THE WONDERS OF THE REFLEXION OF LIGHT.
Hitherto Humphry had considered only the laws which regulate the
transmission of light through transparent bodies. This constitutes the
branch of the subject called _dioptrics_ (from δια, through, and οπτομαι,
to see). The other branch, termed _catoptrics_ (from κατα, from, or
against, and οπτομαι, to see), deals with the laws of light when it is
reflected or thrown back from the surface of any body _against_ which it
falls. Accordingly the lad passed, in due order, from the _transmission_
to the _reflexion_ of the luminous rays.
To explain this part of the subject the youth first procured a piece of
an old looking-glass, and having got Kitty to close the shutters once
more, he placed the looking-glass upon the ground, so that the ray might
fall just in the middle of it; when, as the room was thoroughly darkened,
it was easy to observe the inclination, or angle, at which the light fell
on the reflector, as well as to perceive the course it took afterwards.
“Why, I declare,” cried Kitty, as she looked at the bright streak, “it
goes down and then up again; and I can see the beam slanting away from
the glass on each side, for all the world like a big letter V!”
“Yes,” returned Humphry, “you see the course of the beam is stopped by
the looking-glass, and instead of going through it, the thread of light
that streams _down_ from the hole in the shutter no sooner falls on the
mirror than it is driven up from it, precisely in the same manner as if
the luminous particles were a series of hard balls projected against the
glass, and so made to bound off from its surface.”
The youth then called for his arc, and proceeded to measure the angle at
which the light fell upon the glass, and also the angle at which it was
reflected from it—thus:
[Illustration]
“Do you see, Kitty,” he cried, as the eager girl stooped down beside her
brother, “the ray that slants down from the shutter falls upon the glass
at an angle of 45°, and this is what is called the angle of _incidence_;
while the ray which slants upwards from it is reflected from the glass
at 45° also, and this is what is called the angle of _reflexion_: so
that, you perceive, _the one is exactly equal to the other, and this
constitutes what is termed the law of reflexion_. For, no matter what the
form of the mirror itself, or in what direction a ray of light falls upon
it, it is always reflected or driven back from the surface at precisely
the same angle as it strikes upon it. As you say, the two rays form a
kind of letter V, and one prong of the letter always slants just as much
as the other.”
“But suppose the surface of the glass, Humphry, was to be hollowed out
like a bowl, would it do so then?” inquired the girl.
“Certainly,” was the reply; “and if the rays falling upon it then were
parallel one to the other, you would find, upon drawing the figure on
paper, that they would all meet together at one point in front of the
glass, which would, consequently, be the focus—_the distance of such
focus being equal to half the radius, or semi-diameter, of the curvature
of the mirror itself_. Give me the compasses and open the shutters,
Kitty, and you shall soon see what I mean.” In a few minutes the
following diagram was described:
[Illustration: _Concave Mirror._
_Convex Mirror._]
“There!” cried Humphry, as he put the last touch to the drawing, “the
two curved lines represent the surfaces of a _convex_ and a _concave_
mirror, the curvatures of which form portions of a circle, having its
centre at the point where the unbroken lines meet. Now, these unbroken
lines, being drawn in each case from the centre to the surface of the
mirror itself, are exactly perpendicular to the points where the rays of
light fall; and if you measure with the arc the angle which the dotted
parallel lines form on one side of the unbroken ones, you will find that
they are, in every case, here equal to that which the dotted slanting
lines form on the other side of the same perpendicular. Consequently,
you perceive that, by a concave mirror, the rays are made to _converge_
to a focus in front of the mirror itself; whereas by a convex mirror
the rays are made to _diverge_, as if they came from a focus behind the
mirror itself. Now this, you remember, is precisely the same as what
takes place with concave and convex lenses; for a concave lens has its
focus in front of it, like a concave mirror, but, owing to the rays
passing _through_ the lens in the one case, and being driven back _from_
the mirror in the other, they are made by the lens to _diverge_ and by
the mirror to _converge_. So that, while the concave lens _diminishes_
the apparent size of objects, the concave mirror _magnifies_ them. The
same thing holds good,” continued the boy, “with a convex lens and a
convex mirror; they both have their focus behind them, but the rays, in
passing _through_ the lens, _converge_ to a point, whereas, being driven
_back_ from the mirror, they _diverge_; and so, while the convex lens
_magnifies_, the mirror _diminishes_ the apparent size of objects.”
Next, Humphry directed his sister to place herself alongside the
looking-glass over the mantel-piece, while he did the same facing her,
and in such a manner that neither could see their own figure reflected in
the mirror. It would then be found, he said, that they would each behold
the other, and at exactly the same distance behind the glass as they were
in front of it. In this manner:
[Illustration]
“Now the reason why I see you,” said the lad, “and you see me in another
place than we really occupy, is, because the rays reflected by the glass
enter our eyes in that direction; and, as I told you before, _an object
is always seen by us in the direction which the ray has at the moment
of reaching the eye, without regard to what may have been its course
previously_. Your image, of course, Kitty, is _on_ the surface of the
glass itself, and not _behind_ it, as it appears to you to be; and what,
I dare say, will sound stranger to you, is, that the image itself upon
the glass is exactly half the size that it seems to be behind it: for
since, when you look at yourself in the glass, your image appears to be
just as far at the back as you are standing in front of the mirror, it
is evident that the mirror itself must be half-way between you and your
apparent image; so that it will cut in half the cone of rays which enter
your eye from the surface of the looking-glass.
[Illustration]
“There is a picture,” continued Humphry, as he put the drawing before his
sister, “of a person looking at himself in the glass; and you will see,
by the rays from his chin and forehead, which are reflected in a point to
the eye, that a vertical line A...B, at the surface of the glass, must be
exactly equal to half the length of the image, since the image and the
eye of the spectator are always at equal distances from the glass itself.
But the image, which _appears_ to be behind the glass, is seen under the
same angle as the image, which is _really_ on the surface of it; and so,
for the reasons I before gave you, when speaking of the apparent size of
objects in general, the one behind the glass appearing to be at twice the
distance of the other, naturally seems to be twice as large as the image
on the surface really is.
“I have already shown you, Kitty,” went on the youth, after a pause,
“that if two persons stand in front of a mirror, and each at opposite
sides to it, they will see one another, but not themselves; and this
constitutes the principle of what is termed the ‘magician’s mirror.’
[Illustration]
“Here is a plan,” said Humphry, “of the ordinary arrangement. The black
lines we will suppose to represent the walls of two adjoining apartments.
At the end of each of the rooms there is an aperture, made large enough
to place behind it a looking-glass that is capable of reflecting the
whole figure. In each of these apertures there is inserted a sheet of
plate-glass, which is surrounded with a gilt frame, so as to have the
appearance of an ordinary mirror; and behind this a real looking-glass is
placed, slanting at an angle of 45°, and so large, that a person looking
into the sheet of plate-glass cannot see the edges of the slanting mirror
behind it. With such an arrangement, it is plain that a person looking
into either of the mirrors will not see himself, but any one who may
chance to be looking at the same time into the mirror in the adjoining
room. Consequently, on looking into the mirror and believing that he
should see his own figure reflected in it as in an ordinary looking
glass, his astonishment will be great in beholding himself transformed
into another person, or, indeed, into some living animal that may be
placed in front of the neighbouring glass.”
Kitty observed to her brother, that she remembered having seen the same
kind of an apparatus in a booth in a fair; and by it persons were said to
be shown their future lovers.
Humphry told her that it was by the same means that people were made to
see, apparently, through paving-stones.
“For if,” said the boy, “by the arrangement I have explained to you,
it is possible to see a figure in another apartment—a brick wall
intervening—it is obvious that, by the same device, an object placed on
one side of a paving-stone could be readily seen on the other.
“But the concave mirror,” continued Humphry, “is capable of producing
far more wonderful effects, for the image from this appears suspended
in the air; so that if the mirror and the object are hidden from view,
the effect is almost, supernatural. This illustration represents the
arrangement usually employed in such cases—
[Illustration]
“Here you perceive, Kitty,” added the lad, “the two sides of a room,
at the end of which there is a square opening, with a picture-frame
surrounding it. Outside the room, in an adjoining apartment, is placed
a large concave mirror; and so arranged, that when an object is set a
little above the floor in front of it, a distinct image of it may be
formed in the centre of the aperture at the end of the room, where the
spectators are assembled. Now, if the opening be filled with smoke,
that is made to rise in clouds from a chafing-dish concealed outside,
the image of any object placed in the one focus of the mirror in the
adjoining apartment will appear in the other focus at the centre of
the frame, and seem to be depicted on the clouds of smoke there as a
background. It is a favourite experiment to place a skull, strongly
illuminated, in the outer apartment, and to reflect an image of it amid
the smoke, so as to be visible to the spectators in the inner room. The
trick of the mysterious dagger, too, is very popular. The ordinary way
of performing this is by placing a basket of fruit in the one focus of
the mirror, so that a distinct aërial image may be formed of it in the
frame. One of the spectators is then desired to take some fruit from
the basket; and as he approaches for that purpose, a person, properly
concealed, withdraws the real basket of fruit with one hand, and with
the other substitutes a dagger, the image of which seems to strike at
the body of the spectator, and the thrust of the bright polished steel
at his breast never fails to produce a powerful impression. Now, it can
scarcely be doubted that a concave mirror was the principal instrument
by which the heathen gods were made to appear in the ancient temples.
Jamblichus informs us, that the ancient magicians made the gods visible
to the people among clouds of incense. And in the middle ages the
Pontiff, Theodore Santabaren, who was celebrated for his power in working
miracles, exhibited to the Emperor Basil of Macedonia the image of his
lost son, magnificently dressed, and mounted on a superb charger. The
apparition of the youth seemed to rush towards his father; and, throwing
himself into his arms, vanished. This effect was doubtlessly produced by
reflecting the image of a picture of the emperor’s son on horseback; and
the picture being brought nearer to the mirror, the image, of course,
appeared to advance until it reached the emperor’s arms, where it
naturally eluded his grasp. The celebrated Benvenuto Cellini has left us
an account of a more modern necromancy, in which he himself took a part,
in the middle of the sixteenth century.
“‘It happens,’ says Cellini, proceeded Humphry, as he read the account to
his sister, ‘through a variety of odd accidents, that I made acquaintance
with a Sicilian priest, who was a man of genius, and well versed in
the Latin and Greek authors. Chancing one day to have some conversation
with him, when the subject turned upon the art of necromancy, I, who
had a great desire to know something of the matter, told him that I had
all my life felt a curiosity to be acquainted with the mysteries of the
art. The priest made answer, that the man must be of a resolute and
steady temper who enters upon that study. I replied, that I had fortitude
and resolution enough, if I could but find an opportunity. The priest
subjoined, ‘If you think you have the heart to venture, I will give you
all the satisfaction you can desire.’ Thus we agreed to enter upon a
plan of necromancy. The priest, one evening, prepared to satisfy me, and
desired me to look out for a companion or two. I invited one Vincenzio
Romoli, who was my intimate acquaintance; and he brought another with
him. We repaired to the Coliseum; and the priest, according to the custom
of necromancers, began to draw circles upon the ground, with the most
impressive ceremonies imaginable. He likewise brought hither asafœtida,
several precious perfumes and fire, with some compositions also, which
diffused noisome vapours. As soon as he was in readiness, he made an
opening to the circle; and having taken us by the hand, ordered the
other necromancer, his partner, to throw the perfumes into the fire at
a proper time, entrusting the care of the fire and the perfumes to the
rest; and thus he began his incantations. This ceremony lasted above an
hour and a half, when there appeared several legions of devils, insomuch
that the amphitheatre was quite filled with them. Cellini afterwards
tells us, ‘that the necromancer called by their names a multitude of
demons, who were the leaders of the several legions, and questioned
them by the power of the eternal, uncreated God, who lives for ever,
in the Hebrew language, and likewise in Latin and Greek, and then the
amphitheatre was almost in an instant filled with demons, more numerous
than at the former conjuration. The necromancer requested me to stand
resolutely by him, because the legions were now above a thousand more in
number than he had designed; and, besides, these were the most dangerous.
The boy who had accompanied us was in a terrible fright, saying that
there were in that place a million of fierce men, who threatened to
destroy us; and that, moreover, four armed giants of enormous stature
were endeavouring to break into our circle. Vincenzio Romoli quivered
like an aspen leaf. Though I was as much terrified as any, I did my
utmost to conceal the terror I felt; so that I greatly contributed to
inspire the rest with resolution. But the truth is, I inwardly gave
myself over as a dead man. The boy placed his head between his knees,
and said, ‘In this posture will I die, for we shall all surely perish.’
In this condition, concludes Benvenuto, we stayed till the bell rang for
morning prayers.’”