Transcript document

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  is the
wavelength in
vacuum
Medium 2
 n2  n1
Lecture 23-2
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  cannot be greater
than 90 !
medium 1
In general, if sin 1 > (n2 / n1), we have NO refracted ray;
we have TOTAL INTERNAL REFLECTION.
c  sin
1
 n2 / n1 
Critical angle above which this occurs.
Lecture 23-3
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 23-4
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 23-5
Mirage and Rainbow
Mirage
nhot air  ncold air
water droplet
 red is outside.
 intensity
max at 42
rainbow
Lecture 23-6
Double Rainbow
Secondary rainbow
Primary rainbow
Lecture 23-7
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 23-8
Elliptic (or circular) polarization
y
E  E1 cos  kz  t  1   E 2 cos  kz  t  2 
e. g., E1  E1 i, E 2  E2 j
x
 E rotates unless E1 and E2 are in phase
(or out of phase by ).
 |E| changes unless amplitudes E1 = E2
and the phase difference is /2.
Elliptic polarization
Constant |E| case is called
circular polarization
Lecture 23-9
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 =/2, I0 if =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 23-10
Non scored test quiz
•
A beam of un-polarized lights with intensity
I is sent through two polarizers with
transmission axis perpendicular to each
other. What’s the outgoing light intensity?
a)
b)
c)
d)
½I
2I
0
1.5 I
Lecture 23-11
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   I 0 cos2 
2
2
= 0 if  = /2
(i.e., crossed)
Lecture 23-12
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 23-13
Example: Sunglasses cut down glare
transmission axis
Lecture 23-14
Physics 241 –Quiz a
Unpolarized light of intensity I0 is sent through 3
polarizers, each of the last two rotated 45 from
the previous polarizer so that the last polarizer is
perpendicular to the first. What is the intensity
transmitted by this system?
a) 0.71 I0
b) 0.50 I0
c) 0.25 I0
d) 0.125 I0
e) 0
Lecture 23-15
Physics 241 –Quiz b
Unpolarized light of intensity I0 is sent through 3
polarizers, each of the last two rotated 60 from
the previous polarizer so that the last polarizer is
rotated by 120 from the first. What is the
intensity transmitted by this system?
a) 0.25 I0
b) 0.125 I0
c) 0.0625 I0
d) 0.03125 I0
e) 0
Lecture 23-16
Physics 241 –Quiz c
Unpolarized light of intensity I0 is sent through 3
polarizers. The second one is rotated 90 from the
first polarizer, but the last one is again aligned in
the same direction as the first. What is the
intensity transmitted by this system?
a) 0.71 I0
b) 0.50 I0
c) 0.25 I0
d) 0.125 I0
e) 0