7 Dispersion

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Physics 1230: Light and ColorGeometrical 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


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speed= c =distance

time=

T= f

Each color has a different wavelength and frequency, but theSAME SPEED in air

http://science.hq.nasa.gov/kids/imagers/ems/index.html


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Light slows down in materials compared with air

Speed in medium = speed in vacuumn

n = speed of light in vacuumspeed of light in substance


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Concept Question

Speed in medium = speed in vacuumn

n = speed of light in vacuumspeed of light in substance

What is the refractiveindex of diamond?

A. 1B. 0C. 1.5D. 2.4


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Concept Question

Consider light propagating in glass where the index isn=1.5

What is the speed of light in glass?

A) 3 x 108 m/secB) 1.5 m/sec

C) 2 x 108 m/sec


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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 transmittedinto 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

this picture shows refraction without

dispersion, as would occur withmonochromatic light


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Concept Question

Which ray is drawn correctly?

A, B or C?

normal to surface

glass or water

incident ray

A

B

C


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normal to surface

glass or water

refracted rays

incident

ray

reflected

rays

Concept Question

Which ray is drawn correctly?A, B or C?

A

B

C


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http://acept.la.asu.edu/PiN/rdg/refraction/refraction2.shtml

Concept Question

What is the angle of total internal reflection here?

A) 41 degreesB) 90 degreesC) 49 degrees


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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.RedB.BlueC.Green


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Dispersion

Dispersion is a kind of refraction in which the amount of bending dependson 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


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Dispersion by prisms

In a prism, the amount of bending depends on the wavelength orcolor 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


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Dispersion by prisms

In a prism, the amount of bending depends on the wavelength orcolor 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


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Dispersion and Rainbows

What is a rainbow?

The traditional rainbow is sunlight spread out into its spectrum of colors anddiverted to the eye of the observer by water droplets. The "bow" part of theword describes the fact that the rainbow is a group of nearly circular arcs ofcolor 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 thedirection opposite to that of the sun. The rain, of course, is in the direction ofthe rainbow.


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How Rainbows Work

Light is first refractedby the raindrops, thenreflected once, and thenrefracted once again.

Dispersion causes the angleof refraction to be differentfor blue light than for redlight. This is because theblue light travels more slowlyin the raindrop than redlight.

Sunlight


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What makes the colors in the rainbow?

This is illustrated in the figure. Thisrainbow of two colors would have a widthof almost 2 (about four times larger thanthe angular size of the full moon). Notethat even though blue light is refractedmore than red light in a single drop, wesee the blue light on the inner part of thearc because we are looking along adifferent line of sight that has a smallerangle (40) for the blue.

Rene Descartes and Willebrord Snell had determined how a

ray of light is bent, or refracted, as it traverses regions ofdifferent densities, such as air and water. When the lightpaths 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 thatwhen we see a rainbow and its band of colors we are looking at light refracted andreflected from different raindrops, some viewed at an angle of 42; some, at an angle of

40, and some in between. Why?


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http://science.howstuffworks.com/rainbow2.htm


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http://astro.temple.edu/~dhill001/MCRain/MCRain.html


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Concept Question

When is the sunlight separated into its component colors?

A) When it first enters the raindropB) When it reflects perfectly from the back of the dropC) When it exits the raindrop


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Concept Question

Why dont you see the blue at top and red at bottom of rainbow?

How Rainbows Happenhttp://www.rebeccapaton.net/rainbows/index.htm

A. I can explain thisB. I dont know


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Why are rainbows bowed?

The rainbow rayfor red light makesan angle of 42 between the directionof the incident sunlight and the lineof sight. Therefore, as long as theraindrop is viewed along a line of sightthat makes this angle with thedirection of incident light, we will seea brightening. The rainbow is thus a

circle of angular radius 42, centeredon the antisolar point.

Why don't we see a full circle?

A) Because the earth gets in theway

B) Because there is no light toscatter

C) This light becomes the secondrainbow


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Why are rainbows bowed?

The rainbow rayfor red light makes anangle of 42 between the direction of the

incident sunlight and the line of sight.Therefore, as long as the raindrop isviewed along a line of sight that makes thisangle with the direction of incident light,we will see a brightening. The rainbow isthus a circle of angular radius 42,centered on the antisolar point.

We don't see a full circle because theearth gets in the way. The lower the sun isto the horizon, the more of the circle wesee -right at sunset, we would see a fullsemicircle of the rainbow with the top ofthe arch 42above the horizon. The higher

the sun is in the sky, the smaller is thearch of the rainbow above the horizon.

On an airplane, if you look into the cloudswhile the sun is behind you, you may beable to see a full 360 rainbow!


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Sometimes we see two rainbows at once.What causes this? We have followedthe path of a ray of sunlight as it entersand is reflected inside the raindrop. Butnot all of the energy of the ray escapesthe raindrop after it is reflected once.A part of the ray is reflected again andtravels along inside the drop to emergefrom the drop. The rainbow we normally

see is called the primary rainbow and isproduced by one internal reflection; thesecondary rainbow arises from twointernal reflections and the rays exitthe drop at an angle of 50 rather thanthe 42for the red primary bow. Bluelight emerges at an even larger angle of

53. This effect produces a secondaryrainbow that appears higher in the skyand has its colors reversed compared tothe primary.

What makes a Double Rainbow?

the secondary (upper) rainbowalways appears fainter: why?


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Sometimes we see two rainbows at once.What causes this? We have followedthe path of a ray of sunlight as it entersand is reflected inside the raindrop. Butnot all of the energy of the ray escapesthe raindrop after it is reflected once.A part of the ray is reflected again andtravels along inside the drop to emergefrom the drop at a different angle. The

rainbow we normally see is called theprimary rainbow and is produced by oneinternal reflection; the secondaryrainbow arises from two internalreflections and the rays exit the dropat an angle of 50 rather than the 42for the red primary bow. Blue light

emerges at an even larger angle of 53.This effect produces a secondaryrainbow that appears higher in the skyand has its colors reversed compared tothe primary.




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http://mathdemos.gcsu.edu/mathdemos/MCRain/MCRain.html



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Get a fine misting sprinkler and set the water pressure high enough to get a largevolume 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 theshadow of your head to the rainbow arc. Use the "hand and fist" method tomeasure this angle: if you stretch out your arm and make a fist, the width of your

fist is about ten degrees.

Making your own rainbows

http://www.youtube.com/watch?v=ck7A9vufrX4&feature=related

Crazy Sprinkler Lady


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Concept Question

Can the person see the rainbow?A.YesB. NoC. Maybe


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RAINBOW PUZZLER

http://www.hands-on-optics.org/puzzler/

Rainbows are one of nature's awe inspiring sights. Artists have usedthem for inspiration without always understanding the physics behind

a rainbow. The painting below, "Niagara", was painted by HenryFreeman in 1873. What is wrong with the rainbows in this picture?


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Galen Rowell: Potala Palace, Lhasa

How did he achieve thiscomposition?


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Rainbows in Art

Whats wrong with this painting?

Heroic Landscape, Joseph Anton Koch


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Moonbows: Lunar Rainbows

time exposure taken at 8:30 pm, Victoria Falls, Zambia


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Rainbows in Mythology

Whats the problem with this proposition?

"There is a pot of gold at the end of every rainbow."


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Rainbows in Religion: Navajo Rainbow Guardian

Isanakleshe (Changing Woman) andNatseelit (the Rainbow Goddess) andSacred Corn Sandra Stanton

Navajo sand painting: Father Sky, Mother Earthenclosed on three sides by Rainbow Goddess

http://www.jedisteve.com/navajo.html


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Rainbows and the Story of Noah


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Rainbows and the Story of Noah

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