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3/25/15
Chapter #35 Light and Optics
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35.1: The Nature of Light
35.2: Measurements of the Speed of Light
35.3: The Ray Approximation in Ray Optics
35.4: Analysis model: Wave Under
Reflection
35.5: Analysis Model: Wave under
Refraction
35.6: Huygens's Principle
35.7: Dispersion
35.8: Total Internal Reflection
Wave Fronts
•  Wave front is the
locus of all adjacent
points at which the
phase of vibration is
the same.
•  Read yourself “Two personalities
of light” at page 1011.
Electromagnetic Wave Fronts
and Rays
•  Electromagnetic Wave moves outwards from a small
source in three dimensions. It forms spherical wave.
At far distance from the source front becomes flat and
rays become parallel.
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Plane Wave
•  We can simplify our
representation by
omitting the wave
fronts and plotting
rays only.
•  Such approximation
is called Geometric
Optics
Geometric Optics
•  Geometric Optics assumes that
light travels in fixed direction in a
straight line as it passes through a
uniform media and changes its
direction when it meets the surface
of a different medium (with different
optical properties).
•  This approximation works when
wavelength is much less than size
of the object and aperture.
The speed of light
•  Modern experiments:
•  C = 2.99792458×108 [m/s] ≈ 3.0×108 [m/s]
•  Ole Romer (1676)
observed eclipses
of Jupiter’s moon
behind the planet.
His result was
2.25×108 [m/s]
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Calculate speed of light yourself
•  Radius of Sun orbit 150 million kilometers,
delay time ~ 1000 sec.
•  Later it was shown by Maxwell that we can
calculate speed of light with a help of two
constants ε0 and µ0.
c=
1
= 2.99792458 ⋅10 8 [m /s]
ε 0 µ0
€
The Law of Reflection
•  The incident ray,
the normal, and
the reflected ray
all lie in the same
plane.
•  Law of reflection:
θi = θ r
€
Specular reflection versus Diffuse
reflection
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Two-dimensional corner reflector
•  A ray
incident on
these two
mirrors is
sent back in
the same
direction
from which it
came.
Corner Reflector or Retroreflector
•  Reflects ray exactly
in the direction of
incident ray.
•  Astronauts placed
retroreflectors on the
lunar surface
(Appolos 11,14,15)
that is why we can
measure the EarthMoon distance with
accuracy 3 cm!
Retroreflectors
•  The Earth-Moon
distance: Moon is
moving away from
the Earth at a rate
3.5 cm/year
•  At automobile
taillights
•  A STOP sign.
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The refraction of light
•  If light ray crosses the medium boundary it
changes the direction of propagation. This
phenomenon referred to as refraction.
Law of Refraction
•  The incident ray, the
reflected ray, the
normal, and the
refracted ray all lie in
the same plane and:
sin θ1 v1
=
sin θ 2 v 2
€
Index of Refraction
n=
c
>1
v
• 
€
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Snell’s Law
sin θ1 v1
=
sin θ 2 v 2
€
sin θ1 n 2
=
sin θ 2 n1
⇒
⇒ n1 sin θ1 = n 2 sin θ 2
•  When a ray of light enters a medium where its
speed decreases, it is bent toward the normal.
•  When a ray of light enters a medium where its
speed increases, it is bent away from the normal.
•  Direction of propagation does not change if there
is no change in the index of refraction.
•  If a ray of light goes from one medium to another
along the normal, it is undeflected, regardless of
the index of refraction
Total internal reflection
sin θ a n b
sin θ a n b
=
⇒
=
sin θ b n a
1
na
nb
sin θ critical =
na
€
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Total Internal Reflection
•  At some critical angle of incidence the refracted beam is
directed parallel to the surface (900). This phenomenon
is referred to as TIR.
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Practical use of TIR in binocular
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Fiber optics
Test problem 26-68
•  At what angle must a fish underwater look in
order to see a fisherman at the shore? (Note: n
for water is 1.33.)
•  A) 41.2°
•  B) 48.8°
•  C) 60.0°
•  D) 90.0°
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Polarization
•  Polarization of electromagnetic wave
refers to the direction of its electric field.
•  Wave to the left
polarized in z
direction.
•  Wave to the right
is polarized in y-z
plane at an angle
of 600 relative to
the y axis.
Polarized and unpolarized light
•  (a) beam of light
polarized in the
vertical direction
•  (b) unpolarized
beam of light
Unpolarized light can be polarized
•  Mechanical Analogy.
•  Light Polarizer
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How it is working?
•  Polarizer is a material that is composed of long,
thin, electrically conductive molecules oriented in
a specific direction (which is perpendicular to the
transmission axis).
•  Beam of light polarized in the direction parallel to
the molecular chains is readily absorbed.
•  Beam of light polarized in the direction
perpendicular to the molecular chains passes
through the material with little absorption.
Malus Law
•  In a transmitted beam
intensity is reduced by
the factor cos2θ:
•  I = I0 cos2θ
•  The transmitted beam
is no longer polarized
in its original direction;
it is polarized in the
direction of polarizer.
Transmission of unpolarized light
•  Because each
direction gives its
deposit the total
result is:
•  I = I0/2
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Polarizer and Analyzer
•  Analyzer is
simply a
polarizer
which is
used to
analyze
polarized
beam of
light.
Polarization by Scattering and
Reflection.
•  Read it yourself please. Page 1142.
Test problem 25-64
•  64) A polarizer is oriented at an angle θ to the
vertical. If the vertically polarized beam of light
of intensity 200 W/m2 passes through the
polarizer, what is the transmitted intensity of
light for an angle of 20.0°?
•  A) 35.0 W/m2
•  B) 177 W/m2
•  C) 23.0 W/m2
•  D) 200 W/m2
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Test problem 25-68
•  Which of the following expressions is
correct for the transmitted intensity of an
unpolarized beam of light with an
intensity Ii passing through a polarizer?
•  A) It = Ii
•  B) It = (1/2) Ii
•  C) It = (1/4) Ii
•  D) It = 2 Ii
Huygens’s Principle
•  Every point of a wave front may be considered
as the source of secondary wavelets that
spread out in all directions with a speed equal
to the speed of propagation of the wave.
Optical illusion 1
• 
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Very Good Reflection
•  Great!
110 Fahrengeit
•  Previous
picture is
much better
Example 1
•  Mirage seen in the desert of Namibia. Images
are upside down.
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