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Homework #1 - UGA
Transcript of Homework #1 - UGA
8/19/2015
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Homework #1
Reading: Chaps. 14, 20, 21, 23
Suggested exercises: 23.6, 23.7, 23.8, 23.10,
23.12, 23.13, 23.14, 23.15
Problems: 23.39, 23.40, 23.41, 23.42, 23.44 ,23.45, 23.47, 23.48, 23.49, 23.53, 23.54 (due:
Fri., Aug. 28)
A Brief History of Light
Willebrod Snell 1580-1626 Dutch
discovered law of refraction (Snell's law)
A Dutch mathematician who is best known for the
law of refraction, a basis of modern geometric
optics; but this only become known after his death
when Huygens published it.
Sir Isaac Newton 1643-1727 English
developed theories of gravitation and mechanics, and
invented differential calculus
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A Brief History of Light
Robert Hooke 1635-1703 English
discovered Hooke's law of elasticity
made contributions to many different fields including
mathematics, optics, mechanics, architecture and
astronomy. He had a famous quarrel with Newton.
Christiaan Huygens 1629-1695 Dutch
proposed a simple geometrical wave theory of light,
now known as ``Huygen's principle''; pioneered use of
the pendulum in clocks
A Brief History of Light
Thomas Young 1773-1829 British
studied light and color; known for his double-slit
experiment that demonstrated the wave nature of light
did work in surface tension, elasticity, and gave one of
the earliest scientific definitions of energy. His studies
of the Rosetta stone contributed greatly to the
deciphering of the ancient Egyptian hieroglyphic
writing.
Augustin-Jean Fresnel 1788-1827 French
studied transverse nature of light waves, and he was
one of the founders of the wave theory of light.
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A Brief History of Light
James Clerk Maxwell 1831-1879 Scottish
propounded the theory of electromagnetism;
developed the kinetic theory of gases
Chapter 23. Ray Optics (Geometric Optics)
Our everyday experience
that light travels in straight
lines is the basis of the ray
model of light. Ray optics
apply to a variety of
situations, including mirrors,
lenses, and shiny spoons.
Chapter Goal: To
understand and apply the ray
model of light.
Lecture #1
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Topics:
• The Ray Model of Light
• Principles governing Ray model:
Reflection
Refraction
• Image Formation by Refraction
• Color and Dispersion
• Thin Lenses: Ray Tracing
• Thin Lenses: Refraction Theory
• Image Formation with Spherical Mirrors
Chapter 23. Ray Optics
Chapter 23. Basic Content and Examples
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Propagation
In a homogenous medium, a light ray propagates
along a straight line
Point light
source
Object
Shadow
Propagation
http://www.youtube.com/watch?v=WVuV_xVDJDY
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Ray Model of Light
• Light rays travel in straight lines
• Light ray can cross
• A light ray travels forever unless it interacts
with matter (why?)
• An object is a source of light rays (self-
luminous objects or reflective objects)
• The eye sees by focusing a diverging bundle of
rays
Definitions
• Object
• Point source
• Parallel bundle (beam)
• Aperture
Questions regarding shadows: point source, parallel
source, no shadow?
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Reflection
Specular reflection Diffuse reflection
Light interacts with an opaque object.
Reflection
The law of reflection states that
1. The incident ray and the reflected ray are in the same
plane normal to the surface (incident plane)
2. The angle of reflection equals the angle of incidence:
θr = θi
How about
reflection from a
curved surface?
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The Plane Mirror
s s’
The Plane Mirror
Consider P, a source of rays which reflect from a mirror. The reflected rays appear to emanate from P', the same distance behind the mirror as P is in front of the mirror. That is, s' = s.
Virtual image
Under what condition can
you see the image of the
object?
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Refraction
Light interacts with transparent object.
Refraction
Light interacts with transparent object.
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Refraction
Snell’s law states that if a ray refracts between medium 1 and medium 2, having indices of refraction n1 an n2, the ray angles θ1 and θ2 in the two media are related by (1621
Willebrord Snellius, Dutch mathematician)
Notice that Snell’s law does not mention which is the incident angle and which is the refracted angle.
v
c
mediumainlightofSpeed
vacuuminlightofSpeedn
Index of refraction
Speed of Light
In vacuum,
smc /109979.2 8
In medium,
cv
Thus,n 1
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Can n be negative?
What would happen if
n becomes negative?
http://en.wikipedia.org/wiki/Metamaterial
http://people.ee.duke.edu/~drsmith/negativ
e_index_about.htm
Metamaterials !!!
Electromagnetic cloaking devices, super lenses, filters,
sub wavelength waveguides and antennas
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Refraction
2211 sinsin nn
If n1 < n2, then θ1 > θ2
Snell’s law
n1
n2
1
2
Refraction
2211 sinsin nn Snell’s law
n1
n2
1
2
If n1 > n2, then θ1 < θ2
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Refraction
2211 sinsin nn Snell’s law
n1
n2
If θ1 = 0, then θ2 = 0, regardless the values of n1 and n2
Total Internal Reflection
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Total Internal Reflection
2211 sinsin nn
If n2 < n1, then θ2 > θ1
cn
n sinsin
1
21 When
o902 1
21sin
n
nWhen
Total internal reflection occurs
n1
n2
Snell’s law
1
2
12 sinsin
n
n
Total Internal Reflection
Optical fibersA laser bouncing down a perspex rod
illustrating the total internal reflection of light
in a multimode optical fiber
Charles Kuen Kao
The Nobel Prize in Physics 2009Watch this video:
https://www.youtube.com/watch?v=0MwMkBET_5I
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Total Internal Reflection
Invisible Glass
https://www.youtube.com/watch?v=wlELYZJ5JF4
Why does the glass rod vanish in another liquid?
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Color
Different colors are associated with light of different wavelengths. The longest wavelengths are perceived as red light and the shortest as violet light.
Color Questions
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Dispersion
The slight variation of index of refraction with wavelength is known as dispersion.
Notice that n is larger when the wavelength is shorter, thus violet light refracts more than red light.
Dispersion
https://www.youtube.com/watch?v=uucYGK_Ymp0
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Dispersion
https://www.youtube.com/watch?v=uucYGK_Ymp0
Dispersion
If n1 < n2,
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Three Laws of Geometric Optics
1. Propagation in homogenous medium
2. Law of reflection
3. Law of refraction
Ray Model
Example 1.1
An albatross glides at a constant 15m/s horizontally above level
ground, moving in a vertical plane that contains the Sun. It glides
toward a solid wall of height h = 2.0 m, which it will just barely
clear. At that time of day, the angle of the Sun relative to the
ground is = 30o. At what speed does the shadow of the albatross
move (a) across the level ground and the (b) up the wall?
h
Sunray
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Reflection
The following figure shows light reflecting from two
perpendicular reflecting surfaces A and B. Find the
angle between the incoming ray i and the outgoing ray
r’.
i
r r’A
B
In-Class Activity #1
Reflection
In-Class Activity #2
The following figure shows the
multiple reflections of a light ray
along a glass corridor where the
walls are either parallel or
perpendicular to one another. If the
angle of incident at point a is 30o,
what are the angles of reflection of
the light at point b, c, d, e, and f?
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Example 1.2
A basketball player with a height of 191cm wants to see
his entire height in a “full-length” mirror mounted on a
wall. What is the least length the mirror must have?
Example 1.3
In the figure you look into a system of two vertical parallel mirrors A
and B separated by distance d. A toy monkey is hanged at point O, a
distance 0.2d from mirror A. Each mirror produces a first (least deep)
image of the monkey. Then each mirror produces a second image
with the object being the first image in the opposite mirror. Then each
mirror produces a third image with the object being the second image
in the opposite mirror, and so on – you might see hundreds of
monkey images. How deep behind mirror A are the first, second and
third images in mirror A?
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In-Class Activity #3
The following figure shows rays of monochromic light passing
through three materials a, b, and c. Rank the materials according to
their indexes of refraction, greatest first.
Tactics: Analyzing refraction
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EXAMPLE 23.4 Measuring the index of refraction
QUESTION:
EXAMPLE 23.4 Measuring the index of refraction
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EXAMPLE 23.4 Measuring the index of refraction
EXAMPLE 23.4 Measuring the index of refraction
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EXAMPLE 23.4 Measuring the index of refraction
EXAMPLE 23.4 Measuring the index of refraction
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Example 1.4
In the figure, a 2.00-m-long vertical pole extends from the
bottom of a swimming pool to a point 50.0 cm above the
water. Sunlight is incident at 55.0o above the horizon. What
is the length of the shadow of the pole on the level bottom
of the pool?
Example 1.5
The following figure shows a triangular prism of glass in
air; an incident ray enters the glass perpendicular to one
face and is totally reflected at the far glass – air interface
as indicated. If 1 is 45o, what can you say about the
index of refraction n of the glass?
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Example 1.6
A submerged swimmer is looking directly upward through
the air-water interface in a pool. Over what range of
angles do rays reach the swimmer’s eyes from light
sources external to the water? Assume that the light is
monochromatic and that the index of refraction of water is
1.33.
Similar to example 23.5
Optional Course Materials