Download Chapter 35.

Ch. 35
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Reflection
•What happens when our wave hits a conductor?
•E-field vanishes in a conductor
Ei  E0 sin  kx  t 
•Let’s say the conductor is at x = 0
•Add a reflected wave going other direction
Er  E0 sin  kx  t 
•In reality, all of this is occurring in
three dimensions
Incident Wave
Reflected Wave
Total Wave
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Law of Reflection
ki = kr
i = r
•We assume the mirror is infinitely large
•If the wavelength is sufficiently tiny compared
to objects, this might be a good approximation
i r
•For the next week, we will always make
this approximation
Mirror
•It’s called geometric optics
•In geometric optics, light waves are represented by rays
•You can think of light as if it is made of little particles
•In fact, waves and particles act very similarly
•First hint of quantum mechanics!
Ans d
Concept Question
•This works for any angle
•In 3D, you need three mirrors
 = 47
47
43
47
47
4343
Mirror
Mirror
A light ray starts from a wall at an angle
of 47 compared to the wall. It then
strikes two mirrors at right angles
compared to each other. At what angle
 does it hit the wall again?
A) 43 B) 45 C) 47 D) 49 E) 51
The Speed of Light in Materials
•The speed of light in vacuum c is the same for all wavelengths of
light, no matter the source or other nature of light c  3.00 108 m/s
•Inside materials, however, the speed of light can be different
•Materials contain atoms, made of nuclei and electrons
•The electric field from EM waves push on the electrons
•The electrons must move in response
Indices of Refraction
•Absorption and scattering
Air (STP)
1.0003
•This generally slows the wave down
Water
1.333
•n is called the index of refraction
Ethyl alcohol 1.361
•The amount of slowdown can depend
Glycerin
1.473
on the frequency of the light
Fused Quartz 1.434
c
v
n
Glass
1.5 -ish
Cubic zirconia 2.20
Diamond
2.419
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Refraction: Snell’s Law
ck

n
•The relationship between the angular frequency 
and the wave number k changes inside a medium
•Now imagine light moving from one medium to another  f  c n
•Some light will be reflected, but usually most is refracted
•The reflected light again must obey the law of reflection 1 = r
k1sin1
n1 sin 1  n2 sin  2
index n1
1 r
index n2
Snell’s
Law
y
x
2
k2sin2
Snell’s Law: Illustration
A light ray in air enters a region at an
angle of 34. After going through a layer
of glass, diamond, water, and glass, and
back to air, what angle will it be at?
A) 34
B) Less than 34
C) More than 34
D) This is too hard
n5 = 1.5
6
n6 = 1
5
5
n3 = 2.4
n4 = 1.33
4 4
n1 = 1 n2 = 1.5
3
3
2
2
34
n1 sin 34  n2 sin 2 n3 sin 3
 n4 sin 4  n5 sin 5  n6 sin 6 n1 sin 1  n2 sin  2
1 sin 34  1 sin 6 6  34
Ex - (From MCAT practice book). If a ray is refracted from air into a
medium with n = 1.47 at an angle of incidence of 50, the angle of refraction
is
A. 0.059
B. 0.087
C. 0.128
D. 0.243
Ans A
Image Formation
Reflection
Refraction
I
O
CT-1- A fish swims below the surface of the water at P. An observer at O
sees the fish at
A. a greater depth than it really is.
B. the same depth.
C. a smaller depth than it really is.
Ans C
CT –2 A fish swims below the surface of the water. Suppose an observer is
looking at the fish from point O'—straight above the fish. The observer sees
Ans C
the fish at
A. a greater depth than it really is.
B. the same depth.
C. a smaller depth than it really is.
Ex- (Serway 35-27) An opaque cylindrical tank with an open top has a
diameter of 3.00 m and is completely filled with water. When the setting Sun
reaches an angle of 28.0° above the horizon, sunlight ceases to illuminate
any part of the bottom of the tank. How deep is the tank?
Solve on Board
Ex- (Serway 35-22) When the light illustrated below passes through the
glass block, it is shifted laterally by the distance d. If n = 1.50, what is the
value of d?
Solve on Board
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Dispersion
•The speed of light in a material can depend on frequency
•Index of refraction n depends on frequency
• Its dependence is often given as a function of wavelength in
vacuum
•Called dispersion
•This means that different types of light
bend by different amounts in any given
material
•For most materials, the index of refraction
is higher for short wavelength
Red Refracts Rotten
Blue Bends Best
Prisms
•Put a combination of many wavelengths (white light) into a triangular
dispersive medium (like glass)
•Prisms are rarely used in research
•Diffraction gratings work better
•Lenses are a lot like prisms
•They focus colors unevenly
•Blurring called chromatic dispersion
•High quality cameras use a combination of
lenses to cancel this effect
Rainbows
•A similar phenomenon occurs when light bounces off of the inside of a
spherical rain drop
•This causes rainbows
•If it bounces twice, you can
get a double rainbow
http://www.globalgiving.org/double-rainbow/
JIT
Ans C
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Total Internal Reflection
A trick question:
A light ray in diamond enters an air gap at an
angle of 60, then returns to diamond. What
angle will it be going at when it leaves out the
bottom?
A) 60
B) Less than 60
C) More than 60
D) None of the above
n1 = 2.4
60
2
2 n2 = 1
3
n3 = 2.4
n1 sin 60  n2 sin 2
sin 2  2.4  0.866  2.07
•This is impossible!
•Light never makes it into region 2!
•It is totally reflected inside region 1
•This can only happen if you go from a high index to a low
•Critical angle such that this occurs:
n2
sin  c 
•Set sin2 = 1
n
1
View from the pool
Which diver is more likely to see the lifeguard (Do as
clicker question)?
A) Guy on left
B) Guy on right
C) I don’t know
D) Same
How to get
TIR in prism.
 Looking at complementary angles inside
the triangles we have
90-2 + 90-3 = 120
 2 + 3 = 60
 As 1 increases 2 increases (snell’s law)
and 3 decreases
 Avoid TIR as 1 increases
Serway 35-44, Solve on Board
A triangular glass prism with
apex angle F = 60.0° has an
index of refraction n = 1.50
(Fig. P35.43). What is the
smallest angle of incidence
1 for which a light ray can
emerge from the other side?
Optical Fibers
Protective
Jacket
Low n glass
High n glass
•Light enters the high index of refraction glass
•It totally internally reflects – repeatedly
•Power can stay largely undiminished for many kilometers
•Used for many applications
•Especially high-speed communications – up to 40 Gb/s
Chapter 36
Mirrors and
Lenses
Lenses and Mirrors Summarized
•The front of a lens or mirror is the side the light goes in
R>0
p>0
q>0
Concave Object Image
mirrors
front in front in front
lenses
f
f  12 R
 1
1 
Convex Object Image 1  n2
   1 

front in front in back f  n1
 R1 R2 
1 1 1
 
p q
f
Variable definitions:
•f is the focal length
•p is the object distance from lens
•q is the image distance from lens
•h is the height of the object
•h’ is the height of the image
•M is the magnification
h
q
M  
h
p
Other definitions:
•q > 0 real image
•q < 0 virtual image
•M > 0 upright
•M < 0 inverted
Summary of Geometric Optics Rules
1. Object distances, p are always positive (except in the case of more than one lens or mirror when the first image is on
the far side of the second lens or other cases where you have a virtual object like object behind mirror).
2. Image distances, q, are positive for real images and negative for virtual images.
3. Real images form on the same side of the object for mirrors and on the opposite side for refracting surfaces (lenses).
Virtual images form on the opposite side of the object for mirrors and on the same side for refracting surfaces.
4. When an object faces a convex mirror or concave refracting surface the radius of curvature, R, is negative. When an
object faces a concave mirror or convex refracting surface the radius of curvature is positive.
Object
object
location
image
location
image
type
image
orientation
Plane mirror
anywhere
virtual
Concave
mirror
concave
mirror
convex
mirror
converging
lens (convex)
converging
lens
diverging
lens
inside f
opposite
object
opposite
virtual
same
object
same
outside f
same
real
anywhere
opposite
inside f
sign of f
sign of R sign of q
(R1
for
lens)
sign of m
∞
negative
=+1
positive
positive
negative
positive
inverted
positive
positive
positive
negative
virtual
same
negative
negative
negative
positive
same
virtual
same
positive
positive
negative
positive
outside f
opposite
real
inverted
positive
positive
positive
negative
anywhere
same
virtual
same
negative
negative
negative
positive
as f=∞