Transcript W11Physics1CLec24Afkw

Physics 1C
Lecture 24A
Spectrum of EM Waves
There are distinct forms of EM waves at different
frequencies (and wavelengths).
Recall that the wave speed is given by:
vwave = c = l f.
Wavelengths for visible light range between
400nm (violet) and 700nm (red).
There is no sharp division between one kind of EM
wave and the next.
For example, you can have an X-ray and a Gamma
Ray with the exact same wavelength.
EM Spectrum
Note the overlap between
types of waves (such as UV
and X-rays).
All EM waves have the
same speed in a vacuum,
what distinguishes the types
are their frequencies or
wavelengths.
Note that the visible section
is a quite small portion of
the spectrum.
EM Spectrum
Wavelengths of light can
range from very long (radio,
~100km) to very short
(gamma, ~1fm).
Frequencies have an
equally long range of
possible values: (gamma,
~1022Hz) to (radio, ~10Hz).
Visible light ranges from
Red (700nm, 4x1014Hz) to
Violet (400nm, 7x1014Hz)
EM Spectrum
Radio waves have a long
wavelength (~100m) and
thus are good for use as a
communication tool (TV,
AM, FM).
Microwaves are smaller
(~1cm) and interfere easily
with common things
(μwave oven grates).
Infrared waves are
produced by hot objects.
EM Spectrum
Visible light (~500nm)
is detected by the
human eye. We are
most sensitive to
yellow-green (560nm).
UV light (~100nm) that
comes from the Sun is
mostly absorbed by the
Earth’s ozone layer.
EM Spectrum
X-rays (~0.1nm) are
associated with fast
electrons hitting off of a
metal target (medical
applications).
Gamma rays (~1fm) are
emitted by radioactive
nuclei. They can cause
serious damage to living
tissue as they penetrate
deeply into most matter.
Spherical Waves
A spherical wave propagates radially outward from
the source (for instance, your cell phone).
The energy propagates equally in all directions.
The intensity is:
The average power is the
same through any spherical
surface centered on the source.
Intensity will decrease as r
increases.
Cell Phone Intensity
Example
A cell phone emits 0.60Watts of 1.9GHz radio waves.
What are the amplitudes of the electric and
magnetic fields at a distance of 10cm?
Answer
Assume the cell phone is a point source of
electromagnetic waves (or r = 0).
Cell Phone Intensity
Answer
The intensity of the radio waves at 10cm is:
We want the maximum values
(amplitudes) for the electric and
magnetic fields.
Cell Phone Intensity
Answer
For magnetic field we can turn to:
Concept Question
The amplitude of the oscillating electric field at your cell
phone is 8μV/m when you are 10km from the broadcast
antenna. What is the electric field amplitude when you
are 20km from the antenna?
A) 8μV/m.
B) 4μV/m.
C) 2μV/m.
D) 1μV/m
Doppler Effect for Light
Since light is an EM wave, if the source or the observer
moves with respect to each other the frequency of the
wave will be Doppler shifted.
But since the speed of light is so large it takes a large
relative speed, u, between the observer and the source for
there to be any noticeable effect on the observed
frequency, fo.
For light the Doppler equation becomes:
where fs is the frequency emitted by the source
and c is the speed of light.
Doppler Effect for Light
As with the previous Doppler equation, you take the top
sign (positive) if the observer and the source are moving
toward each other.
You take the bottom sign (negative) if the observer and
the source are moving away from each other.
Note that this equation is valid only when the relative
speed, u, is much smaller than c.
Astronomers use the Doppler Effect for light to see if
distant objects are moving toward or away from us.
How do we know that the
Universe is expanding ?
•
Chemical Elements have characteristic frequencies. (We’ll
discuss this more later in the course)
•
We assume that chemical elements are the same, and thus
have the same characteristic frequencies everywhere in the
universe.
•
We observe the frequencies from distant stars to be “redshifted”, i.e. at frequencies lower than expected.
•
fo < fs means distant stars are moving away from us.
Polarization of Light
Light from the sun is produced by the vibrations
of multitude of atoms located there.
Each atom produces a wave with its own
orientation of the electric field.
All directions of the
electric field vector are
equally possible and are
in a plane perpendicular
to the direction of
propagation.
This type of wave is
known as an
unpolarized wave.
Polarization of Light
A wave is said to be linearly polarized if the
resultant electric field vibrates in the same
direction at all times at a particular point.
It is possible to polarize an unpolarized beam.
The most common
technique for
polarizing light is
called polarization
by selective
absorption.
Polarization of Light
In this technique, you use a material that transmits
waves whose electric field vectors in that plane are
parallel to a certain direction (transmission axis).
This material also absorbs waves whose electric
field vectors are perpendicular to that direction.
This device is
known as a
polarizer.
The material is
known as a
Polaroid (1932).
Polarization of Light
When you place a second polarizing sheet (called the
analyzer) behind the polarizer, the intensity of the polarized
beam that is transmitted will vary as:
I  Io cos2 
where Io is the intensity of the polarized wave
incident on the analyzer.
The angle 
θ is the
angle between the
transmission axes
of the two polarizing
sheets.
This is Malus’ Law.
Polarization of Light
The intensity of the transmitted beam is the highest
when the transmission axes are parallel.
The intensity is zero when the transmission axes are
perpendicular to each other.
This would cause complete absorption.
In the middle, the axes are at 45º and less intensity
occurs.
The Nature of Light
An interesting question developed as to the nature of light: if
light is indeed a wave then why can it travel from the Sun to
Earth when there is no medium present?
The answer: Light is a particle (photon), particles do not
require a medium.
But if light is a particle, then how can it bend around
corners?
The answer: Light is a wave, waves that
propagate outward can bend around an
obstacle.
The Nature of Light
But, if light is a wave how does that
explain the photoelectric effect?
The answer: Light is a particle, only
particles with high energy can eject the
electrons.
But if light is a particle, then how does
this explain the “standing wave” pattern I
see with interference from double slits?
The answer: Light is a wave, waves
will create bright/dark spots depending
on path length difference.
The Nature of Light
But how can light be both a particle and a wave?
We say that light can have both wavelike properties
and particle-like properties.
This is called wave-particle duality.
In some experiments light acts as a wave and in
others it acts as a particle.
Experimenters will find whatever they are testing for.
Nature prevents testing both qualities at the same
time.
The Nature of Light
We can identify light as being “particles” called photons.
Each photon has a particular energy which is quantified by
its frequency.
E  hf
h is called Planck’s constant and is:
34
h  6.63 10
Js
Note how
wave-particle duality is incorporated here,
light interacts like a particle with other particles but its
energy is for a given frequency like a wave.

The Ray Approximation
From now on we will have to treat light as having both
properties (wave and particle).
The ray approximation is used in geometrical optics to
approximately represent beams of light.
We draw imaginary lines (known
as light rays) along the direction of
propagation of a single wave.
We can also represent this wave
with wave fronts.
A wave front is a surface where
the wave has the same phase and
amplitude.
The Ray Approximation
Light rays travel in straight lines in a given medium.
Light rays can cross. They do not interact with each other.
Two rays can cross without either being affected in any way.
A light ray travels forever unless it interacts with matter.
It can interact with matter by either: reflection, refraction,
scattering or absorption.
Light ray can also bend around sharp edges (diffraction)
depending on the wavelength.
Ray Approximation: Barrier
A wave meets a barrier with l<<d
(d is the diameter of the opening).
The ray approximation assumes
that the individual waves emerging
from the opening continue to move in
a straight line.
The wave meets a barrier with an
opening size on the order of the
wavelength: l~d.
The waves undergo diffraction and
spread out from the opening in all
directions.
Ray Approximation: Barrier
The wave meets a barrier with an opening size much
smaller than the wavelength: l>> d.
In this case, the opening can be approximated as a
point source.
Ray Model of Light
An object is a source of light rays.
Rays originate from every point on the object, and each
point sends rays in all directions.
If the object is far away, the rays will appear parallel to the
observer.
We make no distinction
between self-luminous objects
and reflective objects.
5) The eye sees by focusing a
diverging bundle of rays.
The Nature of Light
The incident light ray will move in a straight line path
as long as the medium does not change.
But, when it encounters a boundary with a second
medium, (at least) part of this incident ray is reflected
back into the first medium.
If the boundary is a smooth
surface, the reflection is
known as specular
reflection.
This means all the reflected
rays will be parallel to one
another.
The Nature of Light
If the boundary is a rough surface, the reflection is known
as diffuse reflection.
This means that the reflected rays will travel in a variety of
directions.
Diffuse reflection is how you can see most everyday
objects.
Although diffuse reflection is
more common, it is harder to
mathematically model than
specular reflection.
Law of Reflection
We define a normal (perpendicular line to the surface) at the
point where the incident ray hits strikes the surface.
The incident angle, θ1, is the angle that the incident ray
makes with respect to the normal.
The reflected angle, θ’1, is the angle that the reflected ray
makes with respect to the normal.
The angle of incidence
is equal to the angle of
reflection.
For Next Time (FNT)
Continue Chapter 24 homework.
Start reading chapter 25.