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

Index of Refraction of Selected Materials

• Vacuum

• Air

• Water

• Glass

• Diamond

1.00000000000..

1.0003

1.333

1.5 (depends on type)

2.4

Optical density is characterized by the Index of Refraction

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

http://acept.la.asu.edu/PiN/rdg/refraction/refraction.shtml

•  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

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

Diagram works in either direction

Air (fast medium)

Glass or water (slow)

Normal

Glass or water (slow)

Normal Air (fast medium)

nair < nwater 1.001 < 1.5

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

glass or water (large n)

Diagram works in either direction

incident rays

refracted rays

air (small n)

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):

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

incident ray

transmitted ray

normal

image of fish for someone above the water

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.

Refraction - Real Depth and Apparent Depth

Material

• Vacuum

• Air

• Water

• Glass

• Diamond

Index

1.00..

1.0003

1.333

1.5 (depends on type)

2.4

Concept Question: Index of Refraction

normal to surface

The ray shown here will bend most if the second medium is A.  Air B.  Glass C.  Water D.  Diamond

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

Glass or water (slow)

Normal Air (fast medium)

Just below the critical angle for total internal reflection there is a reflected and a transmitted (refracted) ray

Glass or water (slow)

Normal

Just above the critical angle for total internal reflection there is a reflected ray but no transmitted (refracted) ray

•  For incident angles in glass/water greater than the critical angle, ALL the light is reflected back into the dense substance

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

http://www.tradeshop.com/master/ideal.shtml

Marcel Tolkowsky (1919)

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

http://www.unmuseum.mus.pa.us/mirage.htm

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)

MORE MIRAGES

http://www.unmuseum.mus.pa.us/mirage.htm

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.

Antarctic Fata Morgana

http://climate.envsci.rutgers.edu/Antarctica/views.html

STILL MORE MIRAGES

http://www.unmuseum.mus.pa.us/mirage.htm

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 or disappear.

MIRAGES AT SEA

http://www.unmuseum.mus.pa.us/mirage.htm

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.

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

http://www.youtube.com/watch?v=e1SdC9KnsGg

Movie of the Moon

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

Raindrop

Dispersion occurs here during refraction

white light comes in

Reflections

Dispersion occurs here during refraction

A spectrum of colors comes out

Double Rainbow in Alaska