Physics 1230: Light and Color
Geometrical optics - how does light change direction?
•  Reflection (mirrors, seeing your image)
•  Refraction (bending light, light in water)
http://www.colorado.edu/physics/phys1230
Refraction
Ever notice how your leg looks bent
as you dangle them in the water
from the edge of a pool? Why do
fish seem to radically change
position as we look at them from
different viewpoints in an
aquarium? What makes diamonds
sparkle so much?
These are all questions that can be addressed with the concept of
refraction. Refraction is the bending of light when it goes from one
transparent medium to another (e.g. air-to-glass or air-to-water). This
meeting place of two different media is called the interface between the
media. All refraction of light (and reflection) occurs at an interface.
Examples of Refraction
•  Bending of light in glass
•  Mirages
•  Total internal reflection
•  Fiber optics
•  Sparkle of diamonds
Demonstrations
•  Refraction e.g. stick in tank of water, pencil in glass of water
•  Total internal reflection - light pipe
Changing the speed of light - refraction
Refractions occur because the speed of light changes (slows down)
when the light enters a “denser” material
Applet on Speed of Light
http://micro.magnet.fsu.edu/primer/java/
speedoflight/index.html
Optical Density of selected materials
Question: What determines if one material is more or less
dense than another from the point of view of light?
Answer: The speed of light is slower in denser materials
We define the index of refraction n of a substance as n=
speed of light in vacuum
speed of light in substance
So n = c/v or v = c/n
Optical density is characterized by the
Index of Refraction
Index of Refraction of
Selected Materials
• Vacuum
1.00000000000..
• Air
1.0003
• Water
1.333
• Glass
1.5 (depends on type)
• Diamond 2.4
Speed of light in different materials
Speed of visible light in different media.
The value of 100% refers to the speed of light in vacuum.
http://acept.la.asu.edu/PiN/rdg/refraction/refraction.shtml
Speed of light in different materials
Applet on Speed of Light
http://micro.magnet.fsu.edu/primer/java/
speedoflight/index.html
Light slows down in denser materials
•  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
Applet on Refraction
http://acept.la.asu.edu/PiN/rdg/refraction/refraction.shtml
Law of Refraction
•  Light going from a substance of small n to a substance of large n
is bent TOWARD the normal
•  Light going from a substance of large n to a substance of small n
is bent AWAY from the normal
Normal
Air (fast medium)
Glass or
water
(slow)
Normal
Diagram works in
either direction
nair < nwater
1.001 < 1.5
Air (fast medium)
Glass or
water
(slow)
Law of Refraction
•  Light going from a substance of small n to a substance of large n
is bent TOWARD the normal
•  Light going from a substance of large n to a substance of small n
is bent AWAY from the normal
incident
rays
glass or water
(large n)
air
(small n)
refracted
rays
Diagram works in
either direction
Refraction - Real Depth and Apparent Depth
Ray-bending together with our psychological straight-ray
interpretation determine the location of images underwater
•  The precise amount of bending
is determined by the
Law of Refraction
(also called Snell's law):
normal
image of fish for
someone above
the water
ni sinθi = nt sinθt
•  Here, θi = angle between incident
ray and normal,
•  and θt = angle between transmitted
ray and normal
•  ni and nt are the indices of
refraction in the medium containing
the incident ray and in the medium
containing the transmitted ray
•
YouTube Video of Archer Fish
•
YouTube Video of Refraction
transmitted
ray
incident
ray
fish
•  In order to observe the fish from
outside the water a transmitted ray must
enter your eye.
•  You will think it comes from a point
obtained by tracing it backwards,
•  Extend any 2 of the many, many
transmitted rays from the nose of the fish
backwards to find the image of the nose
of the fish (where they intersect).
•  The location of that image will be the
same for any observer outside of the
water.
Concept Question: Index of Refraction
Material
Index
• Vacuum
1.00..
• Air
1.0003
• Water
1.333
• Glass
1.5 (depends on type)
• Diamond
2.4
The ray shown here will bend
most if the second medium is
A.  Air
B.  Glass
C.  Water
D.  Diamond
normal to surface
ray
Air
APPLET ON REFRACTION
Applet on Refraction
http://micro.magnet.fsu.edu/primer/java/
scienceopticsu/refraction/
refractionangles/index.html
Underwater at the Great Barrier Reef, Australia
why can’t you see the sky?
TOTAL INTERNAL REFLECTION
•  Total internal reflection happens when light is
incident from a more dense medium to a less dense
medium at a large angle of incidence
•  Examples: light going from glass-to-air or from
water-to-air
•  As the angle on the water side increases, the angle
on the air side eventually goes past 90 degrees,
which means that the light stays in the water! This
happens at the critical angle
•  For incident angles in glass/water greater than the critical angle, ALL the
light is reflected back into the dense substance
Just below the critical angle for total
internal reflection there is a reflected
and a transmitted (refracted) ray
Normal
Glass or
water
(slow)
Just above the critical angle for total
internal reflection there is a reflected ray
but no transmitted (refracted) ray
Air (fast medium)
Normal
Glass or
water
(slow)
TOTAL INTERNAL REFLECTION
Applet on Critical Angle
http://micro.magnet.fsu.edu/primer/java/
refraction/criticalangle/index.html
TOTAL INTERNAL REFLECTION
Total internal reflection occurs when light rays incident at angles to the normal
at greater than the critical angle (here, 41° for glass to air) do not leave the
material and are reflected at the glass/air interface.
http://acept.la.asu.edu/PiN/rdg/refraction/refraction2.shtml
DIAMONDS ARE FOREVER….
•  The index of refraction for diamond is very high compared to ordinary glass
(2.4 versus 1.5)
•  As a result, the critical angle for light to be reflected totally as it travels from
diamond-to-air is small (24° versus 42° for regular glass). Therefore most light is
re-reflected back from a diamond, and dispersion separates the colors. This gives
the characteristic fire or brilliance to a diamond
The cut of the diamond determines its brilliance
Marcel Tolkowsky (1919)
http://www.tradeshop.com/master/ideal.shtml
MIRAGES
MIRAGES
•  Mirages are formed when a layer of hot air forms close to the ground
•  This hot air is less dense than the cold air above it - and therefore has
a lower index of refraction (e.g. 1.0002 versus 1.0003)
•  Light refracts gradually as it enters the hot, less dense layer,
continually bending away from the normal
•  This gives rise to mirages (e.g. water on hot road or in desert)
Concept Question
Why does the road appear wet in the mirage?
A.  Road is wet
B.  Road surface has melted in the heat
C.  Rays from sky refract and make image of sky
D.  Rays from sky reflect and refract from wet road
Mirages can lead to “reflections” and double images
Atmospheric Refraction
Decreasing density of the atmosphere with height causes
refraction of light from the Sun and the Moon, delaying the
sunset and ”flattening” the heavenly disks. The effect is similar
to that of a mirage but with the less dense air now above.
Mirages can lead to “reflections” and double images
Fata Morgana in Greenland
COMMON MIRAGES
Peary could clearly see the mountain tops of "Crocker Land" across the polar ice
pack, but it was only an Arctic Mirage. (Copyright Lee Krystek, 1998)
http://www.unmuseum.mus.pa.us/mirage.htm
MORE MIRAGES
On June 23, 1744, a phantom army appeared floating above a mountain in
Scotland. Twenty seven people, who later gave sworn testimony to what
they'd seen, watched the strange vision for two hours till it ended with
darkness. In the summer of 1897 in Alaska, an expedition to the wilderness
near Mount St. Elias saw a "Silent City" over a glacier. A member of the
expedition, C. W. Thornton, wrote, "It required no effort of the imagination
to liken it to a city, but was so distinct that it required, instead, faith to
believe that it was not in reality a city." Another witness reported, "We could
plainly see houses, well-defined streets, and trees. Here and there rose tall
spires over huge buildings..."
The above incidents are examples of a startling optical atmospheric effect
known as a mirage. Though we associate mirages with the illusion of distant
water in a desert, the phantom oasis is actually just the simplest example of
this bizarre effect.
http://www.unmuseum.mus.pa.us/mirage.htm
Antarctic Fata Morgana
http://climate.envsci.rutgers.edu/Antarctica/views.html
STILL MORE MIRAGES
A mirage is generated by two layers of air at different temperatures.
Because cold air is more dense than hot air, the boundary between the layers
can reflect light, especially if the light bounces off the boundary at an
extreme angle. The oasis mirage occurs when the air just above the ground
gets hot because the ground heats it.
This effect can commonly be seen on asphalt roads during the summer. The
black color of the road gets the air above it hot very quickly. At the boundary
of the hot and normal air, light is reflected. The viewer no longer sees the
road or desert floor, but light reflected from the blue sky which, because it
is on the ground, looks like water.
A mirage can also be the result of a temperature boundary between layers of
air in the sky. If the boundary is not flat, but curved, the mirage will not only
act as a mirror, but a lens, and magnify distant images. Sir David Brewster
speculated that the phantom soldiers above the mountain were caused by a
mirage that reflected troops on maneuvers on the other side of the mountain
from the witnesses.
Mirages in the sky may also be the source of many UFO reports. The planet
Venus magnified and distorted by a mirage makes a believable flying saucer.
Since the properties of the mirage change with the movement of the air
masses, objects in the mirage may twinkle, jump around, seem to speed away
http://www.unmuseum.mus.pa.us/mirage.htm
or disappear.
MIRAGES AT SEA
When the effect appears above the water, it is often referred to as a Fata Morgana. The
phrase comes from the Italian version of the name of the sorceress Morgan Le Fay from
the legends of King Arthur and Camelot. In ancient times these strange effects were
considered the work of witchcraft. The schooner Effie M. Morrissey was sailing the
North Atlantic on July 17, 1939 when a Fata Morgana appeared. Though the coast of
Iceland was some 320 miles away, Captain Bartlett indicated that it appeared as if it was
only twenty five miles away. "The contours of the land and the snow-covered summit of
the Snaefells Jokull showed up almost unbelievably near." Fata Morganas may also be the
cause of legends about phantom ships that sail the sky. Reports of the ghost ship Flying
Dutchman may well have been the reflection of some distant vessel.
Scientists believe Fata Morganas are most likely to form when the sea is much colder than
the atmosphere. As the water cools the air directly above it, a boundary layer forms.
These types of mirages are most likely to show up after dawn, before dusk or as a storm
is building up. They also tend to favor particular locations. The Straits of Messina,
between Sicily and the Italian mainland, are famous for its Fata Morganas.
When several boundaries of air are involved, a mirage can become even more complex as
the light is reflected and refracted multiple times. This can make natural objects, like
cliffs, appear as city buildings, or castles. This is probably the best explanation for the
Alaskan City mirage, though some contend that it was actually a magnification of the
English city of Bristol some 2,500 miles away.
http://www.unmuseum.mus.pa.us/mirage.htm
MIRAGES AT SEA
http://www.unmuseum.mus.pa.us/mirage.htm
Anther Example of Refraction: Atmospheric Turbulence
when atmospheric refraction is
not homogenous, for example
when there is turbulence in
the air, then celestial objects
appear to shimmer or twinkle
Movie of the Moon
http://www.youtube.com/watch?
v=e1SdC9KnsGg
Dispersion is responsible for rainbows
Dispersion is responsible for rainbows
•  Dispersion causes the spreading of
all of the colors in white light
•  This can be done by a prism to
create a spectrum or by raindrops
to create a rainbow
•  Dispersion occurs because the
speed of short wavelength light
(blues) is slightly slower than that
of long wavelengths (reds) in glass
or water
•  Hence short wavelengths (blues)
bend more towards the normal than
long wavelengths (reds) when
white light enters glass or water
–  Blues also bend more away from
the normal than reds when leaving
glass or water
•
We can understand this by thinking
of the reds as marching soldiers and
the blues as marching children who
get slowed down more than the
soldiers when they enter the mud!
What is the normal to a curved surface and how is it
used to find rays?
•  To find the normal to a
curved surface at a point
where a ray hits that
surface (and will be
reflected or refracted)
–  First draw a tangent line
to the curve (or tangent
plane to the surface)
–  The normal is
perpendicular to that line
or plane and going through
the point
–  Once you have drawn the
normal you can draw the
reflected or refracted ray
How does a single raindrop contribute to a rainbow?
•  White light enters the waterdrop
–  Remember white light contains rays
of all wavelengths
•  The blue ray is refracted closer to
the normal than the red ray
–  Remember light travels slower in
water than in air
•  This greater bending of the blue
ray than the red ray is called
dispersion
–  We have not shown the green,
yellow, and orange rays but they
each bend by amounts more than
the red and less than the blue
•  All of the rays reflect off the
inside of the raindrop and then
undergo another dispersion as they
exit the raindrop
–  The laws of reflection and
refraction are always obeyed
Dispersion occurs
here during refraction
Reflections
white light
comes in
Raindrop
Dispersion occurs
here during refraction
A spectrum of
colors comes out
Double Rainbow in Alaska