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Lecture 23-1
Review: Laws of Reflection and Refraction
Law of Reflection
• A reflected ray lies in the plane of incidence
• The angle of reflection is equal to the angle
of incidence
Medium 1
1  1
Law of refraction
• A refracted ray lies in the plane of incidence
• The angle of refraction is related to the
angle of incidence by
n2 sin 2  n1 sin 1
Snell’s Law
c / ni c 1 
i 
  
f
f ni ni
Where λ is the
wavelength in
vacuum
Medium 2
 n2  n1
Lecture 23-2
Demo
7A-05
Candle Illusion
Lecture 23-3
Total Internal Reflection
All light can be reflected, none refracting, when light travels from a
medium of higher to lower indices of refraction.
medium 2
e.g., glass (n=1.5) to air (n=1.0)
sin  2 n1

1
sin 1 n2
2  1
But θ1 cannot be greater
than 90 degrees !
medium 1
In general, if sin θ1 > (n2 / n1), we have NO refracted ray;
we have TOTAL INTERNAL REFLECTION.
c  sin
1
 n2 / n1 
Critical angle above which this occurs.
Lecture 23-4
©2008 by W.H. Freeman and Company
Lecture 23-5
Examples
Fish’s view of the world
 1 
  48.8
 1.33 
 c  sin 1 
Prism used as reflectors
 c  sin 1 
1 
  41.8
1.5


Optical fiber
(e.g., glass
with n=1.5)
(e.g., glass with n=1.5)
1 
  41.8
1.5


1.33 
in water  c  sin 1 
  62.5
 1.5 
in air
 c  sin 1 
Lecture 23-6
READING QUIZ 1
One of the following statements is incorrect.
A)
B)
C)
D)
A laser emits light which has a very long coherence length.
An incandescent lamp emits light that has a coherence length
of about three meters.
The Helium-Neon laser emits light through Spontaneous Emission
of photons from an excited state of Helium.
The photon energy increases with the frequency of the light.
Lecture 23-7
Chromatic Dispersion
The index of refraction of a medium is usually
a function of the wavelength of the light. It is
larger at shorter wavelengths.
Consequently, a light beam consisting of rays
of different wavelength (e.g., sun light) will be
refracted at different angles at the interface of
two different media. This spreading of light is
called chromatic dispersion.
White light: It consists of components of
nearly all the colors in the visible spectrum
with approximately uniform intensities.
The component of a beam of white light with
shorter wavelength tends to be bent more.
Spectrometer (such as a prism)
Lecture 23-8
Mirage and Rainbow
Mirage
nhot air  ncold air
water droplet
 red is outside.
 intensity
max at 42
rainbow
Lecture 23-9
Double Rainbow
Secondary rainbow
Two Interactions
Primary rainbow
One Interaction
Lecture 23-10
DEMO 7A-20
Effect Of Warm Air on Laser light
Lecture 23-11
WARM UP QUIZ 2
Unpolarized light is incident on two polarizers.
The axes of the two polarizers are rotated by
30 degrees with respect to each other. If the
intensity of the unpolarized light is IO what is the
intensity of the light after it passes through both
polarizers?
A)√3/2 IO
B)1/2 IO
C)3/8 IO
D) 3/4 IO
Lecture 23-12
Polarization of Electromagnetic Waves
Polarization is a measure of the degree to which the electric field (or the
magnetic field) of an electromagnetic wave oscillates preferentially along
a particular direction.
Linear combination
of many linearly
partially
polarized rays of
polarized
random orientations
unpolarized
linearly
polarized
Looking at E
head-on
components
equal y- and zamplitudes
unequal y- and zamplitudes
Lecture 23-13
Polarizer: polarization by absorption
An electric field component parallel to the
transmission axis is passed by a polarizer; a
component perpendicular to it is absorbed.
transmission
axis
dichroism (tourmaline, polaroid,…)
So if linearly polarized beam with E is
incident on a polarizer as shown,
E y  E cos 
I  I 0 cos 2 
Zero if θ=π/2, or if IO =0
If unpolarized beam is incident instead,
I  I 0 cos2   I 0 / 2
Polarization can rotate in
time if linearly polarized
beams of different phases
are combined.
Lecture 23-14
Example: two polarizers
This set of two linear
polarizers produces LP
(linearly polarized) light.
What is the final
intensity?
– P1 transmits 1/2 of the
unpolarized light:
I1 = 1/2 I0
– P2 projects out the Efield component
parallel to x’ axis:
E2  E1 cos
IE
2
1
I 2  I1 cos   I0 cos2 
2
2
= 0 if θ = π/2
(i.e., crossed)
Lecture 23-15
Demo 7B-22 Two Polarizer Effects
Lecture 23-16
Polarization by Reflection
• Unpolarized light can be broken
into two components of equal
magnitude: one with its electric
vector perpendicular to the
plane of incidence and the other
with its electric vector parallel
to the plane of incidence.
• The reflected (or refracted) light
is partially polarized: due to
difference in the reflectivity of
the two components (larger for
the perpendicular component).
Full polarization occurs at
Brewster’s angle where
n2
tan  B 
 B   r  90
n1
n1 sin  B  n2 sin r  n2 cos B
Lecture 23-17
DEMO 7B-23 Polarization by Reflection
Lecture 23-18
Example: Sunglasses cut down glare
transmission axis
Lecture 23-19
10:30 QUIZ 3 November 15, 2011
Light is emitted internally in a fluid which has an index of
refraction of refraction n =1.75. At the plane interface with the
air, what is the critical angle for total internal reflection?
Remember the angles are defined with respect to the normal
to the plane interface.
A)
B)
C)
D)
θC = 44.6o
θC = 34.8o
θC = 65.2o
θC = 27.3o
Lecture 23-20
11:30 QUIZ 3 November 15, 2011
Light is emitted internally in a fluid which has an index of
refraction of refraction n =2.10. At the plane interface with the
air, what is the critical angle for total internal reflection?
Remember the angles are defined with respect to the normal
to the plane interface.
A)
B)
C)
D)
θC = 48.2o
θC = 14.5o
θC = 35.2o
θC = 28.4o