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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
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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
reached.
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.
Magic ruler.
Put
a ruler vertically in a pitcher of water to a depth of 4
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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 appcar 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 stretch?
Experiment No. 71.
Magic glass.
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 end.
Repeat
with the glasg plate on its edge. Fig. 123 (2).
Experiment No. 72.
Phantom coin.
Fill
a long, deep pan with water. Put a coin on the bottom and view it
vertically and then
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at greater
and
greater slants. Does the coin seem to rise? Why?
Experiment No. 73.
A
disappearing coin.
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 fair imitation.
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.
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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 point.
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?
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Experiment
No. 76.
Shifting pin.
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 air.
Experiment No. 77.
Shifting
line.
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
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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-
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face, however,
through a pipe of any kind, as shown in Fig. 131, because the sides of
the pipe keep the refiected 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-
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flected
vertically upward is not so great as the vertical light received from
objects beneath the surface.
Total Reflection.
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
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of
the prisms and is directed to the back of the building or basement.
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.
ATMOSPHERIC REFRACTION
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
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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
see 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.
COLOR
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
rec-
ognized are in order: red, orange, yellow, green,
blue, indigo, and violet.
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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
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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
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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 darkness.
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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
Experiment
No.84.
The prism
spectrum
.
Allow
a beam of sunlight to pass through
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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 center.
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.
Colors
by interference.
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.
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WHY
OBJECTS ARE COLORED
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.
Changing
colors.
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 now show.
Experiment No. 88.
Changed
spectrum.
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.
Changing
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.
Combining
spectra.
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?
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COMPLEMENTARY
COLORS
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
MIXING PAINTS
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.
Colored
glasses.
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 black?
THE RAINBOW
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-
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tions
at A and C and one internal
reflection at B (2);
it 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
about 52°.
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 reversed. This
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experiment
will show best in your darkened room.
FUN AT NIGHT
Experiment
No.95.
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, orange?
Experiment No. 96.
A tricolored
star.
Fold
a piece of cardboard. Cut a four-pomted 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?
100 GILBERT BOY ENGINEERING
Experiment No. 97.
A ghost
party.
Mix
a half tcaspoonful of salt in three or four teaspoonfuls of alcohol in
a saucer, stand the saucer on a cup on the table (to prevent burning
the table),
"The
Science Notebook" Copyright 2008-2011 - Norman Young
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