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Chapter 4
Light and Atoms
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Hubble
Space
Telescope
(HST)
and
Earth
p.1
How Do Astronomers Learn About the Universe?
• The stars and other objects in space are very far
from Earth. Only a few solar system objects are
close enough to be explored with probes.
• Astronomers rely on electromagnetic waves to
gain information about the universe.
• Electromagnetic waves consist of electric and
magnetic vibrations that travel through space.
(contd.)
Light – the Astronomer’s Tool
• Due to the vast distances, with few exceptions, direct
measurements of astronomical bodies are not
possible
• We study remote bodies indirectly by analyzing their
light
• Understanding the properties of light is therefore
essential
• Care must be given to distinguish light signatures that
belong to the distant body from signatures that do not
(e.g., our atmosphere may distort distant light signals)
• In most cases, light is the only thing that
astronomers can use to study the universe
– An understanding of light is very important to understanding
astronomy
• Light can be thought of as a wave of
electromagnetic energy
– Demonstrated by interference; polarization by magnetic fields
– Frequency and wavelength are important
• Light can also be thought of as a particle
– Demonstrated by photo-electric effect
• Speed of light is constant
– Time and distance are relative
– Can be used to measure distance
Properties of Light
– Light is radiant energy: it does not require a medium
for travel (unlike sound!)
– Light travels at 299,792.458 km/s in a vacuum (fast
enough to circle the Earth 7.5 times in one second)
– Speed of light in a vacuum is constant and is
denoted by the letter “c”
– However, the speed of light is reduced as it passes
through transparent materials
• The speed of light in transparent materials is dependent on
color
• Fundamental reason telescopes work the way they do!
Sometimes light can be described as a wave…
– The wave travels as a result of a fundamental
relationship between electricity and
magnetism
– A changing magnetic field creates an electric field
and a changing electric field creates a magnetic field
…and sometimes it can be described
as a particle!
– Light thought of as a stream of particles called
photons
– Each photon particle carries energy, depending
on its frequency or wavelength
So which model do we use?
– Well, it depends!
• In a vacuum, photons travel in straight lines, but
behave like waves
• Sub-atomic particles also act as waves
• Wave-particle duality: All particles of nature
behave as both a wave and a particle
• Which property of light manifests itself depends
on the situation
• We concentrate on the wave picture henceforth
Light is Electromagnetic Radiation, a self-propagating
Electromagnetic disturbance that carries energy at the
speed of light.
•
•
•
The nature of light is electromagnetic radiation
In the 1860s, James Clerk Maxwell succeeded in describing all
the basic properties of electricity and magnetism in four
equations: the Maxwell equations of electromagnetism.
Maxwell showed that electric and magnetic field should travel
space in z/.z,
Light: Wavelength
and Frequency
• Example
– FM radio, e.g., 103.5 MHz (WTOP station) => λ = 2.90 m
– Visible light, e.g., red 700 nm => ν = 4.29 X 1014 Hz
– The speed of light (c) is the same for all light waves:
– c = 299,792.458 km/sec
– This speed is independent of the wavelength or
frequency of the light wave!
– The speed of light, c, is the only constant of nature we can
state "exactly", only because our metric system of
measuring lengths is defined in terms of the speed of light.
This seems a somewhat circular argument, but what it
amounts to is saying that our measurement system is tied
directly to the speed of light.
Light and Color
• Colors to which the human
eye is sensitive is referred to
as the visible spectrum
• In the wave theory, color is
determined by the light’s
wavelength (symbolized as
l)
– The nanometer (10-9 m) is
the convenient unit
– Red = 700 nm (longest
visible wavelength), violet
= 400 nm (shortest visible
wavelength)
The sequence of photon energies running
from low energy to high energy is called the
Electromagnetic Spectrum.
Photon Energy
low energy = low frequency = long wavelength
Examples of low-energy photons: Radio Waves,
Infrared
high energy = high frequency = short wavelength
Examples of high-energy photons: Ultraviolet, X-rays,
Gamma Rays
Electromagnetic Spectrum
• Visible light falls in the 400 to
700 nm range
• In the order of decreasing
wavelength
– Radio waves: 1 m
– Microwave: 1 mm
– Infrared radiation: 1 μm
– Visible light: 500 nm
– Ultraviolet radiation: 100 nm
– X-rays: 1 nm
– Gamma rays: 10-3 nm
The Visible Spectrum
This is all forms of light we can see with our eyes.
Wavelengths: 400 - 700 nanometers (nm)
Frequencies: 7.5x1014 - 4.3x1014 waves/second
We sense visible light of different energies as different colors. The
basic colors of the visible spectrum are defined roughly as follows, in
order ofincreasing photon energy:
Note:The wavelengths assigned to the colors in this table are meant only to be
illustrative. Color is a physiological response of our brains to visible light of different
energies. Our division of the visible spectrum into named colors is very subjective, and
certainly not a matter of uniform divisions at every 50 nm of wavelength! An oft-cited
example of the subjectivity of color names is the color "orange". It did not enter the
language until the Middle Ages, when the fruit of the same name reached Europe from
the Middle East. Before that, the color would have been called a reddish shade of
yellow.
Frequency
• Sometimes it is more convenient to talk about light’s
frequency
– Frequency (or n) is the number of wave crests that pass a
given point in 1 second (measured in Hertz, Hz)
– Important relation: nl = c
– Long wavelenth = low frequency
– Short wavelength = high frequency
– The higher the frequency, the shorter the wavelength (and viceversa).
– ex. Even though X-rays have higher energy, they move with
the same speed as that of visible light
examples...
White light – a mixture of all colors
• A prism demonstrates
that white light is a
mixture of
wavelengths by its
creation of a spectrum
• Additionally, one can
recombine a
spectrum of colors
and obtain white light
Light and Color
Light has two complementary aspects: waves and particles.
By passing light through a prism, Newton showed that white light is made of a
rainbow of different colors. These colors can be recombined to get white light.
But each individual color is “pure” — when passed through a second prism, it
remains unchanged.
Note: 1 Å = 1  10-10 m.
What property of light distinguishes one color
from another? Answer: Wavelength.
Violet
Blue
Green
Yellow
Orange
Red
≈
≈
≈
≈
≈
≈
4100 Å
4600 Å
5000 Å
5700 Å
6000 Å
6500 Å
The Electromagnetic Spectrum
• The electromagnetic spectrum is composed
of radio waves, microwaves, infrared,
visible light, ultraviolet, x rays, and gamma
rays
• Longest wavelengths are more than 103 km
• Shortest wavelengths are less than 10-18 m
• Various instruments used to explore the
various regions of the spectrum
Infrared Radiation
• Sir William
Herschel (around
1800) showed
heat radiation
related to visible
light
• He measured an
elevated
temperature just
off the red end of
a solar spectrum
– infrared energy
A night vision
camera uses a
detector sensitive to
infrared light, so you
can see objects that
are warmer than
their surroundings.
• Our skin feels
infrared as heat
Ultraviolet Light
• J. Ritter in 1801
noticed silver
chloride
blackened when
exposed to “light”
just beyond the
violet end of the
visible spectrum
• Mostly absorbed
by the
atmosphere
• Responsible for
suntans (and
burns!)
range in wavelength from millimeters to hundreds of meters
Radio Waves
• Predicted by Maxwell in mid-1800s,
Hertz produced radio waves in 1888
• Jansky discovered radio waves
from cosmic sources in the 1930s,
the birth of radio astronomy
• Radio waves used to study a wide
range of astronomical processes
• Radio waves also used for
communication, microwave ovens,
and search for extraterrestrials
• Range in wavelength from
millimeters to hundreds of meters
(can be a wavelength that is about
the size of a person)
Even though X-rays have higher energy, they move with the same speed as that of visible light
X-Rays
– Roentgen discovered X rays in
1895
– First detected beyond the
Earth in the Sun in late 1940s
– Used by doctors to scan bones
and organs
– Used by astronomers to detect
black holes and tenuous gas in
distant galaxies
– Are completely blocked by the
Earth's atmosphere
completely blocked by the Earth's atmosphere
Gamma Rays
• Gamma Ray region of
the spectrum still
relatively unexplored
• Atmosphere absorbs
this region, so all
observations must be
done from orbit!
• We sometimes see
bursts of gamma ray
radiation from deep
space
Energy Carried by Electromagnetic
Radiation
– Each photon of wavelength l
carries an energy E given by:
E = hc/l
–
–
–
–
where h is Planck’s constant
Notice that a photon of short
wavelength radiation carries
more energy than a long
wavelength photon
Short wavelength = high
frequency = high energy
Long wavelength = low
frequency = low energy
A photon of blue light has more
energy than a photon of red light.
Photon: Massless particles that carry energy at the speed of light.
Photons are characterized by their Energy, which is proportional
to their Frequency, f.
Photon Energy:
E = hf where: f = frequency of the light, and h = Planck's Constant
In words:
Higher Frequencies mean Higher Energies
Note: Energy, E, is a "particle property", whereas frequency, f, is a
"wave property". They are related through Planck's Constant, h.
Planck's constant is one of the "Fundamental Constants" of Nature
(another one we've met in this lecture is the speed of light, c). One can
think of Planck's constant as serving as the "link" between the wave
and particle natures of light, and indeed h is the fundamental constant
in "quantum mechanics", the modern view of matter and radiation as
entities ("quanta") that have the properties of both waves and
particles.
Matter and Heat
• The Nature of Matter and Heat
– The ancient Greeks introduced the idea of the atom
(Greek for “uncuttable”), which today has been
modified to include a nucleus and a surrounding
cloud of electrons
– Heating (transfer of energy) and the motion of
atoms was an important topic in the 1700s and
1800s
A New View of Temperature
• The Kelvin Temperature Scale
– An object’s temperature is directly related to its
energy content and to the speed of molecular
motion
– As a body is cooled to zero Kelvin, molecular
motion within it slows to a virtual halt and its
energy approaches zero  no negative temperatures
– Fahrenheit and Celsius are two other temperature
scales that are easily converted to Kelvin
The Kelvin Temperature Scale
A temperature of 0 Kelvin means there is essentially no motion at the atomic level
Parts of the electromagnetic spectrum lowest to highest energy
- gamma rays, infrared, ultraviolet, radio waves, visible ….etc
atmospheric window - a range of wavelengths of electromagnetic
radiation which transmit through the Earth's atmosphere
Radiation and Temperature
• Heated bodies generally
radiate across the entire
electromagnetic spectrum
• There is one particular
wavelength, lm, at which the
radiation is most intense and
is given by Wien’s Law:
lm = k/T
Where k is some constant
and T is the temperature
of the body
According to Wein's Law, if the
surface temperature is
increased by a factor of 2, its
peak wavelength will decrease
by a factor of 2.
Radiation and Temperature
– Note hotter bodies radiate
more strongly at shorter
wavelengths
– As an object heats, it appears
to change color from red to
white to blue
– Measuring lm gives a body’s
temperature
– Careful: Reflected light does not
give the temperature
– A stove burner is an example
of a blackbody that you see in
everyday life.
Radiation depending on Temperature
• A general rule:
The higher an object’s temperature, the more intensely
the object emits electromagnetic radiation and the
shorter the wavelength at which emits most strongly
The example of heated iron
bar. As the temperature
increases
– The bar glows more
brightly
– The color of the bar also
changes
Blackbodies and Wien’s Law
– A blackbody is an object that absorbs all the radiation falling on
it
– Since such an object does not reflect any light, it appears black
when cold, hence its name
– As a blackbody is heated, it radiates more efficiently than any
other kind of object
– Blackbodies are excellent absorbers and emitters of radiation
and follow Wien’s law
– Very few real objects are perfect blackbodies, but many objects
(e.g., the Sun and Earth) are close approximations
– Gases, unless highly compressed, are not blackbodies and can
only radiate in narrow wavelength ranges
– The wavelength at which a blackbody radiates most depends on
its temperature
– Wien's law allows astronomers to measure the surface
temperature of the star.
Blackbody Radiation
• Hot and dense objects act like a blackbody
• Stars, which are opaque gas ball, closely approximate the behavior
of blackbodies
• The Sun’s radiation is remarkably close to that from a
blackbody at a temperature of 5800 K
The Sun as a Blackbody
A human body at room temperature
emits most strongly at infrared light
Blackbodies and Wien’s Law
Wien’s Law allows
astronomers to
measure what
property of a star
•Wien’s law states that the dominant wavelength at
which a blackbody emits electromagnetic radiation is
inversely proportional to the Kelvin temperature of the
object
For example
– The Sun, λmax = 500 nm  T = 5800 K (emits a spectrum
very close to a blackbody spectrum)
– Human body at 37 degrees Celcius, or 310 Kelvin  λmax
= 9.35 μm = 9350 nm
Blackbody radiation: Stefan-Boltzmann Law
• The Stefan-Boltzmann law states that a blackbody radiates
electromagnetic waves with a total energy flux F directly
proportional to the fourth power of the Kelvin
temperature T of the object:
F = T4
• F = energy flux, in joules per square meter of surface per
second
•  = Stefan-Boltzmann constant = 5.67 X 10-8 W m-2 K-4
• T = object’s temperature, in kelvins
Each kind of atom has a unique set of
wavelengths at which it emits and absorbs,
allowing us to determining the composition
of many objects.
However, atoms packed close together (in a
dense gas or solid) will generally emit and
absorb over a wide range of wavelengths,
producing a continuous blackbody spectrum
that shifts to shorter wavelengths as the
temperature of the material grows hotter.
The Structure of Atoms
• Nucleus – Composed of
densely packed neutrons
and positively charged
protons
• Cloud of negative
electrons held in orbit
around nucleus by
positive charge of
protons
• Typical atom size: 10-10
m (= 1 Å = 0.1 nm)
The identity of a
chemical element
is determined by The
number of
protons in the nucleus
Electrical attraction holds the electron in orbit around the nucleus of the atom
The Chemical Elements
• An element is a substance
composed only of atoms
that have the same number
of protons in their nucleus
• A neutral element will
contain an equal number
of protons and electrons
• The chemical properties of
an element are determined
by the number of electrons
Electron “Orbits”
• The electron orbits are
quantized (The electrons can
stay only in specific orbits),
can only have discrete values
and nothing in between
• Quantized orbits are the
result of the wave-particle
duality of matter
• As electrons move from
one orbit to another, they
change their energy in
discrete amounts
Energy Change in an Atom
• An atom’s energy is increased
if an electron moves to an
outer orbit – the atom is said
to be excited
(occurs when an electron in an
atom jumps from a lower energy
orbital to a higher energy orbital)
• When an electron in an atom
absorbs a photon (a particle
of light) the electron
moves to a higher
energy level.
• An atom’s energy is decreased
if an electron moves to an
inner orbit
Conservation of Energy
• The energy change of an atom must be compensated
elsewhere – Conservation of Energy
(Conservation of energy requires that if an atom absorbs a
photon an electron rises to a new orbital with an energy
equal to that of the previous orbital plus the energy of the
photon.)
• Absorption and emission of EM radiation are two ways to
preserve energy conservation
• In the photon picture, a photon is absorbed as an electron
moves to a higher orbit and a photon is emitted as an
electron moves to a lower orbit
Emission
Absorption
The key to determining the composition and
conditions of an astronomical body is its
spectrum.
The technique used to capture and analyze such a
spectrum is called spectroscopy.
In spectroscopy, the light (or more generally the
electromagnetic radiation) emitted or reflected by
the object being studied is collected with a
telescope and spread into its component colors to
form a spectrum by passing it through a prism or
a grating consisting of numerous, tiny, parallel
lines.
Spectroscopy
• Allows the determination of
the composition and
conditions of an astronomical
body
• In spectroscopy, we capture
and analyze a spectrum
• Spectroscopy assumes
that every atom or
molecule will have a
unique spectral
signature
Formation of a Spectrum
• A transition in energy level produces a photon
The study of light
Spectroscopy
•Types of spectra
•Continuous spectrum: A spectrum that contains
all colors or wavelengths.
•Produced by an incandescent solid, liquid, or high
pressure gas
•Uninterrupted band of color
•Dark-line (absorption) spectrum
•Produced when white light is passed through a
comparatively cool, low pressure gas
•Appears as a continuous spectrum but with
dark lines running through it
Formation of the three types of spectra
Emission spectrum of hydrogen
Emission Spectrum
Absorption Spectrum
A spectrum consisting of individual
lines at characteristic wavelengths
produced when light passes through
an incandescent gas; a bright-line
spectrum.
(has bright lines on dark background)
A continuous spectrum
crossed by dark lines
produced when light
passes through a
nonincandescent gas.
(has dark lines on a
continuous background)
Absorption Spectrum of Hydrogen
Spectra
The spectrum of an object is the amount of energy that it radiates at each wavelength.
Much of what we know about the Universe comes from spectra.
They are much more instructive than images.
Continuous Spectra
All macroscopic objects emit radiation at all times. Their atoms move around by an
amount that increases with temperature. Accelerated charged particles radiate. So:
Everything radiates with a spectrum that is directly related to its temperature.
For example: people are warm; they glow brightly in the infrared. Similarly, a warm
iron glows in the infrared but not in visible light. Then, as it is heated to higher and
higher temperatures, it glows red, then white, then blue.
Continuous Spectra
An idealized object that absorbs all radiation that hits it is called a black body.
In equilibrium with its surroundings, it emits exactly as much radiation as it
absorbs. Then it emits a spectrum as described in Figure 6-6 of (most editions
of) the text. This black body or thermal radiation has the following properties:
– It is continuous radiation (there are no emission or absorption lines):
– Its spectrum is brightest at a wavelength that depends on
temperature, and the brightness falls more quickly toward the
blue than toward the red.
Specifically:
– Wien’s Law: The wavelength of maximum brightness in Å is 30,000,000 K
divided by the temperature in K. That is, lmax = 3.0  107 Å / T(K). Hotter things
radiate bluer light. If the temperature doubles, the wavelength of maximum
brightness gets 2 times shorter.
– Stefan-Boltzmann Law: The total energy emitted varies as the 4th power of
temperature: E = sT4 = s  T  T  T  T. The Stefan-Boltzmann constant s is
given....
A black body is an idealized concept, but for many objects (including
stars), the above are useful approximations.
Types of Spectra
– Continuous spectrum
• Spectra of a blackbody
• Typical objects are solids and dense gases
– Emission-line spectrum
• Produced by hot, tenuous gases
• Fluorescent tubes, aurora, and many interstellar clouds are
typical examples
• bright lines on dark background
– Dark-line or absorption-line spectrum
• Light from blackbody passes through cooler gas leaving
dark absorption lines
• Fraunhofer lines of Sun are an example
• has dark lines on a continuous background
Emission Spectrum
Emission Spectrum
Continuous and Absorption Spectra
Astronomical Spectra
Spectral lines shifted toward
higher frequencies are called
Blue-shifted.
The spectral lines of a star will
appear Red-shifted if the star is
moving away from the Earth
Absorption in the Atmosphere
• Gases in the Earth’s atmosphere absorb
electromagnetic radiation to the extent that most
wavelengths from space do not reach the ground
• Visible light, most radio waves, and some infrared
penetrate the atmosphere through atmospheric
windows, wavelength regions of high transparency
• Lack of atmospheric windows at other
wavelengths is the reason for astronomers placing
telescopes in space
Motion of atoms alters the wavelengths we observe,
creating a Doppler shift from which we can deduce their
speed toward or away from us.
If the source moves toward us, the wavelengths
of its light will be shorter. If it moves away from us, the
wavelengths will be longer.
The Doppler shift occurs for all kinds of waves. You have
perhaps heard the Doppler shift of sound waves from the
siren of an emergency vehicle as it passes you and
moves away: the siren's pitch drops as the wavelength of
its sound increases.
Likewise, the Doppler shift of a radar beam that bounces
off your car reveals to a law enforcement officer how
fast your car is moving
*No shift when object is moving very fast perpendicularly to your line of sight
Doppler Shift in Sound
• If the source of sound is moving, the pitch changes!
It is easy to see why the Doppler shift occurs.
Imagine that the waves from the moving source
are a wiggly line. If the source is moving away
from you, the wiggles get stretched so the spacing
of the waves increases. If the source is moving
toward you, the wiggles are scrunched up so the
spacing of the waves decreases.
△λ = Wavelength shift
λ = Measured wavelength (what we observe)
λ0 = Measured wavelength (what we observe)
c = Speed of light
V = Velocity of source along the line of sight (radial
velocity)
Doppler Shift
in Light
– The shift in
wavelength is given as
Dl = l – lo = lov/c
– If a source of light is set in
motion relative to an
observer, its spectral lines
shift to new wavelengths
in a similar way
where l is the
observed (shifted)
wavelength, lo is the
emitted wavelength, v
is the source nonrelativistic radial
velocity, and c is the
speed of light
Mathematically, the Doppler shift arises because the
wavelength we observe (λ) is the original
wavelength (λ0) plus the distance the source travels during
the time a single wave is emitted.
That distance depends on the speed, V, of the source along the
line from the source to the observer, a speed
astronomers call the radial velocity. Some mathematics
(omitted here) then leads to the Doppler shift
formula
The Doppler shift is the same if the emitting object is moving towards
you at some speed, or you (the observer) are moving towards it at that
speed and it is still.
where c is the speed of the wave and △λ = (λ – λ0) is
simply shorthand for the change in wavelength.*
We will see applications of this law in later chapters.
Here, our goal is simply to indicate that the
Doppler shift allows us to find out how fast a
source is moving away from (positive V) or toward
(negative V) us.
Redshift and Blueshift
• An observed increase in
wavelength is called a
redshift, and a decrease in
observed wavelength is
called a blueshift
(regardless of whether or
not the waves are visible)
• Doppler shift is used to
determine an object’s
velocity
Doppler-shift measurements can be made at any wavelength
of the electromagnetic spectrum. But regardless of the
wavelength region observed or whether the waves are of
visible light, astronomers generally refer to shifts that
increase the measured wavelength as redshifts and those
that decrease the measured wavelength as blueshifts.
Thus, even though we may be describing radio waves, we
will say that an approaching source is blueshifted and a
receding one is redshifted.
Doppler shift measurements are very powerful for
understanding the nature of astronomical objects.
When astronomers study the light emitted from the Sun they
notice that the light emitted from the east limb (edge) is
blueshifted while the light emitted west limb is redshifted.
The reason for this is that the Sun is rotating
Family Photo Album
• Let’s take a look at some of the members of
the astronomical fam seen in different kinds
of light (different radiation wavelengths).
• A planet – Saturn
• A star – our Sun
• A nebula formed by an exploding star
• A couple of galaxies
• The Universe (really !!)
Saturn – Different Wavelengths
Saturn – Different Wavelengths
Ultraviolet
Visible
Infrared
Radio
Sun – Different Wavelengths
Sun – Different Wavelengths
X-Ray
Visible
Ultraviolet
Infrared
Radio
Supernova Remnant (Crab Nebula)
Supernova Remnant (Crab Nebula)
X-Ray
Visible
Radio
Ultraviolet
XR+Vis+Radio
Whirlpool Galaxy M 51
Whirlpool Galaxy M 51
X-Ray
Visible
Infrared
Radio
Our Galaxy – The Milky Way
Where are the Telescopes ?
• For Gamma Rays, X-Rays, Ultraviolet and
Infrared, the telescopes have to be above
the Earth’s atmosphere. Why ?
• For Visible Light and Radio Waves, the
telescopes can be on the Earth’s surface
or above the atmosphere. Why ?
• Following are some famous telescopes.
Thanks to Tim Compernolle
Swift Gamma Ray Telescope
Chandra X-Ray Observatory
Hubble Space Telescope
(Ultraviolet, Visible, Infrared)
Spitzer Space Telescope
(Infrared)
Keck Telescope – Hawaii
(Visible)
Keck Telescope – Hawaii
(Visible)
Keck Telescope – Hawaii
(Visible)
Arecibo Radio Telescope –
Puerto Rico
Arecibo Radio Telescope –
Puerto Rico
Radio Telescope
Radio Telescope
Radio Telescope – Very Long
Baseline Array
Wilkinson Microwave
Anisotropy Probe (WMAP)
Light is Weird – Part 1 – Photons
• Light sometimes behaves like a wave, like we have been
talking about.
• But light also can behave like a particle (called a
photon).
• Einstein proposed that light travels as waves with the
energy enclosed in photons.
• Shorter wavelength = higher energy photon.
• Longer wavelength = lower energy photon.
• So what kind of light has the highest energy photons?
Look at the Electromagnetic Radiation diagram.
• What kind of light has the lowest energy photons? Look
at the diagram.
LOW ENERGY
HIG
Light is Weird – Part 2 –
Doppler Shift
• Light wavelength is changed by motion of the
light source – just like sound waves are.
• This means light changes color according to
how the light source is moving.
• Light source (like a star) moves away from you =
light looks more red to you = Doppler Redshift.
• Light source (like a star) moves toward you =
light looks more blue to you = Doppler Blueshift.
• Look at the following diagrams.
Doppler Shift for Sound
Doppler Shift for Light – Moving Star
More Doppler – What if YOU are Moving?
Electromagnetic Wave Math
1. Electromagnetic radiation was detected with a frequency of 3 x 1010
Hz. What is the wavelength of this wave? What type of wave might
this be?
2. Electromagnetic radiation was detected with a frequency of 3 x 1018
Hz. What is the wavelength of this wave? What type of wave might
this be?
Electromagnetic Wave Math
3. What is the wavelength of the carrier wave received at FM station
100 megahertz on your radio dial
(1 megahertz = 1x106 Hz)?
4. When you look at a distant star or planet, you are looking back in
time. How far back in time are you looking when you observe Pluto
through the telescope from a distance of 5.91 x 1012 m?
Electromagnetic Wave Math
5. If a person could travel at the speed of light, it would still take 4.3
years to reach the nearest star, Proxima Centauri. How far away in
meters, is Proxima Centauri? (need to convert years to seconds)
6. When you go out in the sun, it is the ultraviolet light that gives you a
tan. The pigment in your skin called melanin is activated by the
enzyme tyrosinase, which has been stimulated by ultraviolet light.
What is the wavelength of this light if it has a frequency of 7.89 x
1014 Hz?