G. P. (George Payn) Quackenbos.

A natural philosphy: embracing the most recent discoveries in the various branches of physics .. online

. (page 23 of 42)
Online LibraryG. P. (George Payn) QuackenbosA natural philosphy: embracing the most recent discoveries in the various branches of physics .. → online text (page 23 of 42)
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Itself; and this shadow diminishes according to the dis-
tance of the surface on which it is thrown.

In Fig. 229, let A be a luminous, and Fig. 229.

B an opaque, body. B's shadow, no mat- _$>^^~ T^&S-SB-.

ter how near the surface on which it is ^^J^ B(Jp|B3^ Ss '" C

thrown, must be smaller than B itself; ^><E^ "

and, as the surface is removed from B, the

shadow diminishes, till it is reduced to a point at C.

If, on the contrary, the opaque body is the larger of the
two, it throws a shadow greater than itself; and this shad-
ow increases according to the distance of the surface on
which it is thrown.

600. THE PJEXUMBRA. Every luminous body has an in-
finite number of points, from each of which proceeds a pen-
cil of rays. When an opaque body is interposed, some of
the space behind it is cut off from all the rays of the lumi-
nous body, and this constitutes the shadow proper. Part
of the space, however, while it

is cut off from some of the rays,
is illumined by others; this is
called the Penumbra.

In Fig. 230, let P be the flame of a
candle, and AB an opaque object placed be-
fore it. The space A B C D is not reached SHADOW AND PENUMBRA.




meant by a body's Shadow ? 593. Why arc not all shadows equally dark ? How
may we compare the intensity of different lights ? 599. When does a body throw a
shadow smaller than itself? Illustrate this law with Fig. 229. When does a body
throw a shadow larger than itself? 600. What is meant by the Penumbra? How is



236 OPTICS.

by any ray from P, and is therefore the Shadow of A B. The space A B 0",
while it is cut off from the rays produced by the lower extremity of the flame,
is illumined by its upper extremity ; hence it is nowhere so dark as the shad-
ow, and becomes lighter and lighter as the line AE is approached. So the space
B D F is cut off from the rays produced by the upper part of the flame, but
receives those from the lower part, and is therefore partially illuminated.
The spaces ACE, B D F, constitute the Penumbra, or imperfect shadow,
ofAB.

Reflection of JLiglit.

601. When light strikes an opaque body, some of it is
absorbed, and some reflected, or thrown back into the me-
dium from which it came. According to the Undulatory
Theory, we should say that some of the undulations that
strike the opaque body are brought to rest, while others
are reproduced in the same medium with a different direc-
tion from what they had before.

The reflection of light is analogous to the reflected motion of an india
rubber ball thrown against a solid surface. It is by the light irregularly re-
flected from their surfaces that all non-luminous bodies are seen.

Transparent surfaces, as well as opaque, reflect some of the light that
strikes them ; otherwise, they would not be visible. We see overhanging
objects mirrored in a stream with great distinctness, because a portion of the
rays received from them are reflected by the water to our eyes.

602. That branch of Optics which treats of the laws
and principles of reflected light, is called CATOPTRICS.

603. Rays that strike a body are called Incident Rays.

604. REFLECTIVE POWER OF DIFFERENT SURFACES.
Different surfaces reflect the light that strikes them in dif-
ferent degrees. By none is the whole reflected.

If any surface were a perfect reflector, that is, threw back all the light
that struck it, the eye would fail to distinguish it. Looking at such a sur-
face, we should see nothing but images of the bodies that produced the
incident rays. If, for example, the moon reflected all the light it received,
it would have the appearance of another sun. It is because there is not a

it produced ? Illustrate the mode in which the shadow and penumbra are produced,
with Fig. 230. 601. When light strikes an opaque body, what becomes of it ? Ex-
press this according to the Undulatory Theory. To Avhat is the reflection of light
analogous ? How are non-luminous bodies seen ? Is the reflection of light con-
fined to opaque surfaces ? Prove that it is not. 602. What is Catoptrics ?
603. What is meant by Incident Bays ? 604. What is said of the reflection of light
from different surfaces ? If any surface were a perfect reflector, what would be the



REFLECTION OF LIGHT. 237

perfect and regular reflection that the non-luminous bodies which meet the
eye every moment are visible.

Though incident light is never wholly reflected, yet from some surfaces it
is thrown off with a high degree of regularity, and with its intensity dimin-
ished comparatively little. If, for instance, we look at a good plate-glass
mirror hung opposite to us at the end of a room, we can hardly persuade
ourselves that there is not another apartment beyond, the counterpart of the
one which we are in. The surface of the mirror is not seen at all, in conse-
quence of its great reflective power.

605. The proportion of incident light reflected depends
on two things : 1. The angle at which it strikes the sur-
face. 2. The character of the surface.

The more obliquely light strikes a surface, the greater
is the quantity reflected.

In Fig. 231, let C D be a surface of polished Fig. 231.

black marble. A and B are incident beams,
with an intensity rated at 1,000. Let B strike
the marble at an angle of 3 degrees, and a ^
beam having an intensity of 600 will be re- c : '

fleeted. Let A strike it at an angle of 90 de-
grees, and the reflected beam will have an intensity of only about 20.

Light-colored and polished surfaces reflect a much
greater proportion of incident light than dark and dull
ones. Here again the laws of light and heat agree.

A room with white walls is much lighter than one with black or dark-
colored walls. A house painted some light color, or a dome covered with
polished tin, is more readily seen from a distance than a dark wall or an or-
dinary roof.

606. MIRRORS. The laws of reflected light are best in-
vestigated and explained with the aid of mirrors.

607. Mirrors are solids with regular and polished sur-
faces, having a high degree of reflective power. They are
made either of some metal susceptible of a high polish, such
as silver and steel, or of clear glass covered on the back
with silver or a mixture of tin and mercury. A metallic
mirror is sometimes called a Speculum (plural, specula).



consequence ? "What is said of the reflective power of some surfaces, such as a good
plate-glass mirror ? COS. On what does the proportion of incident light reflected de-
pend ? At what angle is tho most incident light reflected ? Illustrate this with Fig.
231. "What sort of surfaces reflect the most incident light? 606. With what are the
laws of reflected light best investigated ? 607. What are Mirrors ? Of what are they



238 OPTICS.

From glass mirrors there are two reflections ; one from the surface first
struck, the other from the back coated with mercury. Hence two images of
an object before the mirror are presented, the distance between them being
equal to the thickness of the glass. But the image produced by the front
surface is always faint; and, when the back is well coated, the other image
is so much superior that the faint one is entirely lost.

608. Kinds of Mirrors. As regards shape, mirrors are
divided into three classes ; Plane, Concave, and Convex.

A Plane Mirror (AB, in Fig. 232) is one that reflects
from a flat surface, like a common looking-glass.

A Concave Mirror (E F, in Fig. 233) is one that reflects
from a curved surface hollowing in like the inside of the
peel of an orange. k

A Convex Mirror (CD, in Fig. 234) is one that reflects
from a curved surface rounding out like the outside of an
orange.

A concave mirror polished on both sides becomes a convex mirror when
its opposite side is presented to the incident rays.

609. GREAT LAW OF REFLECTED LIGHT. The law of
reflected light is like that of reflected motion : The angle
of reflection is always equal to the angle of incidence. This
law holds good whether the reflecting surface is plane, con-
cave, or convex.

Fig. 232. Fig. 233. Fig. 23-1.






Figs; 232, 233, 234, illustrate this law. In each Figure, I represents the
incident ray, R the reflected ray, and P a perpendicular. I Q P, the angle
which the incident ray makes with the perpendicular, is called the angle of
incidence. R Q P, the angle which the reflected ray makes with the same
perpendicular, is the angle of reflection. From every surface, whatever its
form, the incident ray is thrown off in such a way as to make the angle of
reflection equal to the angle of incidence.

made ? What is a Speculum ? IIo\v many reflections are there from glass mirrors ?
How are they produced ? What is said of the images formed ? 60S. As regards
shape, how are mirrors divided ? What is a Plane Mirror ? What is a Concave Mir-
ror ? What is a Convex Mirror ? How may a concave mirror polished on both sides
be made a convex mirror? G09. Statathclavr of reflected light. Illustrate this with



FOKMATION OF IMAGES.



239



610. From these Figures it is obvious that an object which would not
otherwise be visible can be seen by reflection from a mirror. Thus, let the
upper part of P Q represent an opaque screen, I an object on one side of it,
and R the eye of an observer on the other. I is not visible to a person at R
looking directly at it, on account of the interposition of the screen ; but, as
the angle of reflection is always equal to the angle of incidence, it can be
seen from R by looking at the mirror.

611. IMAGES. By the Image of an object is meant a
luminous picture of it formed by rays proceeding from its
different points. An image is said to be inverted when it
represents its object as upside down, that is, with its low-
est part uppermost.

Fig. 235.




Fig. 235 illustrates the formation of an image. R B represents a soldier
with a red coat and blue trowsers standing in strong sunlight opposite
the white wall W. Let the shutters S S be thrown open, and not only the
light reflected from the person of the soldier, but also other rays, enter the
apartment, making its light a mixture of all colors, or white, in which the
red and the blue tinge of the dress are lost, and no image is formed. Now let
the shutters S S be closed, leaving at A an exceedingly small aperture, through
which the rays reflected from the figure are allowed to reach the wall. As
light is propagated in straight lines, the ray R will strike the wall at r, B at
b, and I at *'. .The image will therefore be inverted ; and, as each ray retains
its color, the coat will remain red and the trowsers blue. This experiment
confirms two principles already stated : 1. That every ray moves in a
straight line ; 2. That an infinite number of rays may cross each other with-
out interfering with the effect which each would separately have.

612. Images formed by apertures are always inverted.



the Figures. 610. What is obvious from these Figures? 611. What is meant by the
Image of an object? When is an image said to be inverted? With Fig. 235, illus-
trate the formation of an image. What two principles does this experiment confirm ?



240 OPTICS.

613. REFLECTION FROM PLANE MIRRORS. Plane mir-
rors do not alter the relative direction of incident rays. If
the incident rays are parallel, they will remain parallel after
reflection ; if divergent, they will continue to diverge ; if
convergent, they will continue to converge.

614. Objects seen in a plane mirror seem to lie in the
direction of the reflected rays that meet the eye, and to be
as far behind the mirror as they really are in front of it.
These principles are illustrated with Fig. 236.

p i(T> 236. A B is a plane mirror. C, D, are parallel rays striking

its surface. They are reflected in parallel lines to c, d ;
and to an observer at those points will appear to come
from G, H, as far behind the mirror as C, D, are in front
of it.

E is a diverging pencil. After reflection, its rays con-
tinue to diverge to e, e, e ; and to an observer there they
appear to diverge in unbroken straight lines from the point
I, as far behind the mirror as E is before it.

F, F, F, represent converging rays. After reflection,
they continue to converge, and meet at the point f. An
observer at/ would suppose them to come in unbroken
lines from J, J, J, as far behind the mirror as F, F, F, are
in front of it.

615. When we walk towards a looking-glass, our image
seems to advance towards us ; and when we recede from
it, the image also recedes. The image always appears to be the same dis-
tance from the mirror that the object is.

616. The angle of reflection being equal to the angle of
incidence, it follows that a person may see his whole figure
Fig. 23T. reflected from a mirror whose

length is but half his own height.
In Fig. 237, CD represents a
man standing before the mirror
A B. The incident ray from the
*> r head C strikes the mirror perpen-

dicularly, is reflected in the same line, and appears to come

612. What kind of images are formed by apertures ? 613. What effect have plane
mirrors on the relative direction of incident rays? 614. How do objects seen in a
plane mirror seem to lie ? With Fig. 236, illustrate the reflection of parallel, diverg-
ing, and converging rays from a plane mirror. 615. When we approach and recede
from a looking-glass, what phenomena are presented ? 616. How is it that a person
ean see his whole figure reflected from a mirror whose length is but half his height ?





REFLECTION FROM PLANE MIRRORS. 241

from E. The ray from his foot D strikes the mirror at B,
is reflected at an equal angle to his eye, and appears to
come in an unbroken line from F. The extremities of his
person being seen, the intermediate parts are also visible,
forming a complete image.

617. Images formed by Plane Mirrors. The size of
images formed by plane mirrors is not changed, except so
far as they seem smaller in consequence of their apparent
distance behind the mirror.

618. As the image faces the opposite way from the object, if the mirror is
vertical (that is, perpendicular to the floor), the right side of the object will
be the left of the image, and the left side of the object the right of the image.
If a person stands before a mirror with a book in his right hand, the book
seems to be in the left hand of his image ; and, if he brings the printed page
near the mirror, he can not read it, for the reflection turns about both letters
and words, side for side.

Place the same plane mirror in a horizontal position (that is, lay it on the
floor with its face up), and the image, which before simply had its sides
transposed, now becomes inverted, or seems to stand on its head. On the
same principle, a tree or other object reflected from the surface of a pond, is
inverted.

619. The Kaleidoscope. When an object is placed be-
tween two parallel plane mirrors, each produces an image
of its own, and reproduces the image reflected to it from
the other. This image of an image is again reflected by
each to the other, and thus a series of images is produced,
till the rays become so faint by successive reflections as to
be no longer discernible.

When the mirrors are placed at right angles to each
other, an object between them forms three images, one
produced by each separately, and one by a twofold reflec-
tion from both. Placed so as to form with each other an
angle of 60 degrees, the two mirrors will produce five im-
ages ; at 45 degrees, seven.

This principle is applied in the Kaleidoscope \Jca-li' -do-
scope], a beautiful toy invented by Sir David Brewster.

617. "What is said of the size of images formed by plane mirrors ? 618. If the mirror
is vertical, how does the imago differ from the object ? How, if the mirror is horizon-
tal? 619. What takes place when an object is placed between two parallel piano
mirrors ? How many images are formed when the mirrors are placed at right angles
11



242 OPTICS.

620. The kaleidoscope consists of two narrow strips of glass running
lengthwise through a tube, and forming with each other an angle of CO or 45
degrees. One end of the tube, to which the eye is to be applied, is covered
with clear glass. The other end terminates in a cell formed by two parallel
pieces of glass an eighth of en inch apart, the outer one of which is ground
to prevent external objects from marring the efi'ect. This cell contains beads
or small pieces of glass of different colors, free to move among themselves.
On applying an eye to the tube, we see the objects in the ceil multiplied by
repeated reflections from the mirrors, and symmetrically arranged, with their
images, around a common centre. By shaking the tube, we bring the ob-
jects into new relative positions, and have new combinations presented.

621. The Magic Perspective. By arranging four plane
mirrors as represented in Fig. 238, a person is enabled to
see an object by looking directly towards it, though an
opaque screen is interposed.

A rectangular box is bent

Fig. 283. four times at right angles ;

and in each of these angles
is placed a piece of looking-
glass, B, C, D, E, at such
an inclination that the inci-
dent ray may strike it at an
angle of 45 degrees. Any
THE MAGIC PERSPECTIVE. ob J ect opposite the aperture

A is visible to an eye ap-
plied at the other extremity, though an opaque screen be placed between the
arms of the instrument. The rays from the object first strike B at an angle
of 45 degrees, and are reflected at the same angle to C, thence to D, thence to
E, and finally to the observer's eye. The inventor of this instrument recom-
mended its use in time of war, for discovering an enemy's movements with-
out any exposure of the observer's person. It is more commonly used, how-
ever, by itinerant showmen, who for a penny allow the curious to read through
a brick.

622. REFLECTION FKOM COXCAVE MIRRORS. In gen-
eral, the effect of concave mirrors is to make incident rays
more convergent or less divergent. In most* cases, the im-
ages they produce appear in front of them.

623. Parallel rays striking a concave mirror are made
to converge to a point called the Principal Focus. This

to each other ? How many, when they form an angle of 60 degrees ? Of 45 degrees ?
In what is this principle applied ? 620. Describe the Kaleidoscope. C21. How is a
person enabled to see an object by looking towards it, though an opaque screen is in-
terposed? Describe the Magic Perspective. By whom is it commonly used?
622. "What is the general effect of concave mirrors ? What is said, of the images they





REFLECTION FROM CONCAVE MIRRORS. 243

point is half way between the surface of the mirror and the
centre of the sphere which the mirror would form if it were
extended with uniform curvature.

In Fig. 239, let A E B be a concave mir- Fig. 239.

ror, forming part of the surface of a sphere,
of which C is the centre. The parallel rays
d, e >f> ff> h> are reflected to the principal fo-
cus F, midway between the surface and the
centre C.

Not only is light concentrated at the fo-
cus, but also heat, as we had occasion to

note in 476. Tinder, wood, or any other combustible material, is readily
ignited, and with a combination of such mirrors the most intense heat can be
produced. Hence concave mirrors are sometimes called Burning Glasses.

624. Converging rays reflected from a concave mirror
are made to converge more.

625. Diverging rays reflected from concave mirrors are
differently affected according to the position of the point
from which they diverge.

626. Diverging rays starting from the principal focus
are made parallel. This is obvious from Fig. 239. The
rays diverging from F, after striking the mirror, are re-
flected in parallel lines to J, e, /, #, h.

This principle is turned to account in light-houses. The light is placed in
the focus of a concave mirror, and its rays are reflected in parallel lines from
every point of the mirror's surface. No image of the light is produced, but
the whole surface of the mirror appears illuminated.

627. Diverging rays coming from a point between the
principal focus and the mirror, become less divergent after
reflection. An object in such a position forms an image
larger than itself, which seems to be situated behind the
mirror.

628. Diverging rays coming from a point between the

produce ? 623. What effect has a concave mirror on parallel rays that strike it ?
How is the principal focus situated ? Illustrate this effect with Fig. 239. What are
concave mirrors sometimes called, and why ? C24. "What is the effect of concave mir-
rors on converging-rays ? G2G. What is the effect of concave mirrors on diverging
rays starting from the principal focus? How is this principle turned to account?
C27. What effect have concave mirrors on diverging rays coming from a point be-
tween the principal focus and the mirror ? What kind of an image is formed ?
62S. What effect have concave mirrors on rays diverging from a point between tho



244 OPTICS.

principal focus and the centre, converge, after reflection,
to a focus on the other side of the centre. An inverted
image will there be visible, suspended in the air. This im-
age is made more distinct, and its effect greatly increased,
by causing a cloud of thin bluish smoke to rise about the
spot from a chafing-dish placed beneath.

By concealing with screens the mirror, the object, and the light that illu-
mines it, and allowing the reflected rays to pass through an aperture, we may
give the image all the appearance of reality. The observer beholds delicious
fruit hanging in the air without any visible support, and can hardly convince
himself that it is a delusion, even when he tries to grasp it without success.
He sees a pail full of water standing bottom upward without spilling its
contents, and men with every semblance of life walking on their heads. It
was with apparatus of this kind that the pretended magicians of the Middle
Ages wrought many of their miracles, terrifying the uninitiated with sudden
apparitions of skulls, drawn swords, skeletons, ghosts, &c.

629. Diverging rays coming from the centre are reflect-
ed by a concave mirror back to the same point. Here, as
in all other cases, the angle of reflection is equal to the an-
gle of incidence. Striking the surface at right angles, they
are reflected at right angles back to the centre.

630. Diverging rays coming from a point beyond the
centre, after reflection by a concave mirror, converge to a
point on the other side of the centre. In this case, the im-
age is inverted and smaller than the object.

631. REFLECTION BY CONVEX MIRRORS. In general, the
effect of convex mirrors is to make incident rays more di-
vergent or less convergent. The images they produce, like
those of plane mirrors, seem to stand behind them, and are
generally smaller than the objects they represent.

632. Parallel rays striking a convex mirror are made to
diverge, as if they proceeded from a point on the opposite
side of the mirror, called the Virtual Focus. This point is



principal focus and the centre ? "What sort of an image is formed ? How is the imago
made more distinct ? How may wonderful effects be produced with this mirror ? By
whom was apparatus of this kind employed? 629. What is the effect of concave mir-
rors on diverging rays coming from the centre ? C30. What is their effect on diverg-
ing rays coming from a point beyond the centre ? In this case, what kind of an image
is produced ? 631. What is the general effect of convex mirrors ? What is said of
toe images thoy produce ? 632. What is the effect of a convex mirror on parallel




REFLECTION BY CONVEX MIRRORS. 245

half way between the mirror and the centre of the sphere
which the mirror would form, if it were extended with uni-
form curvature.

In Fig. 240, let A B represent a Fig. 240.

convex mirror forming part of the
surface of a sphere, of which C is the
centre. The parallel rays a, b, c, d, e,
diverge after reflection to/, g, c, k, i,
as if they had come from the virtual
focus F on the other side of the mir-
ror. F is half way between the mir-
ror and its centre C.

633. Diverging rays fall-
ing on a convex mirror are made more divergent by reflec-
tion. Converging rays are made less convergent, in some
cases even becoming parallel.

Refraction of Uglit.

634. When light strikes a transparent body, some of it
is reflected and makes the body visible. The rest enters
the body, and is partly absorbed and partly transmitted
through it. According to the undulatory theory, we should
say that some of the undulations that strike the transparent
body are reproduced in the same medium with a change of



Online LibraryG. P. (George Payn) QuackenbosA natural philosphy: embracing the most recent discoveries in the various branches of physics .. → online text (page 23 of 42)