and
Office: Gamow Tower, F-521
Email: ivan.smalyukh@colorado.edu
Phone: 303-492-7277
Lectures:
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3:30 PM - 4:45 PM
Office hours:
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TA: Jhih-An Yang jhihan.yang@colorado.edu
Class # 7

and
Lecture 7:
Reading: Finish reading Chapter 2
Demos
2

We are here
1. Shadows
2. Reflection
3. Refraction
4. Dispersion

• Part of the wave can be transmitted into the second medium while part is reflected back
• When light waves are incident on a glass slab they are mostly transmitted but partly reflected
(about 4%) !
Glass slab
Is the speed of light in the glass slab the same as in the free space???
No.

How can reflection require that the speed of the wave changes? c = 3 x 10 8 m/s !
• T he speed of an electromagnetic
(EM) wave is constant (for every wavelength) in empty space!
• The speed of light is slower than c in glass, water and other transparent media
• The speed of light in a medium is v = c/n , where n is a number larger than one called the index of refraction
• n = 1.5 for glass
• n = 1.3 for water
• n = 1.5 for vegetable oil
Glass slab

Material
Air
Water
Glass
Diamond
Ruby
Oil
Refractive
Index
1.0008
1.330
1.5
2.417
1.760
1.5
Can we see a glass rod immersed into the oil with the same refractive index?
• A. Yes
• B. No
Why?

1. Index of refraction: n = c / v
2. Ray in water is closer to the normal
3. Total internal reflection
4. Rainbows, Mirages
7

• Refraction is bending of a ray at a boundary due to a different speed of light in the substance.
Air Air
Water Water
Demo: tank, laser pointer
8

Incident ray
• 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.
• Analogy with car driving
(twee wheels on a slippery part of the road) …

• Refraction is bending of a ray at a boundary due to a different speed of light in the substance.
Air Air
Water Water
Towards or away from the interface
Demo: tank, laser pointer
10

Substance:
Vacuum
Air
Water
Glass
Diamond
v = c / n
Index of refraction n:
1.000000
…
1.0003
1.333
1.5 (depends on kind)
2.4
11

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
12

n
1 sin q
1
= n
2 sin q
2 q
1
Air n
1
= 1.0003
q
2
Water n
2
= 1.33
13

Refraction bending of a ray after it enters a medium where its speed is different
• A ray going from a fast medium to a slow medium bends towards the normal
• A ray going from a slow to a fast medium bends away from the normal
• Hence, a ray going into a medium with a higher n bends towards the normal & a ray going into a medium with a lower n bends away from the normal
Normal
Normal
Air (fast medium)
Glass or water
(slow) n air
< n water
1.0008 < 1.33
Air (fast medium)
Glass or water
(slow)
How about light going into a medium with exactly the same n ?

Light coming out of water: 2 possibilities
Refraction out OR Total internal reflection!
Refracted
Reflected internally
The critical angle is about 42 degrees.
Air
Water
Case 2, far from normal
Case 1 near normal incidence
(internal incidence (light reflection) comes out)
Demo: tank, laser pointer
15

Total internal reflection
• Show that the internal reflection is a consequence of the
Snell’s law
• The amount of bending is determined by the law of refraction (sometimes called Snell's law):
• n i sin q i
= n t sin q t

Total internal reflection - extreme case of a ray bending away from the normal as it goes from higher to lower n
For the glass-air interface
Just below the critical angle for total internal reflection there is a reflected & a transmitted ray
Normal
Air (fast medium)
Glass or water
Critical
(slow) angle
Above the critical angle for total internal reflection there is reflected ray but no transmitted ray
Normal
Glass or water
(slow)

•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. normal transmitted ray image of fish for someone out of water fish incident ray

What we see and how different it can be from what it seems to be
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
• 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
Two observers, one above the water and one under the water, view an object
(fellow to the left)…
• 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.

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!

We are here
1. Shadows
2. Reflection
3. Refraction
4. Dispersion

Dispersion: refraction (bending) of different colors by different amounts.
Spectrum Prism Light bulb
25

wavelength
300 nm (UV)
500 nm
700 nm (deep red)
Quartz glass n (index of refraction)
1.486 (bent more)
1.462
1.455 (bent less)
26

Reflection at a transparent surface occurs because the n values are different. Only a few percent of the light is reflected this way.
27

28

Rainbows: dispersion & by water raindrops
180 degree rainbow is possible. Double rainbow is possible.
Both together is very rare.
29

Sun
(behind you) this ray not seen these rays are seen this ray not seen big raindrops
30

The colors are spread inside the prism as well as outside.
The colors start to spread inside the raindrop.
Dispersion occurs here during refraction white light comes in
Reflections
Raindrop
Dispersion occurs here during refraction
A spectrum of colors comes out

sun
three total internal reflections two total internal reflections
32

Waterfall droplets create rainbows
33

34

(sun behind you) (sun if front of you)
22 degrees, center to edge 35

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.
36

(image below the object) sky appears to be on the ground
The ray bends from the low n material toward the high n material.
37

(image above the object)
38

39

How do these work?
40

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
41

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.
42

This illustration appears in "La Nature" magazine in 1884.
Demo: tank
43

1. Shadows
2. Reflection
3. Refraction
4. Dispersion
Move to Chap. 3
We are here