Electromagnetic Radiation

Notes on Light (Electromagnetic Radiation)

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At least 95% of the celestial information we receive is in the form of light. Because of this fact, we have devised many techniques to decode as much as possible the messages that are encoded in the often extremely faint rays of light. These messages include information about the object's temperature, motion, chemical composition, gas density, surface gravity, shape, structure, and more! Roughly 85% of the information in light is uncovered by using spectroscopy---spreading the light out into its different constituent colors or wavelengths and analyzing the spectrum. The first part of this document covers the characteristics of all forms of light and the following sections cover spectroscopic analysis. The vocabulary terms are italicized.

Properties

Light, electricity, and magnetism are manifestations of the same thing called electromagnetic radiation. The energy you see coming out of the computer screen you are using to read this page is made of fluctuating electric and magnetic energy fields. The electric and magnetic fields oscillate at right angles to each other and the combined wave moves in a direction perpendicular to both of the electric and magnetic field oscillations.

This energy comes in many forms that are not detectable with our eyes such as infrared (IR), radio, X-rays, ultraviolet (UV), and gamma rays. We feel infrared light as heat and our radios pick up the messages encoded in radio waves emitted by radio stations. Ultraviolet light has high enough energy to damage our skin cells, so our bodies will produce a darker pigment in our skin to prevent exposure of the deeper skin cells to the UV (we tan as a defense mechanism). The special bulbs called ``black lights'' produce a lot of UV and were used by hospitals to kill bacteria, amoebas, and other micro-organisms. X-rays are produced by very hot things in space. X-rays have more energy than UV so they can pass through skin, muscles, and organs.

The form of electromagnetic radiation our eyes can detect is called ``visible'' or ``optical''. We have only recently (within the past few decades) been able to use the other forms of electromagnetic radiation or light. Every time we have developed the technology to detect another form of light, a revolution in our understanding of the universe has occurred. The figure below shows all of the forms of electromagnetic radiation in order of INcreasing wavelength (given in nanometers (nm)) and DEcreasing energy. Notice how tiny the visible band is!

There are some general properties shared by all forms of electromagnetic radiation:

  1. It can travel through empty space. Other types of waves need some sort of medium to move through: water waves need liquid water and sound waves need some gas, liquid, or solid material be heard.
  2. The speed of light is constant in space. All forms of light have the same speed of 299,800 km/s in space (often abbreviated as c). From highest energy to lowest energy the forms of light are gamma rays, X-rays, Ultraviolet, Visible, Infrared, Radio. (Microwaves are high-energy radio waves.)
  3. A wavelength of light is defined similarly to that of water waves---distance between crests or between troughs. Visible light (what your eye detects) has wavelengths 4000-8000 Angstroms (‰). 1 ‰ = 10-10 meter (m). Visible light is sometimes also measured in nanometers (nm): 1 nm = 10-9 m = 10 ‰. Radio wavelengths are often measured in centimeters (cm): 1 cm = 10-2 m = 0.01 m. The abbreviation used for wavelength is the greek letter lambda: l.

White light is made of different colors (wavelengths). When white light is passed through a prism or diffraction grating, it is spread out into all of its different colors. You see this happen every time you see a rainbow. Not all wavelengths of light from space make it to the surface. Only long-wave UV, Visible, parts of IR, and parts of the radio band make it to surface. More IR reaches elevations above 9,000 feet (2765 m) elevation. That is one reason why modern observatories are built on top of very high mountains. Fortunately, as far as life is concerned, our atmosphere shields us from the gamma rays, X-rays, and most of the UV. It also blocks most of the IR and parts of the radio. We were not able to detect these forms of energy until the space age, when we could put satellite observatories in orbit.

Besides using wavelength to describe the form of light, we also use the frequency--the number of crests of the wave that pass by a point every second. Frequency is measured in units of hertz (Hz): 1 Hz = 1 wave crest/second. There is a simple relation between the speed of light (c), wavelength (l), and frequency f:

f = c/l.
Since the wavelength l is in the denominator, the frequency is inversely proportional to the wavelength. This means that light with a smaller wavelength has a higher (larger) frequency. Light with a longer wavelength has a lower (smaller) frequency.

Some colors and their approximate wavelength, frequency and energy ranges are given in the table below. The unit of energy is the Joule (J). Sometimes light energy is also measured in ``ergs'' = 10-7 J.

color l (‰) f (*1014 Hz) Energy (*10-19 J)
violet 4000 to 4600 7.5 to 6.5 5.0 to 4.3
indigo 4600 to 4750 6.5 to 6.3 4.3 to 4.2
blue 4750 to 4900 6.3 to 6.1 4.2 to 4.1
green 4900 to 5650 6.1 to 5.3 4.1 to 3.5
yellow 5650 to 5750 5.3 to 5.2 3.5 to 3.45
orange 5750 to 6000 5.2 to 5.0 3.45 to 3.3
red 6000 to 8000 5.0 to 3.7 3.3 to 2.5
Note the trends: blue light has shorter l, higher f, more energy. Redder light has longer l, lower f, and less energy. In the early part of the 20th century Albert Einstein found a very simple relationship between the energy of a light wave and its frequency:
Energy of light = h * f
Energy of light = (h * c)/l,
where h is ``Planck's constant'' = 6.626 * 10-36 J…s.

At the beginning of the 20th century Max Planck discovered that if we consider light as packets of energy called photons, we can accurately explain the shape of continuous spectra. A photon is a particle of electromagnetic radiation. Bizarre though it may be, light is both a particle and a wave. Whether light behaves like a wave or like a particle depends on how the light is observed (it depends on the experimental setup)! Experiments set up to show interference and diffraction effects will show electromagnetic radiation to be a wave. Experiments set up to show the photoelectric effect, Compton effect, bremsstrahlung, and pair production will show electromagnetic radiation to be photons.

Light can also behave as a particle and a wave at the same time. An example of light acting as both a particle and a wave is the digital camera---the lens refracts (bends and focusses) waves of light that hit a charge-coupled device (CCD). The photon particles kick electrons out of the silicon in the CCD. The electrons are detected by electronics that interpret the number of electrons released and their position of release from the silicon to create an image. Another example is when we observe the build-up of a diffraction pattern (a wave phenomenon) from light passing through a narrow slit. We see one bright spot (a photon), then another bright spot (another photon), then another... until the diffraction pattern is created from all of the accumulated photons.

To decode the information stored in light, we pass the light through a prism or diffraction grating to create a spectrum---a display of the intensity of light (EM radiation) at different wavelengths or frequencies. If it is white light we are examining, then the spectrum will be a rainbow. We will broaden the definition of a spectrum to include plots of the intensity vs. wavelength or frequency.

The term intensity has a particular meaning here: It is the number of waves or photons of light reaching your detector; a brighter object is more intense but not necessarily more energetic. Remember that a photon's energy depends on the wavelength (or frequency) only, not the intensity. The photons in a dim beam of X-ray light are much more energetic than the photons in an intense beam of infrared light.

The type of light produced by an object will depend on its temperature, so let's digress slightly to investigate what ``temperature'' is. Temperature is a measure of the random motion (or energy) of matter. Higher temperature (T) means more random motion (or energy). A natural scale would have zero motion at zero degrees (absolute zero). This scale is the Kelvin scale. It scales exactly like the Celsius system, but it is offset by 273 degrees. Here is a comparison of the Kelvin, Celsius, and Fahrenheit temperature scales:

K C F
0 -273 -459 absolute zero
100 -173 -279.4
273 0 32 water freezes
310 37 98.6 human temperature
373 100 212 water boils (STP)
755 482 900 oven on ``clean'' setting
5840 5567 10053 Sun's temperature

Temperature is related to the average kinetic energy (energy of motion) of a group of particles: T = (kinetic energy)/(3*k/2), where k is another universal constant of nature called the ``Boltzmann constant.'' An object with mass m moving at speed v has kinetic energy = (1/2)*m*v2. Plugging this into the temperature relation, we find that T = m*v2/(3*k). Since the speed v is in the numerator, particles with the same mass m will move faster as the temperature increases. How fast a particle moves also depends on its mass. For different types of gases at the same temperature, the more massive gas particles will be moving slower than the lower-mass gas particles. For example, an atmosphere made of carbon dioxide and hydrogen will have the very light hydrogen molecules moving much faster than the massive carbon dioxide molecules. This fact is important in determining how a planet's atmosphere will leak away to space.

Vocabulary

electromagnetic radiation frequency hertz
intensity Kelvin kinetic energy
photon spectroscopy spectrum
temperature wavelength

Formulae

  1. Frequency and wavelength relation: f = c/l.
  2. Energy of a photon: E = h*f, where h is a constant of nature.
  3. Energy of a photon: E = (h*c)/l.
  4. Temperature, mass, speed relation: T = mv2/(3k).

Review Questions

  1. Why is light so very important to astronomy? What kinds of information can we get from it?
  2. Why is light called electromagnetic radiation? Is radio a form of light?
  3. Put the following forms of light in order of increasing frequency (lowest frequency first): ultraviolet, infrared, gamma rays, visible, radio, X-rays. Put them in order of increasing wavelength (shortest wavelength first). Put them in order of increasing energy (lowest energy first).
  4. Do all forms of light travel at the same speed in a vacuum (empty space)? Why is it important that light can travel through empty space?
  5. What forms of light can be observed from the ground (including high mountains)? What forms can be observed at high altitudes in our atmosphere? What forms must be observed in space?
  6. Is electromagnetic radiation a wave or a particle? What determines if we will see light as a wave or a photon?
  7. Which of these are a spectrum: plot of intensity vs. wavelength, plot of intensity vs. brightness, plot of frequency vs. wavelength, rainbow, plot of acceleration vs. time, plot of energy vs. frequency.
  8. What is the difference between intensity and energy? If a particular CCD chip requires light energies of 4.2 * 10-19 J to release electrons from the silicon, which will produce more electrons (and hence, a brighter computer image): an intense beam of yellow light or a dim beam of UV light?
  9. How does temperature depend on the average kinetic energy? At a given temperature, which particles will be moving faster: a low-mass particle or a high-mass particle?
  10. Why is the Kelvin scale preferred over the Celsius or the Fahrenheit scales?
  11. Where is absolute zero on the three temperature scales? Where is the Sun's temperature on the three temperature scales?

Production of Light

When light is passed through a prism or a diffraction grating to produce a spectrum, the type of spectrum we will see depends on what kind of object is producing the light: is it a thick or thin gas, is it hot or cool, is it a gas or a solid? There are two basic types of spectra: continuous spectrum (energy at all wavelengths) and discrete spectrum (energy at only certain wavelengths). Astronomers usually refer to the two types of discrete spectra: emission lines (bright lines) and absorption lines (rainbow with dark lines) as different types of spectra.

Continuous Spectrum

A rainbow is an example of a continuous spectrum. A continuous spectrum is also called a thermal spectrum, because hot, dense objects will emit electromagnetic radiation at all wavelengths or colors. Any solid, liquid and dense (thick) gas at a temperature above absolute zero will produce a thermal spectrum. A thermal spectrum is the simplest type of spectrum because its shape depends on only the temperature. A discrete spectrum is more complex because it depends on temperature and other things like the chemical composition of the object, the gas density, surface gravity, speed, etc.

Sometimes astronomers use the term ``blackbody'' spectrum. A ``blackbody'' is an object that absorbs all the light falling on it, reflecting none of it, hence, it appears black. When the ``blackbody'' object is heated, it emits light very efficiently without any gaps or breaks in the brightness. Though no object is a perfect ``blackbody'', most stars, planets, moons and asteroids are near enough to being ``blackbodies'', that they will produce spectra very similar to a perfect thermal spectrum.

Some thermal spectra for objects of different temperatures are illustrated in the figure below.

Some key features of a thermal (continuous) spectrum are as follows:

  1. There is light from the dense object at all possible l IF the object is above 0 K (absolute zero). Since everything in the universe is above 0 K, all dense objects (solids, liquids, thick gases) will produce a thermal spectrum.
  2. The shape of continuous spectrum depends only on the temperature of the object NOT its chemical composition. This allows us to determine remotely the temperature of an object.
  3. As the temperature of an object increases, more light is produced at all wavelengths than when it was cooler. You can see this effect with a light bulb hooked to a dimmer switch. As you raise the current going to the bulb, the bulb's filament gets hotter and brighter.
  4. As the temperature of an object increases, the peak of thermal spectrum curve shifts to smaller wavelengths (higher frequencies)---cool things appear red or orange, hotter things appear yellow or white, and very hot things blue or purple. This is opposite to what artists use for ``cool'' colors (blues) or ``hot'' colors (reds)!

    Wilhelm Wien (lived 1864-1928) discovered that the peak of the thermal spectrum curve, lpeak, is related to the temperature by lpeak = 2.9 * 106 nm / T (in K). This simple relation is now known as Wien's Law. Using this we see that cool objects like cars, plants, and people radiate most of their energy in the infrared. Very cold objects radiate mostly in the radio band.

  5. A small change in the temperature produces a HUGE change in the amount of energy emitted by every unit area of the object. If we add up all of the energy emitted by a unit area on the object's surface every second, we find it equals sigma*T4, where sigma is a constant of nature [=5.67*10-5 erg/(cm2 K4 s) OR 5.67*10-8 J/(m2 K4 s)]. This relation is called the Stefan-Boltzmann law. Because the temperature is raised to the fourth power, a small rise in the temperature means a HUGE increase in the amount of energy emitted.

    When we add up all of the energy of all of the unit areas on the object's surface, we get the luminosity---the total amount of energy emitted every second by the object. The luminosity = total surface area * sigma*T4. If our Sun were just twice as hot as it is now, it would produce 24 = 16 times more energy than it does now!

Discrete Spectrum

Close examination of the spectra from our Sun and other stars reveals that the rainbow of colors has many dark lines in it, called absorption lines. They are produced by the cooler thin gas in the upper layers of the stars absorbing certain colors of light produced by the hotter dense lower layers. The spectra of thin (low density) gas clouds are a series of bright lines called emission lines. In both of these types of spectra we see spectral features at certain, discrete wavelengths (or colors) and no where else.

The type of spectrum we see depends on the temperature of the thin gas. If the thin gas is cooler than the thermal source in the background, we see absorption lines. Since the spectra of stars show absorption lines, it tells us that the density and temperature of the upper layers of a star is lower than the deeper layers. In a few cases we see emission lines on top of the thermal spectrum. This is produced by thin gas that is hotter than the thermal source in the background. Unlike the case for absorption lines, though, the production of emission lines does NOT require a thermal source be in the background. The spectrum of a hydrogen-emission nebula (``nebula'' = gas or dust cloud) is just a series of emission lines without any thermal spectrum because there are no stars visible behind the hot nebula. Some objects produce spectra that is a combination of a thermal spectrum, emission lines, and absorption lines simultaneously!

What is very useful about discrete spectra is that the pattern of lines we see depends on the chemical composition of the thin gas. Each element or molecule produces a distinct pattern of lines---each element or molecule has a ``fingerprint'' we can use to identify it. This allows us to remotely determine what stars, planets, nebulae, etc. are made of!

The composition can not be found from just one line because one element may have one spectral line at the same wavelength as another element's spectral line. However, an element's pattern of lines is unique. Using a single line to identify a gas would be like identifying the name of someone using just one letter of their name---many people will have that same letter in their name, but the pattern of letters (which letters and how they are arranged) is unique to that one person. Of course, stars, planets, nebulae, etc. are made of more than one type of material, so we see the discrete spectra of many elements and molecules superimposed on each other. An experienced astronomer can disentangle all the different patterns and sort out the elements and molecules (but it does take time!).

Vocabulary

absorption line spectrum continuous spectrum discrete spectrum
emission line spectrum luminosity thermal spectrum

Formulae

  1. Wien's Law: lpeak = 2.9 * 106 nm/T. The units of the wavelength are nanometers (nm) and the temperature is in Kelvin (K).
  2. Stefan-Boltzmann Law: Energy emitted by a unit area on an object's surface = sigma*T4, where sigma is a constant of nature.

Review Questions

  1. What are the three basic kinds of spectrum? Can an object produce more than one type at the same time?
  2. What produces a continuous spectrum?
  3. How can temperature be determined from a continuous spectrum? How would the color of a hot object compare to the color of a cooler object? At what wavelength do you at 98.6 degrees Fahrenheit radiate the most?
  4. How will the thermal spectrum produced by a chunk of lead compare to the thermal spectrum produced by a chunk of iron of the same size?
  5. What produces an emission line spectrum? Do you need a thermal source in the background?
  6. Can you see emission lines if a thermal source is in the background? What does their visibility depend on? (Think about the temperature of the gas producing the emission lines and the temperature of the the background thermal source.)
  7. What produces an absorption line spectrum? Do you need a thermal source? Would you see absorption lines if the gas in front of a thermal source was hotter than the thermal source?
  8. Why must we use a pattern of lines to find the composition? Why is one line not sufficient?
  9. What kind of spectrum and what pattern of lines would you see if you heated up a tube filled with hydrogen, helium and neon gas?

Bohr atom

We have had the technology to observe discrete spectra since the beginning of the 19th century. We had to wait over a hundred years, though, for an explanation of how the discrete spectra were produced. We knew that it was produced by atoms and that atoms had negative and positive charges in them. Some models of the atom were similar to our current one: the positive charges are concentrated in a central nucleus with the negative charges swarming around it, but the atoms should be unstable. As the negative charges (called electrons move around the nucleus, they should radiate light and spiral into the nucleus in about 10-16 second. This is obviously contradicted by common experience!

Niels Bohr (lived 1885-1962) provided the explanation in the early 20th century. He said that the electron can be only found in energy orbits of a certain size and as long as the electron is in one of those special orbits, it would radiate no energy. If the electron changed orbits, it would radiate or absorb energy. This model sounds outlandish, but numerous experiments have shown it to be true.

In Bohr's model of the atom, the massive but small positively-charged protons and massive but small neutral neutrons are found in the tiny nucleus. The small, light negatively-charged electrons move around the nucleus in certain specific orbits (energies) around nucleus. In a neutral atom the number of electrons = the number of protons. The arrangement of an atoms's energy orbits depends on the number of protons and neutrons in the nucleus and the number of electrons orbiting the nucleus. Because every type of atoms has a unique arrangement of the energy orbits, they produce a unique pattern of absorption or emission lines.

All atoms with the same number of protons in the nucleus are grouped together into something called an element. Because the atoms of an element have the same number of protons, they also have the same number of electrons and, therefore, the same chemical properties. For example, all atoms with one proton in the nucleus have the same chemical properties and are called Hydrogen. All atoms with two protons in the nucleus will not chemically react with any other atoms and are known as Helium. The atoms called Carbon form the basis of life and have six protons in the nucleus. In the figure below, atom (a) is Hydrogen, atom (b) is Helium, atoms (c), (d), and (e) are Lithium.

Elements are sub-divided into sub-groups called isotopes based on the number of protons AND neutrons in the nucleus. All atoms of an element with the same number of neutrons in the nucleus are of the same type of isotope. An element's isotopes will have very nearly the same chemical properties but they can behave very differently in nuclear reactions. For example, all of the isotopes of the element Hydrogen have one electron orbiting the nucleus and behave the same way in chemistry reactions. The ordinary Hydrogen isotope has 0 neutrons + 1 proton while another Hydrogen isotope called Deuterium has 1 neutron + 1 proton and another Hydrogen isotope called Tritium has 2 neutrons + 1 proton in the nucleus. Tritium is radioactive---its nucleus spontaneouly changes into another type of nucleus. In the figure above, atoms (c), (d), and (e) are different isotopes of the same element called Lithium.

Most atoms in nature are neutral, the negative charges exactly cancel the positive charges. But sometimes an atom has a hard collision with another atom or absorbs an energetic photon so that one or more electrons are knocked out of the atom. In some rare cases, an atom may temporarily hold onto an extra electron. In either case, the atom has an extra positive or negative charge and is called an ion. For example, the carbon ion C+ has 6 protons and 5 electrons and the iron ion Fe2+ has 26 protons and 24 electrons. Because the number of electrons are different, an ion of an element will behave differently in chemical reactions than its neutral cousins. In the figure above atom (d) is a Li+ ion [compare it with atom (c) or (e)].

In order to explain discrete spectra, Bohr found that atoms obey three basic rules:

  1. Electrons have only certain energies corresponding to particular distances from nucleus. As long as the electron is in one of those energy orbits, it will not lose or absorb any energy. The energy orbits are analogous to rungs on a ladder: electrons can be only on rungs of the ladder and not in between rungs.
  2. The orbits closer to the nucleus have lower energy. The orbit closest to the nucleus available to an electron is called the ground state.
  3. Atoms want to be in the lowest possible energy state (all electrons as close to the nucleus as possible).

How Atoms Produce the Spectra

Let's see how Bohr's model of the atom explains the three types of spectra. An emission line is produced by an atom in a ``excited'' energy state---the electron is not in as low an energy orbit as possible. Remember rule #3! In order to go to a lower energy orbit, the electron must lose energy of a certain specific amount. The atom releases the energy is the form of a photon with that particular energy. The energy of photon = the difference in energy of the energy orbits (energy ladder rungs).

Example: An atom with an electron at the E2 orbit and wants to get to the lower E1 energy orbit. It gives off a photon with energy E = h*f = E2 - E1. The electron may reach the ground state in one jump or it may temporarily stop at one or more energy levels on the way. Different jumps produce photons of different energies. The atom produces light of certain wavelengths. (Remember that light is both a photon and a wave!) The more atoms undergoing a particular transition, the more intense the emission line will be. The intensity depends on the density and temperature of the gas.

An absorption line is produced when a photon of just the right energy is absorbed by an atom, kicking an electron to a higher energy orbit. The photon had energy = the difference in energy of the energy orbits. Other photons passing by with the wrong energy will pass right on by the atoms in the thin gas.

Example: An atom with electron in the E1 orbit sees photon with energy Ephoton = E2 - E1. The photon is absorbed and electron moves to E2. The photon is later re-emitted but in a random direction---not necessarily in the same direction as original photon! An observer will see less photons from the direction of the continuous source at that specific frequency (color) than other frequencies (colors). The more atoms undergoing a particular absorption transition, the darker (or ``stronger'') the absorption line. The strength of the absorption line depends on the density and temperature.

A continuous spectrum is produced by atom that are closely packed together. The energy levels of the atoms are distorted by their neighboring atom's electrons. This smears out the normally sharp spectral lines (they become fatter).

Example: An orange line is fattened so that one edge is in the yellow wavelengths and the other edge is in the red wavelengths. The amount of smearing, or broadening, depends on the density. Eventually the density gets high enough to where the smeared lines all merge together to produce the rainbow of colors of a continuous spectrum.

Vocabulary

element ground state ion
isotope

Review Questions

  1. Where are electrons, protons, and neutrons located in the atom? Can the electron be found at any position or energy in the atom?
  2. How does the Bohr atom model explain emission line spectra?
  3. Which produces a shorter wavelength of light: an electron jumping from the 6th to 2nd energy level, or one jumping from 3rd to 2nd energy level?
  4. How does the Bohr atom model explain absorption line spectra?
  5. Which would produce an absorption line at a longer wavelength: an electron jumping from the 1st to 5th energy level, or one jumping from 1st to 3rd energy level?
  6. Which will produce a stronger absorption line: a 10,000 K cloud with 100 particles in front of a hot star or a 10,000 K cloud with 1,000,000 particles in front of a hot star?
  7. If the atom absorbs a photon and later emits it, why do we see any absorption lines at all?
  8. How does the Bohr atom model explain continuous spectra?
  9. How will the spectra of Deuterium and Tritium atoms compare to the spectra of ordinary Hydrogen atoms?
  10. Why would you not expect the absorption lines of the calcium ion Ca+ to be the same as the ones of neutral calcium Ca?
  11. Will the Hydrogen ion H+ produce any absorption lines or emission lines? Explain your answer.

Doppler Effect

The wave nature of light means there will be a shift in the spectral lines of an object if it is moving. This effect is known as the doppler effect. You have probably heard the doppler effect in the change of the pitch of the sound coming from something moving toward you or away from you (eg., a train whistle, a police siren, an ice cream truck's music, a mosquito buzzing). Sounds from objects moving toward you are at a higher pitch because the sound waves are compressed together, shortening the wavelength of the sound waves. Sounds from objects moving away from you are at a lower pitch because the sound waves are stretched apart, lengthening the wavelength. Light behaves in the same way.

Motion of the light source causes the spectral lines to shift positions. An object's motion causes a wavelength shift dl = lnew - lrest that depends on the speed and direction the object is moving. The shift is given by: dl = lrest * Vradial / c, where c is the speed of light and lrest is the wavelength we would measure if the object was at rest.

There is a lot of information stored in that little formula! First, it says that the faster the object moves, the greater the doppler shift. For example, we observe a particular emission line of Hydrogen from nearby galaxies to be shifted by a smaller amount than the same line from faraway galaxies. This means that the faraway galaxies are moving faster than the nearby galaxies. The ``radar guns'' used by police officers operate on this principle too. They send out a radio wave of a set wavelength (or frequency) that reflects off a car back to the ``radar gun''. The device determines the car's speed from the difference in the wavelength (or frequency) of the transmitted beam and reflected beam.

Second, the term Vradial means that only the object's motion along the line of sight is important. If object moves at an angle with respect to the line of sight, then the doppler shift (dl) tells you only about the part of its motion along the line of sight. You must use other techniques to determine how much of an object's total velocity is perpendicular to the line of sight.

Finally, which way the spectral lines are shifted tells you if the object is moving toward or away from you. If the object is moving toward you, the waves are compressed, so their wavelength is shorter. The lines are shifted to shorter (bluer) wavelengths---this is called a blue shift. If the object is moving away from you, the waves are stretched out, so their wavelength is longer. The lines are shifted to longer (redder) wavelengths---this is called a red shift.

This explanation also works if you are moving and the object is stationary or if both you and the object are moving. The doppler effect will tell you about the relative motion of the object with respect to you. The spectral lines of nearly all of the galaxies in the universe are shifted to the red end of the spectrum. This means that the galaxies are moving away from the Milky Way galaxy and is evidence for the expansion of the universe.

The doppler effect will not affect the overall color of an object unless it is moving at a significant fraction of the speed of light (VERY fast!). For an object moving toward us, the red colors will be shifted to the orange and the near-infrared will be shifted to the red, etc. All of the colors shift. The overall color of the object depends on the combined intensities of all of the wavelengths (colors). The first figure below shows the continuous spectra for the Sun at three speeds (zero, a fast 0.01c, a VERY fast 0.1c). The Hydrogen-alpha line (at 656.3nm) is shown too. Objects in our galaxy move at speeds much less than 0.01c. The doppler-shifted continuous spectrum for the Sun moving at 0.01c is almost indistinguishable from the Sun at rest even when we zoom in to just the optical wavelengths (second figure). However, the doppler shift of the spectral line is easy to spot for the slow speed. By zooming in even further, we can detect spectral line doppler shifts for speeds as small as 1 km/sec or lower (less than 3.334*10-6 c).

Vocabulary

blue shift doppler effect red shift

Formulae

  1. Wavelength shift: dl = lnew - lrest, where lrest is the wavelength measured if the object is at rest and lnew is the wavelength measured for the moving object.
  2. Doppler effect: dl = lrest * Vradial/c, where Vradial is the object's speed along the line of sight and c is the speed of light.
  3. If lnew > lrest, object is moving away (red shift).
  4. If lnew < lrest, object is approaching (blue shift).

Review Questions

  1. What two things can the doppler effect tell you about an object's relative motion?
  2. Which galaxy is moving faster: one with lines red-shifted by 200‰ or one blue-shifted by 300‰? Which one is moving away from us?
  3. Would a star moving left to right with respect to you have a doppler shift? Why or why not?
  4. There are two edge-on binary systems with the two stars separated by 2 AU. Which will produce the largest shifting of their spectral lines: the system with star masses 10 & 15 solar masses or the system with 1.5 & 2.0 solar masses? Explain why.
  5. There are two binary systems with the two stars separated by 2 AU. Which will produce the largest shifting of their spectral lines: an edge-on system with star masses 1.5 & 2.0 solar masses or a face-on system with star masses 10 & 15 solar masses? Explain why.
  6. Why do we use spectral lines to measure velocities rather than the change in color of an object?

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last updated 15 July 1997

Nick Strobel -- Email: strobel@lightspeed.net

(805) 395-4526
Bakersfield College
Physical Science Dept.
1801 Panorama Drive
Bakersfield, CA 93305-1219