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commands
him to rise. Two concealed boys at T pull the rug and the boy appears
to rise. He can then be turned upside down and back again. You can
repeat with the boy lying down.
FUN BY DAY OR NIGHT WITH TWO
MIRRORS
Experiment
No. 41.
Magic money.
Stand
the two mirrors vertically on the table sidewise to a good light and
place a coin between them. Look over each mirror in turn into the other
(Fig. 74). Have you multiplied your money wonderfully?
Experiment No.42.
Magic lights.
Repeat
the above in the dark with a lighted candle between the mirrors
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GILBERT BOY
ENGINEERING
(Fig.
75). Do you find many, many lights?
Experiment No. 43.
Magic army.
Put
a number of lead soldiers on a narrow strip of paper and draw them
between the vertical mirrors (Fig. 76). Do you see an immense army
marching in perfect order?
Experiment No. 44.
Magic
dancers.
Cut
out of paper or cardboard a small figure of a man dancing. Attach him
to a string and make him dance between the mirrors in a good light
(Fig. 77). Do you find a multitude of dancers who keep time perfectly ?
Experiment No. 45.
Magic silver
or copper
mine.
Separate
the mirrors by two blocks, place them one above the other and face to
face (Fig. 78); place a silver or copper coin on the lower mirror. Do
you find yourself looking down into a very deep hole with many silver
or copper coins in it?
Why you see Many Images
in
Parallel Mirrors. You
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see many images
between two parallel mirrors because the image formed in one mirror is
an object in the other, and so on.
In
Fig. 79, two mirrors, A
and B, 4
inches apart are facing each other and
a candle between them is 1 inch from B and 3 inches from A.
In
B the image Bl is formed 1 inch
behind B
and in A
the image Al
is formed 3 inches behind A.
Now
image Al is
7 inches in front of B
and it forms an image B2
7 inches
behind B;
similarly image Bl
is 5 inches in front of A
and forms an
image A2 6
inches behind A.
Again, A2
is 9 inches in front of B
and
forms an image B3
9 inches behind B,
and so on.
You see many
images because the light which enters your eyes has been reflected one
or more times. If you are looking at Bl, the light which
enters your
eye appears to come from Bl,
but it comes from the candle and is
reflected from B.
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If
you are looking at B2,
the light appears to come from B2,
but B2 is
an
image of A1,
and the light goes from the candle and is reflected twice
before it enters your eye.
Image B3 is
an image of A2,
which
in turn is an image of Bl, and
you see B3
by means of light which
has been three times reflected. Similarly you would see B4, B10, and
B50 by means
of light reflected 4, 10, and 50 times.
It is good
practice to locate the images in parallel mirrors and to trace the
paths of the light.
Why the Images become dim.
The images become dimmer the farther they are
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away:
first, because some light is absorbed by the mirrors at each
reflection; and, second, because the light has traveled a long distance
in being reflected back and forth between the mirrors.
Experiment No.46
The trench
periscope.
To
illustrate how the periscope works, look over the top of a tall book as
shown in Fig. 80. Place one mirror against the book at an angle of
45° and hold the second mirror above the book at the same
angle. Can you see over the top easily without being seen yourself?
Turn the upper mirror until it looks backward (Fig. 81), Can you see
back over your head, but is everything upside down ? Turn the upper
mirror until it looks sidewise (Fig. 88). Can you see things, but are
they turned on their sides?
THE "WHY" OF THE PERISCOPE
Now
let us see why the image is right side up in some cases and not in
others,
The
mirrors in the regular periscope are
parallel to each other, and you can locate the image in each mirror in
turn as you
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did
in the case of parallel mirrors.
Let
the arrow, Fig. 83, represent the object; its image in A is Al and
the top and bottom of Al
are as far behind the mirror extended as the
top and bottom of the arrow are in front.
Now let
us suppose
mirror B to
be extended as shown by the dotted line, then Bl is the
image of Al in this extended mirror and the top and bottom of Bl are as
far behind B
as the top and bottom of Al
are in front of B,
and
therefore Bl
is right side up.
In the
second case, the mirrors
are at right angles (Fig. 84). Al is the image of the arrow in A
extended and Bl
is the image of Al
in B
extended; Al is
on its side
and Bl is
inverted for the reasons given above.
In the third
case, the image is on its side in the upper mirror, and since the lower
mirror is parallel to this image, the image in the lower mirror is
still on its side.
Experiment No. 47.
To make a
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trench
periscope.
Get
a block of wood 4" X 4" X 6", measure down 1 inch from each end and
draw a line across diagonally. This line will be at 45° to the length
of the block. Cut the block through on this diagonal line, see right
side Fig. 85.
Now
attach a mirror to each diagonal face by
means of tacks. Cut a piece of stiff cardboard 17 inches wide and as
long as you wish to make the periscope. Tack this to the block,
overlapping 1 inch on one side. Paste the overlapping parts together.
Cut a hole 3" oppo the upper mirror and a hole 2" X
2"
opposite the lower mirror, and your periscope is finished.
You
can use this periscope in your trench battles; also you can use it on a
train to see forward without putting your head out of the window. In
this case, however, you should fasten the window glass over one of the
holes to keep cinders out of your eyes.
FUN WITH MIRRORS AT DIFFERENT
ANGLES
Experiment
No. 48.
Mirrors
at
different angles.
Stand
the mirrors vertically and at right angles on the table (Fig.
86) and place a lighted candle
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ENGINEERING
between them. Do
you see four candles, the real candle and three images?
Make
the angle 60°. Do you see six candles, the original candle and five
images?
Make the angle 45°.
Do you see eight candles?
Make the angle 30°.
Do you 'see twelve candles?
There are 360°
in a complete circle, and the number of candles you see in each case is
360 divided by the angle between the mirrors. For example,
when
the angle is 90°, you see
360
----
90
or
4 candles;
and when
the angle is 60°, you see
360
----
60
or
6 candles; and so on.
Experiment No. 49.
A one-boy
crowd.
Stand
the mirrors at 90° and put your face close to the mirrors. Are there
four of you, yourself and three images?
Repeat
with the mirrors at the angles mentioned above. Do you find yourself a
crowd all in a circle?
Experiment No. 50.
Arrows.
Stand
the mirrors at 90°
on a piece of white paper and draw an arrow pointing at one
of
the mirrors. Do some of the arrows point in one direction and some in
the opposite direction? Keep one mirror in such a position that the
arrow points directly at it and move the other mirror until the angle
is 60°. Do the six arrows
point toward
each other in pairs?
Repeat
with the mirror at the other angles mentioned above.
Experiment No. 51.
An
infinite number of
candles.
Light
a candle and stand the mirrors close to it and gradually make them
parallel. Do you see very, very many candles?
When
the mirrors are parallel the angle between them is 0°
and
360
----
0
is infinity,
so
you should see an infinite number of
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images.
You cannot, because some light is lost at each reflection and finally
all is lost.
EDITOR'S NOTE:
(Not in the original text!) While the experts say
it is possible
to define anything divided by zero as "infinity" as the author did
here, today most math whizzes choose to say that anything divided by
zero is "undefined." In this case, there still are
theoretically
an infinite number of images, but the math would probably not be
considered "right" today.
Experiment No. 52.
To locate the
images in
mirrors at an angle.
Draw
two lines 4 inches long at right angles to represent two mirrors at
right angles (Fig. 87) and extend them backward by dotted lines to
represent the extended mirrors. Place a dot 1 inch from A and 2 inches
from B,
then image Al
will be 1 inch behind A
and image Bl
2 inches
behind B. The third image A2B2
is an image of both Al
and Bl; it
is 1
inch behind A
extended and 2 inches behind B
extended.
It is
harder to locate the images when the angle is 60° or smaller,
but It will help you to know that the images are always all on the
circumference of a circle of which the angle of the mirrors is the
center.
Practice locating the images in mirrors at
60°.
Experiment
No. 68.
The kaleidoscope.
The
kaleidoscope (Fig. 88) consists of two mirrors at an angle of 30°
in a tube which has an eye opening at one end and at the
other a chamber containing pieces of col-
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ored
glass. When you look through the tube and revolve it, the colored
pieces of glass make beautiful twelve-sided figures by multiple
reflection.
Illustrate
the working of the kaleidoscope as follows: Draw two lines at
an angle of 30°
on a piece of white paper. Stand the mirrors on a block above these
lines with the angle toward a good light (Fig. 89). Now put pieces of
colored paper and other small objects on a strip of paper and draw the
paper under the angle, while you look down between the mirrors with
your eye near the angle. Do you see a series of twelve-sided figures?
ILLUSIONS
The Sphinx.
This illusion shows an Egyptian head without a body (Fig. 90). The
hypnotist shows the audience an empty box with a glass front. He closes
and locks the door over the front, places the box exactly on the center
of the table, unlocks it, opens the door, and, behold, there is an
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Egyptian
head in the box. The hypnotist stands near the audience and addresses
the head. "O ancient Sphinx, awake! Awake! Awake !" The sphinx slowly
opens its eyes and stares straight ahead. The hypnotist then addresses
questions to it and it answers in very deep and very dead tones, and so
on. Finally the hypnotist locks the box, brings it forward to the
audience, opens it, and there is nothing in it but a handful of ashes.
The
mechanism of this illusion is illustrated in Fig. 91. The table is on
three legs. A, B, C,
with mirrors at 60° between A,
C, and A,
B. The curtains at the back and sides are exactly alike,
and to the
audience the images of the side curtains appear to be the back curtain,
and the space under the table appears quite empty.
Cabinet of Proteus.
The performer puts his assistant into the cabinet (Fig. 92), closes the
doors a moment, makes passes, open doors (Fig. 93), and the assistant
is gone. Closes doors again, makes passes, opens doors, and out comes
an entirely different man. Closes doors again, makes passes, opens
doors, and out comes a lady. Closes doors again, makes passes, opens
doors,
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and
out comes
assistant. To the audience, the cabinet appears entirely
empty
except for a post, C, with a strong light at the top. There are,
however, two hinged mirrors, ab and ab. Fig. 94, at an angle of 60° and
the post covers the angle. The sides and back are exactly alike and the
images of the sides in the mirrors appear to the audience to be the
back. The man, lady, and assistant, of course,
hide behind the mirrors. Members of the audience stand behind
and
beside the cabinet all through the performance. The assistant swings
the mirrors against the sides before be comes out the last
time, and then members of the audience are asked to examine the
cabinet, when, of course, they find nothing.
Illusion Show.
Pharaoh's thumb. Make a table out of cardboard (Fig. 95) and stand it
on three legs, each of which is exactly 5 1/4 inches from the other
two, and place your two mirrors between A and B and A and C. Surround
it by screens on three sides, making the sides and
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63
back
exactly alike and exactly the same distance from the table.
Now
have an assistant put his arm through a hole in the back curtain and
put his blackened thumb up through a hole in the table top, and you are
ready to begin the act.
Explain to the audience
that you have
succeeded in bringing to life the thumb of an ancient pharaoh by your
hypnotic power. Explain that the thumb was lost in battle, fell on the
sands of the desert and dried but did not decompose. This pharaoh was a
great hypnotist, which makes it easier for you to bring his thumb back
to life. Explain also that the thumb will answer any question about the
future. If the thumb moves forward it is, yes; if it doesn't move at
all it is, no.
Now open the curtains, address the
thumb, "O
Thumb of an ancient Pharaoh, awake! Awake! Awake!" (slowly and with
passes). The thumb does not move. You now ask, "O ancient and sacred
Thumb, will Charles get his wish?" (Thumb slowly nods, yes.) "O ancient
and sacred Thumb, will Henry get through his examinations?" (Thumb does
not move. No.) And so on.
Vaudeville Act.
The
acrobat. You can put on a short but very funny act with a mirror (Fig.
96) placed at an angle to the audience.
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FUN
WITH THE CURVED MIRROR
Experiment
No. 54.
Converging
sunlight.
Open
the slit in your darkened room to its full size and allow the sunlight
to fall on the concave (curved-in) side of your curved mirror. Make a
dust. Is the sunlight converged to a point and does it diverge beyond
this point (Fig, 97) ? This point is the focus of the mirror.
Experiment No. 55.
Diverging
sunlight.
Turn the convex
(curved-out) side of the mirror to the sunlight (Fig. 98). Is the
sunlight reflected and diverged or spread?
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65
Experiment No. 56.
Picture of
the sun.
Remove
the shutter, stand the mirror on the table in the sunlight, and focus
the sunlight on a strip of paper 1/2 inch wide (Fig. 99). Is the
picture of the sun round and very bright?
Experiment No.57.
The focus is
very hot.
Focus
the sunlight on your hand with the concave mirror (Fig. 100). Is it
hot? It is, because all the heat of the sunlight is concentrated at the
focus.
Experiment No. 58.
To
light a match with sunlight.
Place
a match in front of a narrow strip of paper (Fig. 101) and focus the
sunlight on the head. Does the match light?
Experiment No. 59.
A magic
cannon.
Stick
a needle into the under side of a cork and stick a match on the other
end of the needle (Fig. 108), with a small piece of paper at one side
of the head. Insert the stopper in an empty bottle, focus the sunlight
on the match head through the glass sides (Fig. 103). Does the match
light and are the cork, needle, and match driven out with a
satisfactory pop?
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ENGINEERING
The lighted
match heats the air and the expanding air drives out the cork.
Experiment No. 60.
Focal
length of concave mirror.
Focus
the sunlight on a narrow piece of paper and measure the
distance
between the back of the mirror and the paper. This is the focal length
of the mirror. Do you find it to be about two inches ?
Experiment No. 61.
Focal length
of convex
mirror.
Make
two pencil dots just 3 inches apart on a piece of cardboard and between
these punch two holes just 1 inch apart. Hold the cardboard between the
convex mirror and the sun and move it until the light which passes
through the holes 1 inch apart is reflected to the dots 2 inches apart,
and measure the distance from the back of the mirror to the card. This
is the focal
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length
of the convex mirror. Do you find it to be 2 inches?
There
is no real focus for a convex mirror because it spreads the
light, but the reflected rays appear to come from a point 2 inches
behind the mirror. An unreal focus of this kind is called a
virtual focus.
Experiment No. 62.
Pictures.
Go
to the back of the room, turn the concave mirror toward the window, and
hold a piece of paper three-quarters inch Wide near the focus (Fig.
104). Do you find a small inverted picture in natural colors of the
window and of the things outside the window?
Have
a
friend move about near the window. Do you get his picture?
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Experiment
No. 63.
Your own
image.
Look
at yourself in the concave mirror. Are you upside down and small? Bring
your eye closer to the mirror than the focus (3 inches) (Fig. 105). Is
your eye large and right side up? Look at yourself in the convex side.
Are you small and right side up in all cases?
THE "WHY" OF THE CURVED MIRRORS
Waves.
When parallel waves (1), Fig. 106, strike the concave side of the
mirror, they are reflected and so curved in that they converge at the
focus and then diverge.
When parallel waves strike
the convex side (2), they are reflected and so curved out that they
diverge and never meet.
Rays.
The curved mirror is part of a sphere and the center of the sphere is
at C, Fig.
107(1). The lines CA
are radii of the sphere and they
are perpendicular to the mirror. When parallel rays strike the concave
mirror they make equal angles with these perpendic-
GILBERT
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ular
radii and cross at the focus
F. The line through the center O of the
mirror and through the center C
of the sphere is called the principal
axis of the mirror. You will notice that the parallel
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rays
which are above the principal axis before they strike the concave
mirror are below it afterward and vice versa. This explains why the
images you see in the concave mirror are reversed.
When
your
eye is nearer than the focus, it intercepts the rays before they can
cross, and your image appears to be behind the mirror, right side up
and large.
When parallel rays strike the
convex side of
the mirror. Fig. 107 (2), they make equal angles with the radii (CA
extended); they diverge but appear to come from the focus F. This is
the unreal or virtual focus.
The rays above the
principal axis
before reflection are above it afterward, and, therefore, the images in
the convex mirror are right side up.
Searchlight Reflectors. The
reflectors on battleship searchlights (Fig. 108) are made in the shape
of a parabola (Fig. 109). Parallel rays which strike parabolic
reflectors converge exactly at the focus, and conversely if a light is
placed exactly at the focus the reflected light consists of parallel
rays which go straight forward. The reflectors on automobile and
locomotive headlights are also parabolic, and the lamp is placed at the
focus.
Spherical Aberration.
Spherical mirrors do not converge all parallel rays at the focus
because those which strike near the edge are reflected behind the
focus (Fig. 110). This is called the spherical error or spherical
aberration of the mirror. Conversely if a light is placed at its focus
a spherical mirror does not reflect it in parallel rays. This explains
why it is not used as a first-class reflector.
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REFRACTION OF LIGHT
When
light passes in a slanting direction from one medium to another, - for
example, from air to water or the reverse, or from air to glass or the
reverse, - part of it is reflected at the surface between the two media
and part of it enters the second medium but is bent out of its path,
from ABC to
ABD, Fig.
111. This bending is called refraction. When
light passes from air to any denser medium as water or glass, it is
bent toward a line NN
drawn perpendicularly through the surface at the
point it enters. See Fig. 112 (1). When light passes from water or
glass to air, it is bent away from the perpendicular NN. See Fig. 112
(2).
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FUN WITH SUNLIGHT
Experiment
No. 64.
Air to water.
Allow
a beam of sunlight to pass through the slit in your darkened room. Cut
a slit 1 inch long and 1/4 inch wide in a piece of cardboard, put this
over your mirror, and reflect sunlight into a glass pitcher full of
water into which you have put 2 or 3 drops of milk (1), Fig. 113. Vary
the slant of the beam of sunlight which strikes the water and view the
beam in the water through the sides of the pitcher. Is some of the
light reflected at the surface of the water? Does some of it enter the
water and is it bent or refracted? Make the beam split on the side of
the pitcher so that half is inside and half outside. Is the beam in the
water bent toward an imaginary perpendicular at the point it enters?
Repeat this with a glass of milky water (2). Repeat with a bottle of
milky water (3). Use a bottle with flat sides.
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Experiment
No. 65.
Air to glass.
Make
the beam split on the thick glass plate standing on its edge, on two
matches, on paper (Fig. 114). You cannot see the light in the glass but
you can see it on the paper below after it has passed through the
glass. Is the light which passes through the glass bent toward an
imaginary perpendicular NN
drawn at the point it enters?
Let
the sunlight enter through a slit 1 inch long and 1/4 inch
wide.
Split the beam of light on the edge of the glass plate and hold a piece
of paper behind the plate. Tilt the plate to different angles. Is the
light which passes through the glass plate always bent toward the
perpendicular NN?
Experiment No. 66.
A
glass of water.
Remove
your shutter and stand a glass of water in sunlight near the window;
fill the glass to the top and put paper around the sides to keep out
the sunlight. Is the sunlight which strikes the water
GILBERT
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75
surface bent
down, as shown in Fig. 116?
Explanation of Refraction.
A beam of sunlight is bent or refracted when it passes from air to
water because light travels more slowly in water than it does in
air. Its velocity in water is only three-fourths of its
velocity
in air.
Now to see the connection between change
in direction
and change in velocity, let us consider what would happen if
a
regiment of soldiers marched in a slanting direction BD from smooth
ground to rough ground, as shown in Fig. 116. The men would march less
rapidly on the rough ground and the direction of the marching lines
would be changed. The line AB
is still on smooth ground and is
straight. Part of the line ab
is on rough ground and this part is
somewhat behind. The line cd
has a larger part on rough ground and this
part is behind. The line CD
is wholly on rough ground and it is
marching in a direction DE
different from BD,
and it would continue in
this new direction. This is exactly what happens to parallel light
waves. They are bent towrard the perpendicular when they pass at a
slant from air to water or glass because they travel more slowly in
water or glass than they do in air. They are bent away from the
perpendicular when they pass at a slant from water or glass to air
because they travel faster in air than they do in water or glass.
REFRACTION OF SPHERICAL WAVES
Experiment No. 67.
A coin under
water.
Put
a coin in a glass of water and look down at it through the water (Fig.
117). Does it appear to be nearer than it really is?
You
see the coin because light passes from it to your eyes. This light is
in the form of spherical waves in the water, but
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