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Physics 1230: Light and Color

Lecture 7:

Refraction, dispersion, and rainbows.

Reading: Chapter 2, start Chapter 3.

HW5: Due today, Monday, 5PM

Exam 2 is coming on Wed. in class.

PLEASE go to CULearn and finish

your Homework assessments!!! Unsubmitted HW can’t be scored!

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Lec. 6: Ch. 2 - Geometrical Optics

1. Shadows

2. Reflection

3. Refraction

4. Dispersion

We

are

here

3

Refraction

1. Index of refraction: n = c / v

2. Ray in water is closer to the normal

3. Total internal reflection

4. Rainbows, Mirages

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What is refraction?

• Refraction is bending of a ray at a

boundary due to a different speed of light

in the substance.

Air

Water

Air

Water

Demo: tank, laser pointer

• The incident ray has peaks

and troughs in the wave.

• The wave that hits the

material first slows down.

• Causes the wave to bend.

Just like waves hitting the

shoreline.

Incident ray

Why does the ray bend?

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Why does the ray bend?

• Refraction is bending of a ray at a

boundary due to a different speed of light

in the substance.

Air

Water

Air

Water

Demo: tank, laser pointer

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Indices of refraction

Substance: Index of refraction n:

Vacuum 1.000000…

Air 1.0003

Water 1.333

Glass 1.5 (depends on kind)

Diamond 2.4

v = c / n

Clicker Question

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A material with a larger index of

refraction, n, has a:

A)Faster speed of light

B)Slower speed of light

C)Depends upon the particular

material.

Recall: v = c / n

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Optional math: Snell’s law

n1 sin q1 = n2 sin q2

Air

Water

n2 = 1.33

n1 = 1.0003q1

q2

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Light coming out of water: 2 possibilities

Air

Water

Refracted

Reflected

internally

Case 1

near normal

incidence (light

comes out)

Case 2, far

from normal

incidence

(internal

reflection)

Demo: tank, laser pointer

The critical angle is

about 42 degrees.

Refraction out OR Total internal reflection!

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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 (sometimes called

Snell's law):

• ni sinqi = nt sinqt

• Here, qi = angle between incident

ray and normal,

• and qt = 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

• Fig 2.49 Fisherman and fish

incident

ray

transmitted

ray

normal

image of fish for

someone out of 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 fish backwards to find the image of

the fish (where they intersect).

• The location of that image will be the same for

any observer outside of the water.

What we see and how different it can

be from what it seems to be

• The woman will see the underwater part of body being

a) Smaller than it really is;

b) Much larger than it really is;

c) Of natural size;

Two observers, one above

the water and one under

the water, view an object

(fellow to the left)…

• The woman will see the underwater part of body being

a) Smaller than it really is;

b) Much larger than it really is;

c) Of natural size;

What we see and how different it can

be from what it seems to be

What we see and how different it can

be from what it seems to be

• The boy will see the underwater part of body being

a) Smaller than it really is;

b) Much larger than it really is;

c) Of natural size;

d) Something else.

Two observers, one above

the water and one under

the water, view an object

(fellow to the left)…

Total internal reflection is an extreme case of a ray bending away

from the normal as it goes from a higher to a lower index of

refraction medium (from a slower to a faster medium)

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

Critical

angle

For the glass-air

interface

What we see and how different it can

be from what it seems to be

• If the critical angle condition is satisfied, will the boy see the upper part of the man’s body?

a) Yes;

b) No.

What we see and how different it can

be from what it seems to be

• The boy will see the underwater part of body being

a) Smaller than it really is;

b) Much larger than it really is;

c) Of natural size;

d) Something else.

Legs up and down!

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Total internal reflection makes

fiber optic communication possible

The ray bends from the low n

material toward the high n material.

Demo: glass tube, laser pointer

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Fiber optics makes endoscopy possible

polyp (precancer condition)

[after age 50]

Time for a demo!

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If we pull the cork, and water starts to pour

out of the tank, the laser light will…

A) Shine across the room to the wall.

B) Stay entirely inside the tank

C) Stay entirely inside the water stream

D) Something else happens.

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This illustration appears

in "La Nature" magazine

in 1884.

Demo: tank

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Lec. 6: Ch. 2 - Geometrical Optics

1. Shadows

2. Reflection

3. Refraction

4. DispersionWe

are

here

25

Dispersion

Dispersion: refraction (bending) of different

colors by different amounts.

Light bulbSpectrum Prism

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Index n varies with color

wavelength n (index of refraction)

300 nm (UV) 1.486 (bent more)

500 nm 1.462

700 nm (deep red) 1.455 (bent less)

Quartz glass

Prisms demonstrate

refraction and dispersion

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Reflection at a transparent surface

occurs because the n values are

different. Only a few percent of the

light is reflected this way.

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Rainbows: dispersion by water raindrops

180 degree rainbow is possible. Double rainbow is possible.

Both together is very rare.

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How we see a rainbow

big

raindrops

Sun

(behind you)

this ray not seen

this ray not seen

these rays are seen

Raindrop

Dispersion occurs

here during refraction

white lightcomes in

Reflections

Dispersion occurs

here during refraction

A spectrum ofcolors comes out

Pink Floyd is slightly wrong.

The colors are spread inside the

prism as well as outside.

The colors start to spread inside

the raindrop.

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How we see two rainbows

sun

two total

internal

reflections

three total

internal

reflections

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Waterfall droplets create rainbows

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Fogbow(sun behind you) (sun if front of you)

22 degrees, center to edge

Circles around the Moon

also occur.

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Sun pillar and sun dogs

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What is a mirage?

A mirage is an image (often upside down) caused by

heated air refracting rays.

n falls from 1.003 at room temperature to 1.002 when the

temperature goes up 100 C.

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Inferior mirage (image below the object)

sky appears to be

on the ground

The ray bends from the low n

material toward the high n material.

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Superior mirage (image above the object)

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The green flash at sunset is rare!

Pekka Parvianen

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Lec. 6: Ch. 2 - Geometrical Optics

1. Shadows

2. Reflection

3. Refraction

4. Dispersion

Move to Chap. 3We

are

here