76 GILBERT BOY
when these waves enter the
air they become more curved (see BC, Fig. 118) because the parts which
enter the air first travel faster and get ahead of the parts
still in water.
Now your eye estimates the
distance of an object partly by the curvature of the
waves which enter it from the object. The curvature of the
waves which enter your eye from the coin is the same as
though the coin were at a point A only three-fourths the depth, and this is
the reason the coin appears to be at A.
If you look at the coin in a slanting direction, it appears
to be nearer the surface still, because the light is bent
more and more the greater the slant of the rays from the
coin to the surface.
RELATION BETWEEN ANGLES OF REFRACTION AND INCIDENCE
If the light ray in Fig. 119 is passing from air to water,
then the line
RM is always exactly three-fourths the
length of IM no
matter how large or small i
may be. If the light passes in the opposite direction, the
same relation holds until the critical angle is reached.
(See page 87 for definition of critical angle.)
If the ray is passing from
air to glass, RM
will always be two-thirds of IM, and this relation holds if the light
passes from glass to air, until the critical angle is
This gives you the relation between the angle of incidence
and the angle of refraction in all cases.
FUN BY DAY OR NIGHT
Experiment No. 68.
Magic lead pencil.
Put a pencil in a glass of
water in a slanting direction and sight along it (Fig. 120).
Does it appear to be bent up? It does, because the light
from it is bent as shown in Fig. 121.
Experiment No. 69.
Put a ruler vertically in a pitcher of water to a depth of 4
78 GILBERT BOY
inches (Fig. 122). Does the
part under water appear to be only 3 inches long when viewed
vertically? It does, because light travels in water only
three-fourths as fast as it does in air.
Does it appear much shallower when viewed at a slant? It does,
because light is bent more the greater the angle at which it
leaves the water.
Experiment No. 70.
An elastic ruler.
Shove the ruler to the
bottom of a pail of water and lift it out Does it appear to
Experiment No. 71.
Stand a ruler at one end of
the glass prism held on one edge. Fig. 123 (1). Does the
bottom appear only two-thirds its real depth when viewed
vertically? It does, because light travels only two-thirds
as fast in glass as it does in air.
Does it appear even shallower when viewed at a slant? It
does, because light is bent more the greater the angle at
which it leaves the glass. Repeat this with the prism on
Repeat with the glasg plate on its edge. Fig. 123 (2).
Experiment No. 72.
Fill a long, deep pan with water. Put a coin on the bottom and
view it vertically and then
at greater and greater slants. Does the coin seem to rise?
Experiment No. 73.
Stand a coin on edge in a
tin funnel full of water, ask a friend to stand so that he
can just see the top over the edge of the funnel, and then
let the water run out. Does he find that he can no longer
see the coin from where he stands ? Why ?
Experiment No. 74.
A broken looking-glass.
Play this trick on your
family. Take a piece of soap and mark a star with radiating
lines near one edge of a looking-glass (Fig. 124). The
family will think the glass is broken. A real break shows up
because the light is refracted at the break and this gives a
Where is the Fish?
The three boys 1, 2, and 3 in Fig. 135 are
looking at the same fish and they see it at the three
different positions 1, 2, and 3, because the light
from the fish is bent more the greater the slant it has when
it reaches the water surface. None of them see the
fish where it is.
GILBERT BOY ENGINEERING
How Deep is the Water? If you have gone
swimming in very clear water you know that it always looks
shallower than it is. If the water is at the same depth
everywhere it will look to you shallower in the distance,
for the reasons given above.
How Tall are You to a Fish?
If you are 6 feet tall a fish (Fig. 186) sees you as 8 feet
tall, because the curved waves from you are made less curved
in water and, therefore, appear to come from a more distant
Experiment No. 75.
Breaking a pencil without touching it.
Look at a pencil in a
slanting direction through a bottle of water with flat sides
or through the edges of the glass plate.
Does it appear to be broken into three parts? Why?
82 GILBERT BOY
Experiment No. 76.
Put the glass plate flat on
a piece of paper on the table. Stick the pins A, B on each
side (Fig. 127) and sight from pin A to B through the glass.
Does B appear to be shifted? Draw lines around the edges of
the plate, aim a ruler at the two pins through the glass,
and draw a line along the ruler; then draw a line from B to
A and draw a line perpendicular to the edge of the plate at
A. This shows that the light which passes from B to A in
glass is bent away from the perpendicular when it enters
Experiment No. 77.
Put the plate on a piece of
paper (Fig. 128) and draw lines around the edge. Now draw a
slanting line AB, sight along a ruler through the glass at
this line, and draw the line CD along the ruler. Is the line
parallel to AB but shifted? Draw perpendiculars at B and C
and draw a line from B to C. The light from A passes into
the glass at B and is bent toward
the perpendicular at B ; it passes from glass to air at C
and is bent away from the perpendicular at C.
Experiment No. 78.
Things are not where they seem.
Look at a lighted candle
through your glass prism (Fig. 129). Does the candle appear
to be in a different place?
Does it also appear to be
beautifully colored? You will experiment with colors soon.
Experiment No. 79.
Bending light around a corner.
Stand the prism on end on
paper and draw a triangle around the end (Fig. 130). Now
draw a line AB
slanting toward one side. Sight along a ruler through the
prism at this line and draw a line CD along the ruler. Now
remove the prism, draw short perpendiculars at B and C, and join BC.
The light from A
enters glass at B
and is bent toward the perpendicular; it enters air again at
C and is bent away
from the second perpendicular. This is why the light is bent
around a comer by your prism.
Experiment No. 80.
To see under water from a boat.
You cannot see things under
water from air usually, because the light reflected from the
surface blinds you to the light coming from beneath the
surface. You can easily see through the sur-
GILBERT BOY ENGINEERING
86 GILBERT BOY
face, however, through a
pipe of any kind, as shown in Fig. 131, because the sides of
the pipe keep the reflected light
out of your eyes. Try this with a pipe 2 or 3 feet long.
Experiment No. 81.
To see the fish you are trying to catch.
If you can fish under a
boathouse or under a wharf, you can see the fish deep down
under water because the house or wharf prevents surface
reflection. You can do this also as follows: Stretch a
blanket or tarpaulin between two boats and put your head
under it. The surface reflection is removed and you will be
able to see to great depths.
Spotting Submarines. Submarines are easily
spotted at great depths from a dirigible or airplane at a
great height above the surface (Fig. 132) because at these
great heights the light re-
flected vertically upward is
not so great as the vertical light received from objects
beneath the surface.
When light passes from water to air in a slanting direction
(Fig. 133), part of it is reflected and the part which
passes through is bent away from the perpendicular. As the
slant becomes greater the bending is greater, and finally
the light which passes into air is at right angles to the
perpendicular. If the light in water is still more slanting
when it reaches the surface, it does not pass into air at
all, but is all reflected back into the water. This is
called total reflection. The angle at which this takes place
in water is any angle greater than 48.5°, and in crown glass
and hard flint glass, any angle greater than 41° and 37°
respectively. These angles are called the critical angles
for these substances.
Experiment No. 82.
A phantom pin.
Cut a slice of cork, attach
a pin to the under side, float the cork on the surface of
water in a full glass, stand the glass on the table, and
look at the cork from the level of the table. Can you see a
phantom pin above the cork (Fig. 134)? You see it by means
of light reflected from the under side of the water surface.
Experiment No. 83.
A broken spoon.
Put a spoon in a glass half
filled with water and look at the under side of the water
surface through the side of the tumbler. Do you find a
brilliant image of the part of the spoon in water? You see
this by light reflected at the under surface.
Prism Glass. These prism glasses, Figs. 136
(1) and (2), are used to throw light to the rear of a store,
or from the sidewalk into the basement. They are made of
glass and have prisms on one side. The light which enters
them is totally reflected from the inside surface
88 GILBERT BOY ENGINEERING
of the prisms and is directed to the back of the building or
Right-angled Prisms. These are made of glass
and act as mirrors, in some opera glasses and other optical
instruments. Light which enters one right-angled face, AC,
Fig. 136, is totally reflected at the slanting face and
passes out through the other right-angled face BC.
Mirages. A ship at sea sometimes appears
upside down (Fig. 137) because the air near the cold water
is colder and denser than the air above and the light from
the ship is refracted as it passes from each layer of cold
air to the warmer layer above and is finally totally
reflected. The light which enters the sailor's eye appears
to come from the image above.
Mirages on the hot deserts are caused by light from the
clouds which passes from the
upper cold air through warmer and warmer lower layers. It is
refracted and finally totally reflected and the clouds look
like a lake of water on the ground.
Sunset and Sunrise. You
the sun before it is up and after it has set because
light from it is refracted by successive layers of air which
are denser the nearer they are to the earth.
The direct ray SD, Fig. 138, could not
be seen at A because the earth is in the way, but the light
SB is seen because
it is refracted to A.
Spectrum. When a beam of sunlight passes
through a glass prism as shown in Fig. 139, it is spread out
into a colored band called the spectrum. This spectrum
contains all the primary colors, of which those most easily
ognized are in order: red, orange, yellow, green,
blue, indigo, and violet.
90 GILBERT BOY
White Light made up of all Colors. The
experiment above shows that white light is made up of lights
of all primary colors. This is proved again by passing the
spectrum through a prism turned in the opposite direction
(Fig. 140); the colors are recombined to produce white light
It can be proved also by
turning the prism back and forth quickly (Fig. 141). The
colors overlap at the center and produce white light.
Dispersion. You know
that light is refracted or bent when
it passes from air to water
or glass or the reverse, because it travels more slowly in
water and glass than it does in air. Now the waves of red
light are longer than those of orange, the waves of orange
are longer than those of yellow, and so on, the waves of
each light beginning at the red end of the spectrum are
longer than those next to it until we get to the very
shortest, namely, the waves of violet light. It has been
found by experiment that the shorter the waves, the more
slowly they travel in water or glass and, therefore, the
more they are refracted or bent when they pass from air to
water or glass, or the reverse. When white light passes
through a prism then, the shorter waves are bent
92 GILBERT BOY
or refracted more than the
longer waves and as a result the white light is spread out
into the spectrum. This spreading of light is called dispersion.
Spectrum by Reflection. Another beautiful
method of producing a spectrum is illustrated in Fig. 142. A
mirror is placed in a slanting position under water in a pan
and a beam of sunlight is allowed to fall on the mirror. The
sunlight, in going through the water to the mirror and back,
really passes through a prism of water and it is spread out
or dispersed into a beautiful spectrum.
If, after the spectrum is formed, the surface of the water
is stirred, the colors of the spectrum are mixed and the
reflected beam is white. This proves again that white light
is made up of all the colors of the spectrum.
Interference. In a water wave the particles
of water simply move up and down, but the wave moves
forward. A wave length is a hill and a hollow. If, now, two
waves of exactly the same length come together in such a way
that one is one-half wave behind the other (Fig. 143), the
hill of one coincides with the hollow of the other, the
particles of water do not move at all, and one wave destroys
the other. This is called interference.
The same thing occurs in light waves; two streams of waves
may come together and destroy each other, that is, produce
Colors by Interference. If a beam of
sunlight is allowed to fall on a soap film held in a
vertical position on the end of a lamp chimney (Fig. 144),
it is found that the soap film when viewed by reflected
light is crossed by horizontal colored bands. These
colors are formed by interference as follows: The soap film
has two surfaces with water between, and when it stands on
edge the water runs toward the bottom and the film becomes a
narrow prism. Now the light is reflected partly from the
front film and partly from the back film, and where the
films are 1-4, 3-4, 5-4 waves of red light apart, the red
waves from the rear are 1-2, 1 1-3, 3 1-3 waves behind the
red waves from the front when they enter your eye. These two
sets of waves, then, interfere and destroy each other, and
all that your eye sees is blue. Similarly a little above and
below these points the blue waves destroy each other, and
you see red light
FUN WITH SUNLIGHT
The prism spectrum.
Allow a beam of sunlight to pass through
94 GILBERT BOY ENGINEERING
the slit in your darkened
room and fall on the prism supported between blocks as shown
in Fig. 145. Cut a piece of cardboard of the exact size of
one face of the prism and put it on the upper face. Do you
find a beautiful spectrum on the wall or ceiling. Do
you find that the violet end is nearest the base of the
prism and the red end nearest the angle, that is, is the
violet end the most bent? Turn the prism over. Do you get a
spectrum on the floor?
Get the spectrum on the wall
or ceiling again and rock the prism quickly. Is the center
of the spectrum white? This proves that white light is made
up of all spectrum colors because they mix at the
Experiment No. 85.
Spectrum by reflection.
Place a mirror in a slanting
position under water and arrange it so that the beam of
sunlight falls on the mirror (Fig. 146). Do you find a
beautiful spectrum on the wall above the slit? Stir the
water. Do the colors mix and produce white light?
Experiment No. 86.
Make soap suds as yon would
for blowing soap bubbles. Put the suds in a saucer. Dip the
end of a lamp chimney in the suds and support the chimney on
its side in sunlight (Fig. 144). Look at the film by
reflected light. Do you find that the film at the top is
crossed by beautiful horizontal colored bands? These colors
are produced by interference. The colors in a soap bubble
and in a fihn of oil on water are produced by interference.
WHY OBJECTS ARE
An object has a certain
color because something in the object absorbs all other
colors. For example, a blue dress is blue because the dye in
the dress absorbs all the other colors of the spectrum. Also
a red dress is red because the dye absorbs the colors in the
blue end of the spectrum, and so on.
An object is white when all of the colors of the spectrum
are partly absorbed and all are reflected.
An object is black when all the colors are completely
absorbed and none reflected.
Experiment No. 87.
Darken your room and allow
sunlight to enter through a slit smaller than your
colored-glass plates. Hold the red glass over the slit and
hold colored objects in the. red light. Are red objects red,
but all other colored objects dark or black? They are dark
or black because the dye in them absorbs the red light.
Repeat with the blue glass. Are the results similar?
Note. The blue glass
lets through a little red, yellow, and green, as you will
Experiment No. 88.
Get the spectrum with the
prism and then put the red glass against the prism. Does the
red glass absorb all colors except red? Repeat with the blue
glass. Does it absorb nearly all colors except blue, but
does it let through a small amount of the other colors?
Experiment No. 89.
colors in spectrum.
Get the spectrum with the
prism and hold colored objects in the different colors. Do
they change colors according to the part of the spectrum
they are in? They are black in the part of the spectrum
which they absorb completely.
FUN BY DAY OR NIGHT
Experiment No. 90.
A colored strip.
Cut a strip of white paper about 1-16 inch wide and 2 inches
long and pin it to a
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black object. Put it in a
good light and look at it through the prism (Fig. 147). Do
you find a spectrum instead of the white paper?
Do you find also that the
spectrum is reversed, that is, that the red is nearest the
base of the prism and the violet nearest the angle? This is
so because your eye sees an object in the direction the
light enters it from the object The red is least bent but
appears to be most bent, and the violet the reverse.
Experiment No. 91.
Cut a strip of white paper 1
inch wide and 2 inches long and look at it through the prism
(Fig. 148). Do the edges appear colored, but is the center
white? The center is white because the spectra formed by the
edges overlap at the center and this combination of all the
colors of the spectrum produces white light.
Experiment No. 92.
Colored candle flame.
Look at the flame of a
candle through a prism. Is it beautifully colored, but
does the center tend to be white and are the colors
reversed as above?
Complementary colors are
those which, when combined, produce white light. If any
colors are taken out of the spectrum, the remaining colors
are complementary to those taken out, because together they
produce white light
A paint which absorbs the colors in the blue end of the
spectrum is red in color and a paint which absorbs the colors
in the red end of the spectrum is blue in color. If, now,
these paints are mixed, they do not produce white paint but
black paint because together they absorb all the colors.
FUN WITH SUNLIGHT
Experiment No. 93.
Stand the red and blue
glasses side by side on a piece of white paper in sunlight.
The red absorbs the blue end of the spectrum and lets
through red light The blue absorbs the red end of the
spectrum and lets through blue light. Now place one behind
the other. Do they absorb all the light and is the shadow
The rainbow (Fig. 149) is
formed by the internal reflection and dispersion of sunlight
by falling drops of water. You see it when the sun is behind
you and not over 48° above the horizon. The first or primary
rainbow is formed by two refrac-
98 GILBERT BOY
tions at A and C and one internal
reflection at B (2);
is violet below and red above and the angle at which the
light enters your eye is about 4° to the direction of the
sunlight. The secondary rainbow is formed by two refractions
A and D and two
internal reflections B
and C (3); it is
red below and violet above and the angle of the light is
Experiment No. 94.
An artificial rainbow.
Place a glass full of water
(Fig. 160) on a table in sunlight and projecting beyond the
edge. Do you get two or more beautiful rainbows on the
floor? Stand the glass on a mirror. Do you get two beautiful
rainbows on the ceiling? These bows, however, are not
experiment will show best in your darkened room.
FUN AT NIGHT
A changing devil.
Cut a little devil out of
cardboard and arrange as shown in Fig. 151. Hold the red
glass in front of the candle at the right. Is the devil at
the right red and is the devil at the left very dim but of
the complementary color, green? Use blue glass. Is one devil
blue and the other very dim but of the complementary color,
Experiment No. 96.
A tricolored star.
Fold a piece of cardboard.
Cut a four-pointed star in one half. Fold the points back,
make a tracing on the other half, and cut out a star very
carefully with the points exactly between those of the
first. Arrange as shown in Fig. 158 and hold the red glass
in front of one candle. Do you get an eight-pointed star
with the points alternately red and green and with a white
or pink eight-pointed star inside? Repeat with the blue
glass. Are the star points blue and orange?
GILBERT BOY ENGINEERING
Experiment No. 97.
A ghost party.
Mix a half teaspoonful of
salt in three or four teaspoonfuls of alcohol in a saucer,
stand the saucer on a cup on the table (to prevent burning
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