Light Waves

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Light Waves
Nature of Light Light can be viewed as both
stream of particles and electromagnetic waves.
One-Dimensional Wave Longitudinal wave the
medium is displaced in a direction of motion of
the wave. Transverse wave the medium is
displaced in a direction of motion of the wave.
Feature the disturbance advances, not the
material medium.
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Light Waves
Wave Profile In positive x-direction In
negative x-direction
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Light Waves
Harmonic Waves (Sine Waves) Propagation
number k Amplitude A Wavelength Temporal
period Frequency
Angular frequency Wave number Various forms
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Light Waves
Example Given the traveling wave function
find the frequency,
the wavelength, the temporal period, the
amplitude, and the direction of motion. The wave
function and x are in meters, t is in
seconds. Example The speed of
electromagnetic waves in vacuum is 3?108 m/s.
Find the frequency of yellow-green light of
wavelength 555 nm. Overhead power lines radiate
electromagnetic waves at a frequency of 50 Hz.
Compare the wavelength with yellow-green light.
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Light Waves
Phase and Phase Velocity Phase
Initial Phase
?0 Phase velocity Properties of
Waves Wavefront line that links all the points
of the same phase Ray line perpendicular to all
wavefronts Plane waves wavefronts are
planes Spherical waves wavefronts are spheres
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Light Waves
Polarization If all the oscillations are
confined within a plane, the wave is called a
plane polarized wave. If the wave oscillations
are random in all directions, it is an
unpolarized wave. Unpolarized wave consists of
randomly oriented plane polarized waves.
Amplitude and Intensity The wave carries an
energy that is proportional to the square of its
amplitude. The amount of energy passing through
unit area per second is defined as the intensity
of the wave. Therefore the intensity is also
proportional to the speed of light in the medium.
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Light Waves
Wavelength and Frequency in a medium The
frequency of light in the medium is unchanged.
Wave Packets or Groups Mathematically, a wave
packet with a finite length consists of a group
of frequencies. The smaller the number of
frequencies in a wave packet then the greater
will be the length of the wave packet. Different
frequencies in a group mean different
wavelengths. It can be shown that the spread of
wavelength ?? about the mean wavelength ? is,
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Light Waves
Reflection and Transmission
For normal incidence
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Light Waves
Reflectance and Transmittance (normal
incidence) Poynting vector
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Light Waves
Phase Change For n?gtn, r?lt0 while r// change
sign at the incidence angle ip, where i?ip90?.
The reflected ray is perpendicular to the
transmitted one. At this incidence angle, r//0,
the reflected electric vector is plane polarized
in a direction perpendicular to the plane of
incidence. The angle ip is called the
polarization angle or Brewsters angle (iB).
In the internal reflection case, there will be
no transmission when the incidence angle is
larger than a critical angle ic,
Phase changes for the reflected components of the
electric vector E at the interface between two
media with refractive indices n?1.5 and n1.
For near normal incidence or the glancing
incidence, there is a phase shift ? for external
reflection and zero phase shift for internal
reflection.
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Light Waves
Stokes Relation Using the principle of
reversibility for optical rays
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Light Waves
Example What is the distance along the wave
(in the direction of propagation) between two
points having a phase difference of 60? if the
wave velocity is 3?108 m/s and the frequency is
6?1014 Hz? What phase shift occurs at a given
point in 10-3 seconds and how many waves pass by
in that time? Example Write an expression
for the infrared wave shown in the right figure.
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Light Waves
Example Given the function
what is the value of the
function at x0 when t0, t?/4, t?/2, t3?/4,
and t? ? Example A parallel circular beam of
light is incident normally on a perfectly
absorbing plane surface. If the intensity of the
beam is 20 W/cm2 and its diameter is cm,
how much energy is absorbed by the surface in 2
minutes? Example The vacuum wavelength of a
light wave is 750 nm. What is its propagation
number in a medium of refractive index 1.5?
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Light Waves
Example An empty tank is 30 m long. Light
from a sodium lamp (?589 nm) passes through the
tank in time t1 when filled with water of
refractive index 1.33. When filled with carbon
disulphide of refractive index 1.63 it takes a
time t2. Find the difference in the transit
times. The speed of light in vacuum is c3?108
m/s. Example A beam of white light is
incident normally on a plane surface separating
air from glass. If the refractive indices for
particular red, green, and violet light
wavelengths are 1.45, 1.50, and 1.55,
respectively, find the reflectances for each
color.
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Light Waves
Example A film of cryolite (Na3AlF6) of
refractive index 1.31 is deposited on a glass
substrate. If three-quarters of a wavelength of
light with vacuum wavelength 555 nm is to occupy
the film, how thick must the film layer be?
Homework 10.1 10.3 10.5 10.7 10.9 10.14