Electromagnetic waves and optics

Chapter 32
Electromagnetic Waves

PowerPoint® Lectures for
University Physics, Twelfth Edition
– Hugh D. Young and Roger A. Freedman

Lectures by James Pazun
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

Goals for Chapter 32
• To do an overview of Maxwell’s equations and
electromagnetic waves
• To study sinusoidal electromagnetic waves
• To consider the passage of electromagnetic waves
through matter
• To determine the energy and momentum of
• To observe wave addition, the formation of a
standing electromagnetic wave


Introduction
• If an electric field vector propagates, it
generates a magnetic field vector. Or,
is it the other way?
• The “chicken and the egg” argument
of which disturbance causes the other
aside, this is often a favorite portion of
a first course in physics.
Electromagnetic waves, at least in the
form of light, are common to many of
our daily experiences. Even without
vision, you can stand in the sun
wearing a dark shirt and perceive
electromagnetic waves.


Maxwell’s equations
• After Ampere and Faraday came James Clark Maxwell. He penned
a set of four equations that draw Gauss, Ampere, and Faraday’s
laws together in a comprehensive description of the behavior of
electromagnetic waves.


Electromagnetic waves are ubiquitous
• If you tried to cite all
the places you notice
in your classroom, you
would conclude in a
few minutes that they
are everywhere.


Electromagnetic waves occur over a wide range
• Where wavelength is large, frequency is small.
• The range extends from low energy and frequency (radio and
television) to high energy and small wavelength (gamma rays).


The propagation of electromagnetic waves
• The wave front moves at speed c, equal to 3.0 × 108 m/s.


Propagation of electromagnetic waves II

index of
refraction


The wave equation

Electromagnetic wave
traveling in the +x direction


The wave


The wave

T = 1.6 s

horizontal axis - time axis

λ

horizontal axis - position axis

• A coating of oil on water or a
delicate glass prism can create a
rainbow. A rainstorm among open
patches of daylight can cast a
conventional rainbow. Both effects
are beautiful and arise from the
wavelength dependence of refraction
angles.
• Eyeglasses or contact lenses both use
refraction to correct imperfections in
the eyeball’s focus on the retina and
allow vision correction.


Reflection and refraction
• The figure below illustrates both reflection and refraction at once. The
storefront window both shows the passersby their reflections and allows them
to see inside.


We will consider specular reflections
• A real surface will scatter and reflect light. Diffuse reflection is the
rule, not the exception. We will use specular reflection as we used
the ray approximation, to make a very difficult problem
manageable.


Laws of reflection and refraction
• Angle of incidence = angle of reflection.

• Snell’s Law of Refraction considers the
slowing of light in a medium other than
vacuum … the index of refraction.


Why should the ruler appear to be bent?
• The difference in index of refraction for air and water causes your eye to
be deceived. Your brain follows rays back to the origin they would have
had if not bent.


Tabulated indexes of refraction

As index of refraction increases, velocity of
light in the medium decreases


Quiz ¼ sheet of paper
1. Write down the relationship of frequency and the wavelength of light in a vacuum.
2. If an EM wave or light enters a dielectric, its frequency remains the same. As it enters
the material, the electrons in the material vibrate with a driving frequency equal to that
of the EM wave but its wavelength would differ.
• The speed of light in vacuum is c = 3.0 x 108 m/s, what would be its speed in water if its
index of refraction is 1.33?
3. Write down the law of reflection and refraction (Snell’s law)
4. Knowing Snell’s law and the theory of index of refaction, rank the speed of light through
each medium from least to greatest.

50o
5o 15o 15o
15o 5o D
C
A B


Quiz (by pair) >:)


Chapter 35
Interference



• To consider interference and coherent
sources
• To study two-source interference of light
• To determine intensity in interference
patterns
• To consider interference in thin films
• To study the Michelson interferometer


Introduction
• Rainbows in the sky: been
there, seen that. A thin-film
soap bubble: why should that
create a rainbow effect?
• This thin film is dispersing
white light and revealing a
r.o.y.g.b.i.v. spectrum of color.


Wave fronts from a disturbance
• Think back to our first slide on
wave motion when the father
threw an object into the pool and
the boy watched the ripples
proceed outward from the
disturbance. We can begin our
discussion of interference from
just such a scenario, a coherent
source and the waves from it that
can add (constructively or
destructively).


A “snapshot”
• The “snapshot” of sinusoidal waves spreading out from two
coherent sources.


Double slit interference of light
We consider
Monochromatic
Single wavelength
Best example is laser

Coherent
Same frequency
Definite constant phase relationship (not necessarily in
phase)


• Two waves interfering constructively and destructively.
• Young did a similar experiment with light.


• Two waves interfering constructively and destructively.
• Young did a similar experiment with light.

L
L


As the waves interfere, they produce fringes


As the waves interfere, they produce fringes

Constructive Interference

Destructive Interference

m is called the order number


Interference from two slits or two radio stations
• In a two-slit interference experiment, the slits are 0.200 mm apart
and the screen is at a distance of 1.00 m. The third bright fringe
(not counting the central bright fringe straight ahead from the slits)
is found to be displaced 9.49 mm from the central fringe. Find the
wavelength of light used.


Interference between mechanical and EM waves


Thin Film Interference

Constructive Interference

Destructive Interference


Thin films will interfere


Quiz. Understanding interference


Chapter 36
Diffraction



• Fresnel and Fraunhofer diffraction
• Single-slit diffraction
• Diffraction gratings


Introduction
• It’s intuitive that sound can diffract
(and travel around corners). Light
doesn’t “show its poker hand” so
easily.
• If you shine light from a point
source to a ruler and look at the
shadow, you’ll see the edges are …
well … not sharp. A close
inspection of the indistinct edge
will reveal fringes.
• This phenomenon may not sound
useful yet but stay with us until the
end of Chapter 36. This line of
thinking has shown the way for
advances in DVD technology and
applications in holography.


Fresnel and Fraunhofer diffraction
• According to geometric optics, a light source shining on an object
in front of a screen will cast a sharp shadow. Surprisingly, this
does not occur.


Diffraction
• If the source and the screen are close to the edge causing the diffraction, the
effect is called “near-field” or Fresnel diffraction. If these objects are far
apart, so as to allow parallel-ray modeling, the diffraction is called “far-
field diffraction” or Fraunhofer diffraction.


Diffraction from a single slit


Dark fringes in single-slit diffraction
• The figure illustrates Fresnel and Fraunhofer outcomes.


Fresnel or Fraunhofer?
• Differentiating Fresnel and Fraunhofer


Fraunhofer diffraction


divide source into two equal parts
destructive interference

divide source into four equal parts

divide source into six equ
and so on...
eight

condition for destructive
interference


condition for destructive
interference


Fraunhofer diffraction and an example of analysis
• A photograph of a Fraunhofer pattern from a single slit.


Resolution


Resolution

Smaller wavelength means less
angle to resolve object

Why electron microscopes can see better than optical microscopes.
Wavelength of electron is small ~10-10 m
Light is ~10-7 m

Quiz!
1. Write down the equation for constructive
interference for thin films given na < nb
< nc given a light of wavelength λ
enters the film. let m be the order
number
na
nb t
nc


Electromagnetic waves and optics

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