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Presented by Ian Anderson on March 23, 2013, as part of the Science Saturday series of lectures sponsored by Oak Ridge National Laboratory at ORAU.
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Somewhere over the Rainbow
Ian Anderson
Peggy Bertrand
.. and team…
2 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
What do we see?
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These are the observations we would like to explain
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These are the observations we would like to explain
We need:
1. White light – which is made up of many colors
2. Rain – which is made up of drops of water
6 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
What happens when a ray of light hits water………?
Air
Water
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Let’s play…..
http://phet.colorado.edu/
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What happens when a ray of light hits water…….. Reflection and Refraction
Air
Water
Incident ray
Refracted ray
Reflected ray
9 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
What happens when a ray of light hits water…….. Reflection and Refraction
Air
Water
Incident ray (white)
Refracted ray (split into colors)
Reflected ray
10 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
What happens when a ray of light hits water…….. Reflection and Refraction
Air
Water
Incident ray
Refracted ray
Reflected ray
i
r
i
11 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
What happens when a ray of light hits water…….. Reflection and Refraction
Air
Water
Incident ray
Refracted ray
Reflected ray
i
r
i
(refractive index)
ia
bsin (i) = a/b
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What happens when a ray of light hits air from water…….. Total Internal reflection
Air
Water
Incident ray
Refracted rayi = 90 degrees
r = θcCritical Angle
(refractive index)
ia
bsin (i) = a/b
sin θc = 1/n
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Your turn- measure the critical angle in a semicircular prism
Normal
Prism
Reflected beam
Laser beam
Refracted beam
q
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Let’s look at the results….
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Some applications….
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What happens when rays of light hit circular drops of water?
Ray of light from sun
Primary Bow
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What happens when rays of white light hit circular drops of water?
Ray of light from sun
Primary Bow
18 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
What happens when rays of white light hit circular drops of water?
Ray of light from sun
Primary Bow
19 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
What happens when rays of white light hit circular drops of water?
Ray of light from sun
Primary Bow
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What happens when rays of light hit circular drops of water?
Ray of light from sun
Primary Bow
One internal reflection
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What happens when rays of light hit circular drops of water?
Ray of light from sun
Secondary Bow
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What happens when rays of white light hit circular drops of water?
Ray of light from sun
Secondary Bow
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What happens when rays of light hit circular drops of water?
Ray of light from sun
Secondary Bow
Two internal reflections
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What happens when rays of light hit circular drops of water?
Ray of light from sun Third Bow !!
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What happens when rays of light hit circular drops of water?
Ray of light from sun Third Bow !!
Three internal reflections!
Guess which way the colors are
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Let’s play…
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What happens when rays of light hit circular drops of water?
Ray of light from sun
Primary Bow
? How does this angle change?
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Your turn…
Ray of light from laser
Primary Bow
Bottle of water
d
What is this angle?
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What did you find?
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We can calculate what we measured!- for those that like a little trigonometry
Ray of light from laser
Primary Bow
Bottle of water
Total Deviation D? What is this angle
d
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We can calculate what we measured!- for those that like a little trigonometry
Ray of light from laser
Primary Bow
Bottle of water
Total Deviation D? What is this angle
d
ir
D = (i-r)
33 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
We can calculate what we measured!- for those that like a little trigonometry
Ray of light from laser
Primary Bow
Bottle of water
Total Deviation D? What is this angle
d
ir
D = (i-r) + (180-2r)
rr
34 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
We can calculate what we measured!- for those that like a little trigonometry
Ray of light from laser
Primary Bow
Bottle of water
Total Deviation D? What is this angle
d
ir
D = (i-r) + (180-2r) + (i-r)
rr
r
i
35 Managed by UT-Battellefor the U.S. Department of Energy The Rainbow
We can calculate what we measured!- for those that like a little trigonometry
Ray of light from laser
Primary Bow
Bottle of water
Total Deviation D ? What is this angle
d
ir
D = (i-r) + (180-2r) + (i-r) = 2(i-r) + (180-2r)
rr
r
i
D doesn’t depend on the size of the drop!!!!
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What’s the answer?A
ngle
of
elev
atio
n (d
egre
es)
Distance from the diameter of the bottle
d/R
d
Remember the Angles do not depend on the drop size!
2R
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Have we explained everything?
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
Primary Red
Primary Violet
Secondary Red
Secondary Violet
Ang
le o
f el
evat
ion
(deg
rees
)
d/R
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Have we explained everything?
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180
Primary Red
Primary Violet
Secondary Red
Secondary Violet
Ang
le o
f el
evat
ion
(deg
rees
)
Fraction of the radius of the drop (bottle)
Alexander’s Dark Band
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The Supernumerary Arcs?
If you want to know the explanation – ask me afterwards
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Let’s make a rainbow….
