D, because the arc A C is the arc of a larger
circle than the arc B D. But to the eye at E
the velocity of both appears to be the same, C ^ B
because both are seen under the same angle of vision.
uri 814. A mirror is a smooth and polished sur-
mirrors, and face, that forms images by the reflection of the
^ ^ n k Mirrors (or looking-glasses) are
made of glass, with the back covered with an
amalgam, or mixture of mercury and tin foil. It is the
smooth and bright surface of the mercury that reflects the
rays, the glass acting only as a transparent case, or cover-
ing, through which the rays find an easy passage. Some
of the rays are absorbed in their passage through the glass,
because the purest glass is not free from imperfections. For
this reason, the best mirrors are made of an alloy of copper
and tin, called speculum metal.
What are the 815> There are three kinds of mirrors,
different kinds namely, the plain, the concave, and the con-
of mirrors f
Plain mirrors are those which have a flat surface, such
as a common looking-glass ; and they neither magnify nor
diminish the image of objects reflected from them.
816. The reflection from plain mirrors is always
By what law
are objects re- obedient to the law that the angles of incidence and
fleeted from a reflection are equal. For this reason, no person
' can see another in a looking-glass, if the other can-
not see him in return.
How do looUng- 817 - Looking-glasses or plain mirrors cause
glasses make all everything to appear reversed. Standing before
Ejects appear? & i oo king-glass, if a person holds up his left
hand it will appear in the glass to be the right.
818. A looking-glass, to reflect the whole person, needs be but half
of the length of the person.
819. When two plain mirroTS stand opposite to each other, the
reflections of the one are cast upon the other, and to a person be-
tween them they present a long-concinued vista.
820. When two reflecting surfaces are inclined at an angle, the
reflected objects appear to have a common centre to an eye viewing
them v obliquely. It is on this principle that the kaleidoscope is
What is a 821. The Kaleidoscope consists of two reflecting
Kaleidoscope? surfaces, or pieces of looking-glass, inclined to
each other at an angle 'of sixty degrees, and placed between
the eye and the objects intended to form the picture.
The two plates are enclosed in a tin or paper tube, and the
objects, consisting of pieces of colored glass, beads, or other
highly-colored fragments, are loosely confined between two cir-
cular pieces of common glass, the outer one of which is slightly
ground, to make the light uniform. On looking down the tube
through a small aperture, and where the ends of the glass plates
nearly meet, a beautiful figure will be seen, having six angles,
the reflectors being inclined the sixth part of a circle. If in-
clined the twelfth part or twentieth part of a circle, twelve or
twenty angles will be seen. By turning the tube so as to alter
the position of the colored fragments within, these beautiful forma
will be changed ; and in this manner an almost infinite variety
of patterns may be produced.
The word Kaleidoscope is derived from the Greek language, and
means " the sight of a beautiful form." The instrument was in-
dented by Dr. Brewster, of Edinburgh, a few years ago.
822. A convex mirror is a portion of the external sur-
face of a sphere. Convex mirrors have therefore a convex
823 A concave mirror is a portion of the inner surface
The outer part of M N is a
of a hollow sphere. Concave mirrors have therefore a con-
Exj-ilain 824. In Fig. 127, M N represents both a convex
rig. 127. and a concave mirror. They are both a portion of a
sphere of which is the centre,
convex, and the inner part is
a concave mirror. Let A B,
C D, E F, represent rays
falling on the convex mirror
M N. As the three rays are
parallel, they would all be per-
pendicular to a plane or flat
mirror ; but no ray can fall
perpendicularly on a concave
or convex mirror which is not
directed tmvards the centre of the sphere of which the mirror is
a, portion. For this reason, the ray C D is perpendicular to the
mirror, while the other rays, A B and E F, fall obliquely upon
it. The middle ray therefore, falling perpendicularly on the
mirror, will be reflected back in the same line, while the two
other rays, falling obliquely, will be reflected obliquely ; namely,
the ray A B will be reflected to G, and the ray E F to H, and
the angles of incidence A B P and EFT will be equal to the
angles of reflection P B G and T F H ; and, since we see objects
in the direction of the reflected rays, we shall see the image at
L, which is the point at which the reflected rays, if continued
through the mirror, would unite and form the image. This point
is equally distant from the surface and the centre of the sphere
and is called the imaginary focus of the mirror. It is called the
imaginary focus, because the rays do not really unite at that
point, but only appear to do so ; for the rays do not pass through
the mirror, since they are reflected by it.
825. The image of an object reflected from a convex
oairror is smaller than the object
What is the ^' This is owing to the divergence of the re-
ooject of fleeted rays. A convex mirror converts, try reflec-
TTV/y "1 9Q 9
ff ' tion, parallel rays into divergent rays; rays that
fall upon the mirror divergent are rendered still more diver-
gent by reflection, and convergent rays are reflected either
parallel, or less con- Oig. 128.
vergent. If, then, an
object, A B, be placed
before any part of a
convex mirror, the
two rays A and B,
proceeding from the
convergent on the
mirror, will be re-
flected less convergent, and will not come to a focus until they
arrive at C ; then an eye placed in the direction of the reflected
rays will see the image formed in (or rather behind) the mirror
at a b ; and, as the image is seen under a smaller angle than the
object, it will appear smaller than the object.
What is the $27. The true focus of a concave mirror is
true focus of a point equally distant from the centre and the
'mirror? surface of the sphere of which the mirror is a
When will 828. When an object is further from the con-
ike image re- cav e surface mirror than its focus, the image will be
aconcaveTe inverted; but when the object is between the
upright, and mirror and its focus, the image will be upright,
'ed T " an ^ S row l ar g er * n proportion as the object is
placed nearer to the focus.
What pe- 829. Concave mirrors have the peculiar prop-
culiar prop- er ty of forming images in the air. The mirror
^oncar^mir- an( * tne OD J ect being concealed behind a screen,
rnrs? or a wall, and the object being strongly illumi-
Dated, the ra^ from the object fail upon the minor, and are
reflected by it through an opening in the screen or wall, forming
an image in the air.
Showmen have availed themselves of this property of concave
mirrors, in producing the appearance of apparitions, which have
terrified the young and the ignorant. These images have been pre-
sented with great distinctness and beauty, by raising a fine trans-
parent cloud of blue smoke, by means of a chafing-dish, around the
focus of a large concave mirror.
When is the 830. The image reflected by a concave
image from a m i rror j s larger than the object when the
concave mirror .T
larger than the object is placed between the mirror and its
What is the de- 831 - This is owin g to the convergent prop-
iign of Fig. erty of the concave mirror. If the object A
B be placed between the concave mirror and ifr
focus /, the rays
A and B from its
fall divergent on
the mirror, and,
on being reflect-
ed, become less
divergent, as if
from C. To an
eye placed in that situation, namely, at C, the image will appear
magnified behind the mirror, at a I since it is seen under a
larger angle than the object.
832. There are three cases to be considered with regard to the
effects of concave mirrors :
1. When the object is placed between the mirror and the princi
2. When it is situated between its centre of concavity and that
3. When it is more remote than the centre of concavity.
1st. In the first case, the rays of light diverging after reflection
but in a less degree than before such reflection took place, the iui
2^6 NATURAL PHILOSOPHY
age will be larger than the object and appear at a greater 01
smaller distance from the surface oi the mirror, and behind it. Tha
Image in this case will be erect.
2d. When the object is between the principal focus and the cen-
tre of the mirror, the apparent image will be in front of the mirror,
and beyond the centre, appearing very distant when the object is
at or just beyond the focus, and advancing towards it as it recedes
towards the centre of concavity, where, as will be stated, the im-
age and the object will coincide. During the retreat of the object
the image will still be inverted, because the rays belonging to each
visible point will not intersect before they reach the eye. But In
this case the image becomes less and less distinct, at the same time
that the visual angle is increasing; so that at the centre, or rather
a little before, the image becomes confused and imperfect, because
at this point the object and the image coincide.
3d In the cases just considered, the images will appear inverted ;
and in the case where the object is further from the mirror than its
centre of concavity, the image will be inverted. The more distant
the object is from the centre, the less will be its image ; but the
image and object will coincide when the latter is stationed exactly
at the centre.
833. The following laws flow from the fundamental law of Catop-
trics, namely, that the angles of incidence and reflection are
always equal. In estimating these angles, it must be recollected
that no line is perpendicular to a convex or concave mirror, which
will not, when sufficiently prolonged, pass through the centre cf the
sphere of which the mirror is a portion. The truth of these state-
ments may be illustrated by simple drawings ; always recollecting,
in drawing the figures, to make the angles of incidence and reflec-
tion equal. The whole may also be shown by the simple experi-
ment of placing tho flame of a candle in various positions before
both convex and concave mirrors. [It is recommended that the learner
be required to draw a figure to represent each of these laws.]
834. LAWS OF REFLECTION FROM CONVEX MIRRORS. (1.) Par-
allel rays reflected from a CONVEX surface are made to diverge.
(2.) Diverging rays reflected from a CONVEX surface are made
(3.) When converging rays tend towards the focus of parallel
rays, they will become parallel when reflected from a CONVEX
(4.) When converging rays tend to a point nearer the surface
* For the sake of distinction, the principal focus is called " the jbcus 0'
than the focus, they will converge less when reflected from a
(5.) If converging rays tend to a point between the focus and
the centre, they will diverge as from a point on the other side
of the centre, further from it than the point towards which they
(6.) If converging rays tend to a point beyond the centre,
they will diverge as from a point on the contrary side of the
centre, nearer to it than the point towards which they con-
(7.) If converging rays tend to the centre, when reflected
they will proceed in a direction as if from the centre
835. LAWS OF REFLECTION FROM CONCAVE MIRRORS.
(1.) Parallel rays reflected from a CONCAVE Kirface are made
converging. [See Note to No. 837.]
(2.) Converging rays falling upon a CONCAVE surface are
made to converge more.
(3.) Diverging rays falling upon a CONCAVE surface, if they
diverge from the focus of parallel rays, become parallel.
(4.) If from a point nearer to the surface than that focus,
they diverge less than before reflection.
(5.) If from a point between that focus and the centre, they
converge, after reflection, to some point on the contrary side of
the centre, and further from the centre than the point from
which they diverged.
(6.) If from a point beyond the centre, the reflected ra>&
will converge to a point on the contrary side, but nearer to it
than the point from which they diverged.
(7.) If from the centre, they will be reflected back to tht
same point from which they proceeded.
How are objects 836. As a necessary consequence of the laws
teen from a con- which have now been recited, it may be stated,
First, in regard to CONVEX MIRRORS, the im-
ages of objects invariably appear beyond the mirror ; in other
. they are virtual images. Secondly, they are seen in
their natural position, and, Thirdly, they are smaller than
the objects themselves ; the further the object is from the mir-
ror, and the less the radius of the mirror, the smaller the image
will be. If the object be very remote, its image will be in the
virtual focus of the mirror.
837, Secondly, in regard to CONCAVE MIRKORS.
(1.) The image of an object very remote from a concave mir-
ror, as that of the sun, will be in the focus of the mirror, and
the image will be extremely small.* 1
(2.) Every object which is at a distance from the mirror
greater than its centre produces an image between this point
and the focus smaller than the object itself, and in an inverted
(3.) If the o'Mect be at a distance from the mirror equal to
the length of its radius, then the image will be at an equal dis-
tance from the mirror, and the dimensions of the image will be
the same as those of the object, but its position will be inverted.
(4.) If the object be between the focus and the centre of
curvature, the image will be inverted, and its size will much
exceed that of the object.
These four varieties of inverted images, produced by th*
reflection of the rays of light from concave mirrors, arc some-
times called "physical spectra."
* This is the manner in which concave mirrors become burning-glasses.
The rays of the sun fail upon them parallel [see No. 835], and they are all
reflected into one point, called the focus, where the light and heat are as
much greater than the ordinary light and heat of the sun as the area of the
mirror is greater than the area of the focus. It is related of Archimedes,
that he employed burning-mirrors, two hundred years before the Christian
era, to destroy the besieging navy of Marcellus, the Roman consul. His
mirror was, probably, constructed- from large numbers of flat pieces. M.
de Vilette constructed a burning-mirror in which the area of the mirror was
seventeen thousand times greater than the area of the focus. The heat of the
sun was thus increased seventeen thousand times. M. Dufay made a concave
mirror of plaster of Paris, gilt and burnished, twenty inches in diameter,
with which he set fire to tinder at the distance of fifty feet. But the most
remarkable thing of the kind on record is the compound mirror constructed!
by Butfon. He arranged one hundred and sixty-eight small plane mirrors
in such a manner as to reflect radiant light and heat to the same focus, like
one large concave mirror. With this apparatus he was able to set wood on
fire at the distance of two hundred and nine feet, to melt U>aJ at a liun-
dreu feet, and silver at fifty feet.
The existence and position of these spectra may easily be shown
experimentally thus :
Experiment. Hold a candle opposite to a concave mirror, at ths
distances named in the last four paragraphs respectively. The
spectrum can, in each case, be received on a white screen, which
must be placed at the prescribed distance from the mirror.
Different optical instruments, especially reflecting telesccpes,
exhibit the application of these spectra.
(5.) If a luminous body, as, for instance, the flame of an
argand lamp, or a burning coal, be placed in the focus of a con-
cave mirror, no image will be produced, but the whole surface
of the mirror will be illuminated, because it reflects in parallel
lines all the rays of light that fall upon it. This may be made
the subject of an experiment so simple as not to require further
'The reflectois of compound microscopes, magic lanterns and light-
houses, by means of which the light given by the luminous bodj
is increased and transmitted in some particular direction that maj
be desired, are illustrations of the practical application of this prin-
(6.) Lastly, place the object between the mirror and the
focus, and the image of the object will appear behind the mir-
ror. It will not be inverted, but its proportions will be enlarged
according to the proximity of the object to the focus. It is
this circumstance that gives to concave mirrors their magnifying
powers, and, because by collecting the sun's rays into a focus
they produce a strong heat, they are called burning-mirrors.
838. MEDIA, OR MEDIUMS, AND REFRAO
What is a Me- TTON - A Medium,* in Optics, is any sub-
dium in Optics? stance, solid or fluid, through which light
What is refrac- 839. When light passes in an oblique
direction from one medium into another, it
is turned or bent from its course, and this is called refrac-
* The proper plural of this word is media, although mediums is frequently
230 NATURAL PHILOSOPHY.
twn. The property which causes it is called
840. DIOPTRICS. That part of the sci-
tri~.9? l P " ence of Optics which treats of refracted light
k called Dioptrics.
What is meant ^^" ^ me dium, in Optics, is called dense or
by a denser and rare according to its refractive power, and not
r Ot>ti T lUm accordin g to its specific gravity. Thus, alcohol,
and many of the essential oils, although of less
specific gravity than water, have a greater refracting power,
and are, therefore, called denser media than water. In the fol-
lowing list, the various substances are enumerated in the order
of their refractive power, or, in other words, in the order of
their density as media, the last-mentioned being th densest,
and the first the rarest, namely : air, ether, ice, water, alcohol,
alum, olive oil, oil of turpentine, amber, quartz, glass, molted
842. There are three fundamental laws of
What are the T .. . . , . , ,, ., , ,
fundamental Dioptrics, on which all its phenomena de-
Imos of Diop- pend, namely :
(1.) When light passes from one medium
to another in a direction perpendicular to the surface, it
continues on in a straight line, without altering its course.
(2.) When light passes in an oblique direction, from a
rarer to a denser medium, it will be turned from its course,
and proceed through the denser medium less obliquely, and
in a line nearer to a perpendicular to its surface.
(3.) When light passes from a denser to a rarer medium
in an oblique direction, it passes through the rarer medium
in a more oblique direction, and in a line further from a
perpendicular to the surface of the denser medium.
843. In Fig. 130, the line A B represents a
*' ray of light passing from air into water, in a
perpendicular direction. According to the first
[aw stated above, it will continue on in the ** 1SO
same line through the denser medium to E.
If the ray were to pass upward through the
denser medium, the water, in the same per-
pendicular direction to the air, by the same
law it would also continue on in the same
straight line to A.
But, if the ray proceed from a rarer to a denser medium, in
an oblique direction, as from C to B, when it enters the denser
medium it will not continue on in the same straight line to D,
but, by the second law, stated above, it will be refracted or bent
out of its course and proceed in a less oblique direction to F
which is nearer the perpendicular ABE than D is.
Again, if the ray proceed from the denser medium, the water,
to the rarer medium, the air, namely, from F to B, instead of
pursuing its straight course to G, it will be refracted according
to the third law above stated, and proceed in a more oblique
direction to C, which is further from the perpendicular E B A
than G is. The refraction is more or less in all
tion is ^refrac cases m proportion as the rays fall more or less
lion in all cases ? obliquely on the refracting surface.
844. From what has now been stated with
f regard to refraction, it will be seen that many
taking the depth interesting facts may be explained. Thus, an
if water, and oar? or a s ti c k, w hen partly immersed in water,
appears bent, because we see one part in one
medium, and tht other in another medium : the part which is in
the water appears higher than it really is, on account of the
refraction of the denser medium. For the same reason, when
we look obliquely upon a body of water it appears more shallow
than it really is. But, when we look perpendicularly down-
wards, we are liable to no such deception, because there will be
845. Let a piece of money be put iito a cup or a bowl, and the
cup and the eye * be placed in such a position that the side of the
*:}< will just hfde the money from the sight; then, keeping the ev
232 NATURAL PHILOSOPHY.
directed to the same spot, let the cup be filled with water, th
monoy will become distinctly visible.
Why do we not 846< The refraction of H g ht prevents our
see the sun, moon seeing the heavenly bodies in their real situa-
and stars, intheir ^j on
The light which they send to us is refracted
in passing through the atmosphere, and we see the sun, the
stars, &c., in the direction of the refracted ray. In conse-
quence of this atmospheric refraction, the sun sheds his light
upon us earlier in the morning, and later in the evening, than
we should otherwise perceive it. And, when the sun is actually
below the horizon, those rays which would otherwise be dissi-
pated through space are refracted by the atmosphere towards
the surface of the earth, causing twilight. The greater the
density of the air, the higher is its refractive power, and, conse-
quently, the longer the duration of twilight
It is proper, however, here to mention that there is another rea-
son, why we do not see the heavenly bodies in their true situ-
ation. Light, though it moves with great velocity, is about eight
and a half minutes in its passage from the sun to the earth, so that
\vhen the rays reach us the sun has quitted the spot he occupied
on their departure ; yet we see him in the direction of those rays,
and, consequently, in a situation which he abandoned eight minutes
und a half before". The refraction of light does not affect the appear-
ance of the heavenly bodies when they are vertical, that is, directly
over our heads, because the rays then pass vertically, a direction
incompatible with refraction.
847. When a ray of light passes from
What effect is ,. , if
produced when one medium to another, and through that
light suffers two into the first again, if the two refractions be
iijual refrac- , , . ,.
f ' on t ? J equal, and in opposite directions, no sen-
sible effect will be produced.
This explains the reason why the refractive power of flat window-
glass produces no effect on objects seen through it. The rays suffer
two refractions, which, being in contrary directions, produce the
game effect as if no refraction had taken place.
848. LENSES. A Lens is a glass, which,
What is a Lens? . .. ,. f '
owing to its peculiar form, causes the rays
of light to converge to a focus, or disperses them, according
to the laws of refraction.
Explain the dif- &49. There are various kinds of lenses,
ferent kinds of named according to their focus ; but they
are all to be considered as portions of the
internal or external surface of a sphere. (See par. 1480.)
850. A single
convex lens has
one side flat and
the other convex ;
as A, in Fig. 131.
851. A single
concave lens is flat on one side and concave on the other, aa
B in Fig. 131.
852. A double convex lens is convex on both sides, as
C, Fig. 131.
A double concave le.ns is concave on both sides, as D,
A meniscus is convex on one side and concave on the
other, as E, Fig. 131.