Somewhere over the Rainbow

Ian Anderson

Peggy Bertrand

.. and team…

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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

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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

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What happens when a ray of light hits water…….. Reflection and Refraction

Air

Water

Incident ray (white)

Refracted ray (split into colors)

Reflected ray

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What happens when a ray of light hits water…….. Reflection and Refraction

Air

Water

Incident ray

Refracted ray

Reflected ray

i

r

i

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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

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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 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)

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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) + (180-2r)

rr

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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) + (180-2r) + (i-r)

rr

r

i

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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) + (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….