Physics 1230: Light and Color
Geometrical optics - how does light change direction?
Reflection (mirrors, seeing your image)
Refraction (bending light, light in water)
Dispersion (rainbows, prisms)
http://www.colorado.edu/physics/phys1230
Each color has a different wavelength and frequency, but the
SAME SPEED in air
http://science.hq.nasa.gov/kids/imagers/ems/index.html
distance λ
speed = c =
= = λf
time
T
Light slows down in materials compared with air
•  Speed in medium = speed in vacuum
n
•  n =
speed of light in vacuum
speed of light in substance
Concept Question
•  Speed in medium = speed in vacuum
n
•  n =
speed of light in vacuum
speed of light in substance
What is the refractive
index of diamond?
A.  1
B.  0
C.  1.5
D.  2.4
Concept Question
Consider light propagating in glass where the index is
n=1.5
What is the speed of light in glass?
A)  3 x 108 m/sec
B)  1.5 m/sec
C)  2 x 108 m/sec
Light slows down in denser materials
this picture shows refraction without
dispersion, as would occur with
monochromatic light
•  Light waves incident on glass change direction and wavelength when transmitted
into the glass because the part of the wave in the medium begins to slow down,
causing the light beam to bend.
•  This is like when a marching band needs to make a turn
http://acept.la.asu.edu/PiN/rdg/refraction/refraction.shtml
Concept Question
Which ray is drawn correctly?
A, B or C?
normal to surface
incident ray
A
glass or water
B
C
Concept Question
Which ray is drawn correctly?
A, B or C?
A
B
refracted rays
normal to surface
reflected
rays
C
glass or water
incident
ray
Concept Question
What is the angle of total internal reflection here?
A)  41 degrees
B)  90 degrees
C)  49 degrees
http://acept.la.asu.edu/PiN/rdg/refraction/refraction2.shtml
Concept Question - Which Color bends more?
If blue light travels slower than red light in glass and other materials,
which color will bend more when it reaches an interface from air to glass?
A.  Red
B.  Blue
C.  Green
Dispersion
•  Dispersion is a kind of refraction in which the amount of bending depends
on the wavelength (i.e., the color)
•  This is because the speed of light in a medium depends on the color
•  In general for glass and similar materials, red light travels faster than
blue light, but both slow down compared with the vacuum
•  Examples are the colors produced by prisms, diamonds and rainbows
Dispersion by prisms
•  In a prism, the amount of bending depends on the wavelength or
color because the speed of light depends on the color
•  In other words, the index of refraction depends on the color
•  Blue light has a higher index of refraction than red light, and
thus is bent (refracted) more
http://csep10.phys.utk.edu/astr162/lect/light/dispersion.html
Dispersion by prisms
•  In a prism, the amount of bending depends on the wavelength or
color because the speed of light depends on the color
•  In other words, the index of refraction depends on the color
•  Blue light has a higher index of refraction than red light, and
thus is bent (refracted) more
incoming light beam
light made up of many colors
Dispersion and Rainbows
What is a rainbow?
The traditional rainbow is sunlight spread out into its spectrum of colors and
diverted to the eye of the observer by water droplets. The "bow" part of the
word describes the fact that the rainbow is a group of nearly circular arcs of
color all having a common center.
Most people have never noticed that the sun is always behind you when you face
a rainbow, and that the center of the circular arc of the rainbow is in the
direction opposite to that of the sun. The rain, of course, is in the direction of
the rainbow.
How Rainbows Work
Light is first refracted
by the raindrops, then
reflected once, and then
refracted once again.
Sunlight
Dispersion causes the angle
of refraction to be different
for blue light than for red
light. This is because the
blue light travels more slowly
in the raindrop than red
light.
What makes the colors in the rainbow?
Rene Descartes and Willebrord Snell had determined how a
ray of light is bent, or refracted, as it traverses regions of
different densities, such as air and water. When the light
paths through a raindrop are traced for red and blue light,
one finds that the angle of deviation is different for the two
colors because blue light is bent or refracted more than is the red light. This implies that
when we see a rainbow and its band of colors we are looking at light refracted and
reflected from different raindrops, some viewed at an angle of 42°; some, at an angle of
40°, and some in between. Why?
This is illustrated in the figure. This
rainbow of two colors would have a width
of almost 2° (about four times larger than
the angular size of the full moon). Note
that even though blue light is refracted
more than red light in a single drop, we
see the blue light on the inner part of the
arc because we are looking along a
different line of sight that has a smaller
angle (40°) for the blue.
http://science.howstuffworks.com/rainbow2.htm
http://astro.temple.edu/~dhill001/MCRain/MCRain.html
Concept Question
When is the sunlight separated into its component colors?
A)  When it first enters the raindrop
B)  When it reflects perfectly from the back of the drop
C)  When it exits the raindrop
Concept Question
Why don’t you see the blue at top and red at bottom of rainbow?
How Rainbows Happen
http://www.rebeccapaton.net/rainbows/index.htm
A.  I can explain this
B.  I don’t know
Why are rainbows bowed?
The rainbow ray for red light makes
an angle of 42° between the direction
of the incident sunlight and the line
of sight. Therefore, as long as the
raindrop is viewed along a line of sight
that makes this angle with the
direction of incident light, we will see
a brightening. The rainbow is thus a
circle of angular radius 42°, centered
on the antisolar point.
Why don't we see a full circle?
A)  Because the earth gets in the
way
B)  Because there is no light to
scatter
C)  This light becomes the second
rainbow
Why are rainbows bowed?
The rainbow ray for red light makes an
angle of 42° between the direction of the
incident sunlight and the line of sight.
Therefore, as long as the raindrop is
viewed along a line of sight that makes this
angle with the direction of incident light,
we will see a brightening. The rainbow is
thus a circle of angular radius 42°,
centered on the antisolar point.
We don't see a full circle because the
earth gets in the way. The lower the sun is
to the horizon, the more of the circle we
see -right at sunset, we would see a full
semicircle of the rainbow with the top of
the arch 42°above the horizon. The higher
the sun is in the sky, the smaller is the
arch of the rainbow above the horizon.
On an airplane, if you look into the clouds
while the sun is behind you, you may be
able to see a full 360° rainbow!
What makes a Double Rainbow?
Sometimes we see two rainbows at once.
What causes this? We have followed
the path of a ray of sunlight as it enters
and is reflected inside the raindrop. But
not all of the energy of the ray escapes
the raindrop after it is reflected once.
A part of the ray is reflected again and
travels along inside the drop to emerge
from the drop. The rainbow we normally
see is called the primary rainbow and is
produced by one internal reflection; the
secondary rainbow arises from two
internal reflections and the rays exit
the drop at an angle of 50° rather than
the 42°for the red primary bow. Blue
light emerges at an even larger angle of
53°. This effect produces a secondary
rainbow that appears higher in the sky
and has its colors reversed compared to
the primary.
the secondary (upper) rainbow
always appears fainter: why?
What makes a Double Rainbow?
Sometimes we see two rainbows at once.
What causes this? We have followed
the path of a ray of sunlight as it enters
and is reflected inside the raindrop. But
not all of the energy of the ray escapes
the raindrop after it is reflected once.
A part of the ray is reflected again and
travels along inside the drop to emerge
from the drop at a different angle. The
rainbow we normally see is called the
primary rainbow and is produced by one
internal reflection; the secondary
rainbow arises from two internal
reflections and the rays exit the drop
at an angle of 50° rather than the 42°
for the red primary bow. Blue light
emerges at an even larger angle of 53°.
This effect produces a secondary
rainbow that appears higher in the sky
and has its colors reversed compared to
the primary.
the secondary (upper) rainbow
always appears fainter: why?
What makes a Double Rainbow?
the secondary (upper) rainbow
always appears fainter: why?
http://mathdemos.gcsu.edu/mathdemos/MCRain/MCRain.html
Making your own rainbows
Get a fine misting sprinkler and set the water pressure high enough to get a large
volume of water droplets in the air.
* Where should you stand with respect to the water and the sun?
* Find the shadow of yourself on the ground. Try to measure the angle from the
shadow of your head to the rainbow arc. Use the "hand and fist" method to
measure this angle: if you stretch out your arm and make a fist, the width of your
fist is about ten degrees.
Crazy Sprinkler Lady
http://www.youtube.com/watch?
v=ck7A9vufrX4&feature=related
Concept Question
Can the person see the rainbow?
A.  Yes
B.  No
C.  Maybe
RAINBOW PUZZLER
Rainbows are one of nature's awe inspiring sights. Artists have used
them for inspiration without always understanding the physics behind
a rainbow. The painting below, "Niagara", was painted by Henry
Freeman in 1873. What is wrong with the rainbows in this picture?
http://www.hands-on-optics.org/puzzler/
Galen Rowell: Potala Palace, Lhasa
How did he achieve this
composition?
Rainbows in Art
What’s wrong with this painting?
Heroic Landscape, Joseph Anton Koch
Moonbows: Lunar Rainbows
time exposure taken at 8:30 pm, Victoria Falls, Zambia
Rainbows in Mythology
"There is a pot of gold at the end of every rainbow."
What’s the problem with this proposition?
Rainbows in Religion: Navajo Rainbow Guardian
Isanakleshe (Changing Woman) and
Natseelit (the Rainbow Goddess) and
Sacred Corn
© Sandra Stanton
Navajo sand painting: Father Sky, Mother Earth
enclosed on three sides by Rainbow Goddess
http://www.jedisteve.com/navajo.html
Rainbows and the Story of Noah
Rainbows and the Story of Noah