral figure. There
was now no doubt that what was termed the ‘Spectre of the Brocken’ was
an enormous image of the spectator himself seen in the distance. M. Haue
was desirous of making other experiments, but the figure disappeared. He
remained, however, in the same position, expecting its return; and in a
few minutes it again made its appearance on the Achtermannshohe, when it
once more mimicked his gestures as before. M. Haue then called another
person to him, and having both taken the same position which he himself
had previously occupied, they looked towards the Achtermannshohe, but saw
nothing. In a very short space of time, however, two colossal figures
were formed above the eminence, and, after bending their bodies, and
imitating the gestures of the spectators, they disappeared. M. Haue and
his companion, nevertheless, retained their position, and kept their eyes
still fixed upon the same spot, when the two gigantic spectres were again
beheld by them, but this time they were joined by a third, and, strange
to say, every movement they made was imitated by _all the three figures_.
The effect, however, varied in its intensity, being sometimes weak and
faint, and sometimes strong and well-defined.
[Illustration]
“These figures were merely shadows of the observers, projected on dense
vapour, or thin fleecy clouds, which have the power of reflecting much
light. They are seen most frequently at sunrise, because at that time the
vapours and clouds necessary for their production are usually generated;
and they can be perceived _only_ when the sun is throwing his beams
horizontally, because the shadow of the observer would be otherwise
projected up in the air, or down upon the ground. It is very probable
that the third figure observed by M. Haue was formed by a duplication of
one of the others, produced by unequal refraction; though M. Haue himself
does not state which of the two figures was doubled.”
It may here be added, that another story of the same kind is told by Sir
David Brewster. “A young lady had ascended to the top of the Mynydd,
a steep hill, about 500 feet above the valley of New Rednor, in South
Wales. The sun was bright and hot (it being about 2 o’clock in the day).
Having picked some flowers on the top of the hill, the girl descended a
little way, to a spot from which she could see the road and the carriage
with her companions whom she had left in it below. After waving the scarf
which she held in her hand to her friends, she suddenly perceived, upon
turning round, a figure standing a few yards from her upon a wet spot,
_from which a little thin mist was rising_. The figure stood exactly
facing her, and wavered a little; but she did not discover it to be her
own image, till she observed that, like herself, it held a scarf and
a bunch of flowers in one hand. The dress and flowers were precisely
similar to her own, and the colours so vivid that she could even trace
her own features in the image. The effect was the same as if she had been
before a looking-glass—when she moved her hand, the figure did the same.
The two friends in the carriage saw the image of the young lady, and
asked her, when she joined them, what companion she had had on the hill.
There can be no doubt,” adds Sir David Brewster, “that the figure was a
reflexion of the young lady, produced by the thin mist rising from the
damp ground; for it may be proved, by experiment, that when the particles
of vapour are sufficiently small, they reflect light as distinctly as a
surface of glass.”
* * * * *
From the production of images, Humphry passed to the consideration of the
circumstances by which lenses appear to _increase the size of objects_,
and so to make them seem as if _brought nearer to us_.
“When a shilling,” said Humphry, “is at the distance of 6 or 8 inches
from the eye, we can read the inscription round it with perfect
distinctness. At the distance of 3 yards, however, we can no longer
make out the inscription, but see only the king’s head upon it. Again,
at the distance of only 20 or 30 yards, we lose sight of the head, and
can then just distinguish that it is a round body; whilst, when placed
at about 100 yards from us, the coin is scarcely visible. The reason of
this is, that the shilling decreases in size the farther it is removed
from us, for we then see it _under a smaller angle_, as it is termed; and
it is found that the smallest angle under which an object can be seen,
is, upon an average for different sights, the 60th part of a degree, or
_one minute_ in space; so that when an object is removed from the eye
about 3000 times its own diameter, it will only just be distinguishable.
Consequently, the greatest distance at which we can behold an object like
a shilling, of an inch in diameter, is 3000 inches, or 250 feet.
[Illustration]
“Another drawing,” added Humphry, “will enable you, Kitty, readily to
comprehend how an object appears to diminish in size, according as it
becomes more and more distant from us, and so gets to be seen under a
smaller angle.”
“There,” continued the boy, “the first arrow is seen under an angle of
120°,[55] whereas the angle under which the second arrow is regarded is
only 60°. Consequently, though the objects are the same in size, the
one will appear only ½ the length of the other. The third arrow, again,
being seen under an angle 4 times smaller, will seem to be only ¼th the
size of the first; whilst the fourth arrow, for the same reason, will
look as if it were only ⅛th the height of the one next the eye; and the
farthest arrow of all but ¹⁄₁₂th as large as the nearest. Moreover, if
we suppose another arrow still to be so far removed that the angle under
which it is seen dwindles down to the 60th part of a degree, or 1′, as it
is called, this will then appear so reduced in size as to be only just
distinguishable to us.
“Well, Kitty,” the youth went on, “you now understand that an object
appears to diminish in size the _farther_ it is removed from us, merely
because it is seen under a _lesser_ angle; and, consequently, an object
must seem to us, on the other hand, to _increase_ in size when the image
of it is brought _nearer_ to the eye, and so gets to be viewed under
a _greater_ angle. This, then, is all that lenses _really_ do when
they appear to magnify objects: that is to say, they do not absolutely
_increase the dimensions_ of the bodies under view, but merely _bring
their images nearer_ to the eye, and so enable us to see them under a
_larger angle_. You remember I told you that, with a shilling, we can
just see the king’s head upon it at the distance of about 10 feet from
the eye. Now, when the coin is at that distance, if a convex lens, having
a focus 2½ feet long, be placed midway between the shilling and the eye,
the lens will, of course, be 5 feet from the eye and 5 from the shilling;
so that, in this case, it is plain, from what I before explained to you
about the size of images,[56] that the image of the shilling seen behind
the lens will be exactly of the same dimensions as the shilling itself in
front of it. The object, therefore, will not have been directly magnified
by the lens. The image, however, will be thus brought so near to the eye,
that the coin may be seen by us at the distance of 6 inches, instead of
10 feet; and, consequently, being viewed under a proportionately larger
angle, the shilling will seem to be magnified as many times as 10 feet is
greater than 6 inches; or, in other words, it will be made to appear 20
times larger in our eyes. Hence the shilling will have been, apparently,
magnified 20 times, merely by bringing the image of it 20 times nearer
the eye—thus. Whereupon the boy proceeded to delineate the following
diagram; in which the dotted lines from the object A represent the angle
that the shilling itself would be viewed under without the lens, C, by
the eye at B, while the dotted lines from the image D show the much
larger angle that such image would be seen under with the lens.”
[Illustration]
Humphry then prepared an experiment illustrative of the apparent
magnifying of objects by lenses, when their images are brought nearer
to the eye. For this purpose he got Kitty to bore a hole in the shutter
large enough to allow a lens to be inserted in it. Then fixing the glass
in the aperture, he bade his sister close the shutters, and place her eye
at about 2½ feet from the lens, for such he knew to be the length of its
focus.
“How beautiful!” cried the girl, as she gazed through the transparent
circle. “I see a tiny image of Madern Church; and so close, too, that I
could fancy it was in the room here.”
“Well,” said Humphry, “the church itself, you know, is about 1½ mile
distant, or, let us say, 7500 feet, and the focus of the lens is 2½
feet; consequently it follows, from what I have before told you, that
the image of the church you see is 3000 times smaller than the church
itself, for 7500 / 2½ = 3000. Nevertheless, if we could copy the image of
the church upon a piece of paper—or, what would be better still, fix it
upon a sheet of glass, we should find that, _on holding it just as far
from the eye as it is now from the lens_, the tiny image that you now
see would exactly cover every part of the distant object, and so appear
precisely of the same size as the church itself—in this manner.
[Illustration]
“Let us suppose the large dart, marked A here,” the lad continued, as
he drew the plan upon paper, “to be the height of the church, and the
smaller dart, _a_, on the other side of the lens, C, to be the size of
the image that we see. Well, if you were to place your eye where the lens
now is, and the image just as _far in front of the glass as it now stands
behind it_, it is plain, by the dotted eye and arrow at _a′_, that the
one would exactly cover the other.
“Hence it is evident,” added Humphry, “that the image which you see
behind the lens is really of the same size as the distant object
_appears_ to be, even though, as in the case of Madern Church, the
image is no less than 3000 times smaller than the object itself _really
is_. But when you look through a glass, Kitty, the image of the distant
object is only about 6 inches from your eyes; so that, though it is of
the same size as the object itself _appears_ to be, you are viewing it
at a shorter distance than the length of the focus of the lens; and,
therefore, owing to your regarding it under a greater angle, it seems to
be magnified. Now, as I told you, the focus of the lens we employed was
2½ feet, or 30 inches long; and, supposing your eye to have been where
the lens was, and the image transferred to the other side of the lens (as
indicated by the dotted eye and arrow marked _a′_), the image would have
seemed exactly the same size as the object itself, provided it had been
placed at a distance of 30 inches in front of you. If, however, the image
had been placed only 6 inches away from your eye, it is plain that you
would have been viewing it 5 times closer than 2½ feet, and this would
be the same as if the dotted arrow had been shifted from _a′_ to _x_;
consequently, it would then have looked to you 5 times larger than it
really was, because you were regarding it under an angle 5 times greater
than its own.
“The result which we come to is, therefore,” concluded the youth, “that
the _magnifying power of a lens is always equal to its focal length,
divided by the distance at which the eye regards the image_. The latter,
in your case, Kitty, was about 6 inches; so that the lens, having its
focus 30 inches off, the magnifying power of it is arrived at in this
manner: 30 / 6 = 5.”
Kitty asked whether it was possible to magnify an object any more than
that; when Humphry told her that, had the focus of the lens he employed
been longer, its magnifying power would have been greater; “as for
instance,” said he, “if the length of the focus had been 5 feet, instead
of 2½, it would have magnified 10 times instead of only 5, for 60 inches
/ 6 inches = 10. So, again, had the focus of the lens been 10 feet, its
magnifying power would have been doubled again, for 120 inches / 6 inches
= 20. But,” continued the boy, “the magnifying power might be increased
in another way—namely, by bringing the eye nearer to the image. As yet
we have estimated the distance at which the eye views the image produced
by the lens at 6 inches, because that is the length at which we see near
objects distinctly. Hold your finger before your eye, Kitty, and you will
see that when you bring it very close you can scarcely distinguish it.
With a lens, however, having a short focus, you would be able to see the
finger much nearer than naturally; and then, for the reason I have before
given you, it would appear to be as much magnified as the distance at
which you beheld it distinctly _with_ the lens was less than 6 inches,
which is the distance at which you beheld it distinctly _without_ the
lens. In my cupboard you will find a burning-glass, and that has a focus
of only 2 inches. Do you get it, Kitty, and look at your finger through
it.”
The girl did as she was bidden, and immediately cried, “Oh, Humphry! what
a horribly ugly, coarse, thick-looking thing it is! Why, I declare my
skin looks like an elephant’s hide through it; and I can see every line
in it, like the veins on a leaf!”
“Yes,” returned her brother, “that is because you are now looking at your
finger 3 times nearer than you could see it distinctly without the lens,
and, consequently, you behold it under a proportionately larger angle; so
that it appears to you to be 3 times magnified—for 6 inches / 2 inches =
3. Let us then apply the same principle to the image of Madern Church as
seen through the lens in the shutter, and which, you remember, appeared
to be magnified 5 times, because you saw it at 6 inches from your eye
instead of 30 inches, which was the focal length of the lens. But now, by
means of this burning-glass held near your eye, do you look at the image
once more, and tell me, Kitty, what you see.”
The shutters were accordingly closed again, and the girl proceeded to
take another peep at the distant church through the two lenses.
“Oh, Humphry!” she cried, “I see it much plainer than ever; and it is, as
you say, a great deal bigger, too.”
“Of course it is,” returned the brother, “for the length of the focus
of the burning-glass is, as I said, 2 inches; so that you now see the
image of the church at that distance from your eye, instead of 6 inches,
as before. The image, therefore, appears to be magnified 5 times by the
first lens, and 3 times by the second, or 5 × 3 = 15 times in all; and
the reason of its appearing to be that number of times larger to you,
is simply because you are looking at it at 15 times a shorter distance
than the focal length of the lens in the shutter, which is called the
‘object-glass,’ and so seeing it by means of the other lens, which is
called the ‘eye-glass,’ _under 15 times a greater angle than you behold
the object itself with your naked eye_.”
“I understand it now perfectly, Humphry, thank you,” said the sister,
pleased with the explanation. “And are the telescopes that the sailors
use made upon the same principle?”
“Precisely so, Kitty,” responded the brother. “And in order to find out
the magnifying power of any of these, we have merely to _divide the
length of the focus of the object-glass by that of the eye-glass, and
the quotient will tell us how many times the objects are enlarged by
them_; whilst in order to make a telescope for ourselves, we have merely
to procure a lens of a long focus—say 12 inches, and one of a short
focus—say 2 inches, and then to set these in a tube at the length of the
two foci, or 12 + 2 = 14 inches apart. This tube, however, should be a
sliding one, so as to admit of the distance between the two lenses being
increased according as the objects viewed are nearer at hand; for I told
you before, you remember, that the _nearer_ the object the _farther_ is
the image from the lens, and _vice versâ_, the more _distant_ the object,
the _shorter_ the focus of the glass becomes.”[57]
Now that Kitty understood the principle upon which telescopes were
constructed, she begged her brother to promise to construct one as soon
as he was well; and Humphry having consented, the two then passed on to
the consideration of the principle of the _microscope_.
“I have already told you,” said Humphry, on entering upon the subject,
“that the nearer an object comes to us, the larger it appears. But, as
you saw, when you held your finger close before your eye, it grew so
indistinct and confused, that the form of it was almost as obscure as if
it had been at a great distance from you. Now this effect is produced
by the greater divergence of the rays of light, whenever an object
is brought nearer to us; and when the divergence is very great, the
crystalline lens within the eye has not power to collect the rays into a
focus on the retina at the back of the eyeball. You will understand how
the rays come to diverge more and more the nearer an object approaches to
us, by the following illustration.
[Illustration]
“There, we will suppose the eye to be looking at some very minute object,
like a speck of the dust from a butterfly’s wing, at the distance of 6
inches, 4 inches, and 2 inches. Well, at 6 inches, the rays of light
given off by it, you perceive, diverge but slightly in comparison with
the angle at which they enter the eye at 2 inches. Consequently, the
image produced within the eye itself would, in the latter case, be so dim
that we should be almost unable to distinguish it. In order, however, to
look at a very small object, we must bring it as close as possible to the
eye; so that, to enable us to see it _distinctly_ at a short distance,
we must find out some means of _decreasing the divergence_ of the rays
of light from near objects—or, what would be better still, of making the
rays enter the pupil in _parallel_ lines.
“Now I showed you, a short while back, that a convex lens causes the rays
of light from objects placed in its focus to pass out on the other side
of the glass parallel to each other. Consequently you perceive that, by
means of a double convex glass, we can see objects distinctly when held
at ½ an inch—or even the ⅒th of an inch—from our eye, provided such be
the focal length of the lens employed; and thus we shall, for the reasons
before explained, obtain a _magnifying power which will be equal to the
distance at which the naked eye can see minute objects distinctly divided
by the focal length of the lens employed_. For example, the distance of
distinct vision for very minute objects may be taken at 5 inches, so
that if we make use of a lens having a focus of 1 inch, the magnifying
power will be equal to 5 inches divided by 1; that is to say, an object
viewed with such a glass will appear to have its length and breadth
increased five-fold; so that its _length_ being magnified 5 times, and
its _breadth_ 5 times also, its _entire surface_ will be increased as
much as 25 times, or 5 × 5. If, however, we employ a lens having a focus
of only ⅒th of an inch, the _linear_ magnifying power will be equal to
5 inches divided by ⅒ (or ⁵⁰⁄₁), that is to say, to 50-fold; while the
_superficial_ magnifying power will amount to 50 × 50, or 2500-fold; and
if, again,” went on the lad, “the lens employed have a focus of only
¹⁄₁₀₀th of an inch, then the _linear_ magnifying power will be equal to
5 inches divided by ¹⁄₁₀₀th (or ⁵⁰⁰⁄₁),—that is to say, to 500, and the
_superficial_ magnifying power to 500 × 500, or 250,000.
“A lens of a very short focus,” added Humphry, “constitutes what is
termed the _single microscope_. For this purpose the lens is usually
made spherical,—as a sphere, or round ball of glass, has its focus at
a distance from its centre equal to 1½ its own _radius_; so that if we
had a small glass ball, of 1 inch in diameter, the focus of such a lens
would fall at ¾ths of an inch from the centre of the ball itself; whereas
if the ball was ¼th of an inch in diameter, it would have the focus at
³⁄₁₆ths of an inch from its centre: so that you will readily comprehend,
Kitty, how tiny a sphere must be used in order to give great magnifying
power with a single microscope. To have a lens of ⅒th of an inch focus
that will, consequently, be able to magnify an object 50 times in length
and breadth, it would require the glass sphere to be only about ¹³⁄₁₀₀ths
of an inch in diameter. The perfect execution of such lenses requires
considerable skill in the grinding and polishing, therefore other means
of constructing them have been desired. One simple method of forming a
microscopic lens consists in drawing out (by means of a spirit-lamp) a
thin strip of window-glass into threads, and holding the end of one of
such threads in the flame until it runs into a globule. The globule is
then cut off and set in a small aperture, in such a manner that none
of the rays may pass through that part of the tiny ball where it was
originally united to the thread. Another process,” continued the youth,
“consists in taking up some fine-pounded glass on the wetted point of a
needle, and then melting it by a spirit-lamp into a globule, after which
the globule is removed, and once more taken up, by the wetted point of
the needle, on its round side, when it is again inserted in the flame,
until it becomes a perfect sphere. Moreover, drops of water, as well as
drops of oil or varnish, have been used for microscopic lenses. These are
placed on a small piece of plate glass, and have considerable magnifying
powers. Further, the lenses from the eyes of fish have been used for the
same purpose; but, in this case, it is necessary to look through the lens
in the direction of its axis—or, in other words, in the same manner as
the fish did.[58]
“A good _extempore_ microscope may be formed out of two test-tubes filled
with water, and placed one across the other, like the algebraic sign +.”
To please his sister, Humphry had his spirit-lamp lighted, and proceeded
to form some little globules of glass in the flame, in the manner before
explained; and then, having set these upon a plate of brass, he showed
the delighted girl how wonderfully objects were magnified by them; and
afterwards he went on to explain to her how it was possible to increase
the microscopic power of lenses, even without diminishing their size.
“Suppose,” said he, “that we have a lens of ½ an inch focus, and which
would, therefore, magnify the diameter of objects 10 times; and then
suppose that, instead of looking directly at the image, we place another
lens of a short focus—say 1 inch—between it and our eye, and so view the
image through the second lens. Well, this second lens would, for the
reasons before given, magnify the object 5 times more; so that it would
thus be made to appear 50 times bigger in all, the image being rendered
ten times greater by the first lens, and that image, again, 5 times
greater by the second. This constitutes what is termed the _compound
microscope_; and, by means of this instrument, objects may be magnified
to almost any extent.”
Humphry having now thoroughly made out to himself, as well as his sister,
the principle upon which the power of the _microscope_ and _telescope_
depends, concluded the subject by drawing the following diagrams,
illustrative of the opposite action of the two instruments:
[Illustration: _Telescopic arrangement._]
[Illustration: _Microscopic arrangement._]
“There,” said the boy, “in the one case, as in the preceding diagram, the
_object_ is at a considerable _distance_ from the lens, and the _image
near_ it; while in the other, as in the above diagram, the _object_ is
_near_ the lens, and the image at a considerable _distance_ from it.
Now if we suppose, Kitty, the object to be 10,000 feet in front of the
first lens, and the image 10 feet behind it, it follows that the image,
in this case, would be 1000 times smaller than the object itself; and
if we suppose, on the other hand, the object to be ¹⁄₁₀₀th of an inch
in front of the second lens, and the image to be 10 inches behind it,
then the image, in that case, would be 1000 times larger than the object
itself. Let us now imagine another lens to be placed before each of the
images—as here shown—so that the eye may view them at a shorter distance
than it could see them distinctly without any such aid; and let us say,
again, that the focal length of this second lens is, in both cases, 1
inch. Well, then, we should be regarding the image in the upper diagram
at a distance of 1 inch instead of 10 feet, which is the focal length of
the object-glass, and so bringing it 100 times nearer to our eye; the
consequence would be, that it would appear to us to be 100 times larger
than it would at the distance of 10,000 feet, so that this would be the
magnifying power of the instrument, which, as I said before, is always
_equal to the focal length of the object-glass, divided by that of the
eye-glass_. Such, then, constitutes the arrangement of the astronomical
telescope. In the compound microscope, however,” added Humphry, “the
magnifying power is estimated by _multiplying_ instead of _dividing_
the power of the object-glass by that of the eye-glass; so that, as we
supposed the first lens in the lower diagram to magnify the object 1000
times, and the second lens now enables us to view the image distinctly
at 5 times nearer the eye than we could without it, the gross magnifying
power, therefore, must amount to no less than 1000 × 5, or 5000 times.”
[Illustration: _Astronomical Telescope._]
[Illustration: _Compound Microscope._]
The youth then went on to explain to his sister that the same relation
which exists between the telescope and the microscope, also holds
good between the _camera-obscura_ and the _magic-lantern_. In the
camera-obscura, for instance, the object, as in the telescope, is at a
considerable distance in front of the object-glass, and the image at a
short distance behind it; whereas in the magic-lantern, the object, as in
the microscope, is at a short distance in front of the object-glass, and
the image at a considerable distance behind it. In the camera, therefore,
the image is as much diminished as it is _nearer_ the lens than the
object; whilst in the magic-lantern the image is as much magnified as it
is _farther_ from the lens than the object.
The annexed drawing will illustrate the action of these two instruments
clearer than words can describe them:
[Illustration]
The reader has only to suppose the image produced by the camera—a
portrait, let us say—to be fixed upon glass (by the “collodion process”
of photography, an invention since Davy’s time), and this image to be
made to serve as the object (or, in plainer language, the slide) of
the magic-lantern, in order to comprehend how the object in the one
instrument may be made the image in the other, and _vice versâ_, the
image of the first the object of the second.