13. Light

 

 Reading: Chapter 7 - plus first part of Chapter 10

 

In this session we will be discussing light and how astronomers use the properties of light to explore the universe. Your textbook covers some of these topics in greater depth. The material in the web sessions should give you an idea of which topics are more important than others for this course. We will also emphasize observations of the solar system rather than distant stars and galaxies.

Information from the Skies

We can start talking about waves in terms of something familiar, like waves in a waterpond. If we chart the shape of the water, we see the peaks and valleys move forward at different times.

The most basic concepts about a wave are wavelength (), frequency (f), velocity (v), and amplitude.

The first three quantities are related by the equation

wave speed = wavelength x frequency 
         v =  x f 



(1) Imagine ocean waves crashing onto the beach. Think of reasonable numbers for the following:

(a) What is the wavelength of the waves? That is, what do you think is the distance separating the crest of one wave from the crest of the next wave?

(b) What is the frequency of the waves? (Hint: use the formula: wave frequency = 1/wave period. If a wave comes once a minute, wave period is 1 minute; if a wave comes once an hour, wave period is 1 hour.)

(c) Fiigure out how fast the waves must be traveling. (Calculate v.)

Waves in What?

The key concepts in this section are:

  • Electromagnetic radiation comprises varying electric and magnetic fields that can be thought of either as waves or as light particles - photons.

  • All electromagnetic radiation travels at the speed of light where speed of light = wavelength x frequency

  • Low frequency = large wavelength = low energy. High frequency = small wavelength = high energy.


  • (2) The speed of light is 3.00 x 108 m/sec = 3 x 105 km/sec. What is the speed of light in miles/hour?


    Example:

    Visible light

    Wavelength = l ~ 600 nanometers 
         = 6 x 102 x 10-9 meters 
         = 6 x 10-7 m 
    

    (1 nanometer = 10-9 meter - TINY!)

    So, what is the frequency of visible light?

    frequency = speed of light / wavelength
         = 3 x 108 m/s  / 6 x 10-7 m 
    
         = 0.5 x 1015 Hz 
    

    - yes! VERY high frequency!

    Example:

    Radio - pick your favorite station! Say, 106 FM

    
         Frequency = 106 Megahertz ("mega" = 1 million) 
         = 1.06 x 102 x 106 Hz 
         = 1.06 x 108 Hz
    
    

    Re-arranging speed of light = wavelength x frquency we can work out the wavelength for radio waves from the 106 FM radio station:

    wavelength = speed of light / frequency
         = 3 x 108 m/s  / 1.06 x 108 Hz 
    
         = 3 meters - about 10 feet.
    

    The Electromagnetic Spectrum

    The next two figures are very important. Make sure you really understand them.

    (3) The figure above shows the visible part of the electromagnetic spectrum--the rainbow of colors that is produced when white light is spread out according to wavelength.

      (a) Which has a longer wavelength, blue or red light?

      (b) Note the units--nanometers (nm)--i.e. 10-9 meter. Green light has a wavelength of 500 nm. How many wavelengths of green light are there in a meter?

    (4) This next figure (above) shows the electromagnetic spectrum from gamma rays to radio. Note that the range of wavelengths covers ten factors of 10, from 10-14 meter to 104 meters (or 10 km).

      (a) Infrared radiation is the energy you feel from a fire. The wavlength of infrared light is about 1 "micro-meter" = 1 micron. How many infrared wavelengths are there in a meter?

      (b) Microwave radiation is easily absorbed by water and allows us to heat up food quickly. How many microwave wavelengths, each 1mm long, are there in a meter?

     

    Here is a site with a Java applet that allows you to get the wavelength for light of a certain frequency, or get the frequency if you know the wavelength.
  • SpectrumTuner Applet from the University of Arizona. May need latest version of a browser to be on your computer - and may not work with Macs - sadly




  • The Distribution of Radiation

    Everything in the universe 'glows' with electromagnetic radiation--hotter objects emit more radiation and at shorter (`bluer') wavelengths. This is called Thermal Radiation. Before we quantify this statement, we need to remind ourselves about temperature.

    In astronomy we often use the absolute temperature scale which is measured in Kelvin. Look at the comparison chart below. It shows the temperatures at different places in the Kelvin, Centigrade and Fahrenheit scales. Page 121 of the text gives the formulae for conversion.

    Shown are the temperatures for absolute zero, the freezing point of water, the boiling point of water, and the temperature at which hydrogen fusion occurs. The typical Earth temperature is 300 K and typical temperatures on the surface of a star is 6000 K.

    (5)(a) Convert the typical Earth temperature to Fahrenheit and Centigrade degrees.

    Is the 273° difference between Centigrade and Kelvin significant when we are talking about

      (b) temperatures of planets?
      (c) temperatures of stars?

    A spectrum is a plot of intensity of radiation vs. wavelength. (Singular = spectrum, plural = spectra). The thermal radiation--the electromagnetic 'glow' emitted by every object in the universe--has a characteristic shape--sketched below. It has a specific mathematical form but the idea that it is like a brontosaurus: "Thin at one end, fat in the middle and thin at the other end" (--Monty Python) is good enough for now.


     

    In our first graph we've plotted wavelength along the x-axis of our figure, while int the second we plot frequency. Remember the two quantities are related: when you increase the wavelength, you decrease the frequency, and if you decrease the wavelength, you increase the frequency. Plotting our original spectrum with respect to frequency instead of wavelength gives the following:

     

    (6) The figure below shows the spectrum of sunlight (the thermal emission from the Sun), as well as that from other kinds of astronomical objects. Comparing this to the last example above, find at what wavelength is the maximum intensity of sunlight? Give both the color and value of the wavelength.

    Thermal Radiation Laws

    The most important aspect of the thermal spectrum is the location of this peak--the wavelength of maximum intensity--which depends on the temperature of the object emitting the radiation. This is Wien's Law .

    Wavelength of Maximum Emission is Inversely Propotional to Temperature

    Hotter objects emit at shorter (`bluer') wavelengths

    Colder objects emit at longer (`redder') wavelengths

     

    (7) Look again at the figure in the last Exercise. To see light from stars like the Sun (and any object that has a temperature of about 6000 K--such as the filament of a light bulb) we can use our eyes or a camera. To observe objects that emit thermal emission at wavelengths that are not visible to the eye, we require special detectors. To detect thermal emission from (a) hot stars and (b) cool stars or planets, we need detectors that are sensitive to what regions of the electromagnetic spectrum?

    Now, let's get more quantitative. Wien's Law for thermal radiation can be written as

     

    
    

    (8) Here is an example of how to use this equation: A hot star looks bluish, with a wavelength of maximum emission of 290 nm. Let us calculate the star's temperature -

      (a) Re-arrange the equation with Temperature on the left side.

      TKelvin =

      (b) Now, evaluate the temperature of this bluish star.

    (9) What happens to the wavelength of maximum thermal emission when an object is cooled down towards absolute zero?

    (10) Look again the example plots, above. How does the Intensity of thermal radiation vary as the temperature increases? Does it increase or decrease? Does the intensity change a large or small amount when the temperature increases (look at the numbers on the intensity scales on the left of the graphs)?

    This variation in the intensity of thermal radiation with temperature is described by the Stefan-Boltzmann Law


    Intensity of Emission is Propotional to Temperature4

    Hotter objects emit much more light

    Colder objects emit much less light


    This means that if one star (say, Hottie) is 2 times hotter than another star (say, Warmie) then the hotter star, Hottie, will emit 24 = 16 times more light than the cooler star, Warmie.

     

    (11) The surface of Jupiter's moon Ganymede is at a temperature of about 120 Kelvin. The surface of Pluto is at at temperature of about 40 Kelvin. So Ganymede's temperature is 3 times Pluto's. How many times more thermal energy is emitted from Ganymede's surface than Pluto's?


    Here is a site where you an create blackbody spectra of different temperatures. It shows you the peak wavelength (as determined from Wien's law). The applet plots the spectrum in logarithm units for both the wavelength and the intensity .
  • Blackbody Applet from the University of Arizona.

    This site allows you to plot two blackbody spectra together to see how they differ when their temperatures are different. Unlike the first applet above, the blackbody spectra are plotted with linear axes, not logarithmic.

  • Blackbody Radiation applet from the University of Oregon's Virtual Laboratory.

    May need latest version of a browser to be on your computer - and may not work with Macs - sadly

  • Inverse-Square Law

    Remember how gravity decreased with distance with an Inverse-Square Law ? Well, light also decreases with an Inverse-Square Law too. This may be discussed much later in your book. But we want to introduce this idea here because it is also useful for the solar system.


    Apparent Brightness is Inversely Proportional to Distance2

    Hotter objects emit much more light

    Colder objects emit much less light

     

    This means that if we double the distance from an object it appears not twice as dim but 22 = 4 times dimmer. If we compare the sunlight received by a planet that is 3 times farther from the Sun then the sunlight is 32 = 9 times weaker.

    (12a) Mars is 1.5 times further from the Sun than the Earth. How many times dimmer will the Sun appear to someone at Mars's distance?

    (b) Jupiter is 5.2 times the distance of the Earth from the Sun. How much dimmer will the Sun appear to a Jovian being?

    (c) What about to someone at Pluto (about 40 times farther away than Earth from the Sun)?

    Spectral Lines

    Distant objects like stars and planets cannot be picked up and analyzed in a laboratory to determine their chemical composition. We have to rely on the information carried in the light that travels to us. Different chemicals are different combinations of atoms and molecules. Each atom, molecule, and chemical has a unique spectral character--the light from distant objects reveals these "fingerprints" and tells us what the stars and planets are made of.

     

    (13) Distinguish between the following:

      (a) Atoms vs. molecules

      (b) Atom vs. nucleus

      (c) Electron vs. element

      (d) Proton vs. photon

    (14)Do all atoms look alike? Do all atoms of hydrogen or of iron look alike?

    (15) Thermal spectra Sketch the spectrum from a regular light bulb where the light is emitted by running electricity through a small wire and heating the wire to temperatures of about 5700 Kelvin. Label the Wavelength axis with appropriate units. What is the wavelength of maximum emission max?

    The Formation of Spectral Lines

    The Particle Nature of Light

    The fact that light can behave like a wave and like a particle is very exciting to a physicist - but to an astronomer it is just two ways of thinking about light. The basic concepts are:

  • Light particles = photons = "massless light particles"
  • Energy of photons is proportional to frequency
  • Energy of photons is inversely proportional to wavelength

  • (16a) Which photons have greater energy, x-ray photons or visible photons? (Hint: look at at the figures of the full electromagnetic spectrum above)

    (b) Which photons have greater energy, infrared photons or radio photons?

    Atomic Structure and Spectra

    Here are the spectra of molecular hydrogen (a), where two atoms of hydrogen are bound together into a molecule, and atomic (single atoms) hydrogen (b).

    Can you see how much simpler it is?

    (17) Emission spectra

      (a) How can an atom become excited?

      (b) Look at the emission spectrum of atomic hydrogen. Which of these emission lines correspond to photons of highest energy?

      (c) Which of these lines is produced when an electron makes the biggest drop in energy?

    (18) Absorption spectra

      (a) Absorption lines occur when an atom "absorbs" a photon. Where does the photon's energy go?

      (b) Compare the wavelengths of the absorption lines in the absorption spectrum of hydrogen to the wavelengths of the emission lines of hydrogen in the emission spectrum. (Click on the words)

    (19) Below are two cases where you might expect to see spectral signatures of hydrogen. Which would produce an emission spectrum and which would produce an absorption spectrum (look in your book for example pictures)?

    (20) At the surface of the Sun the temperature is about 5700 Kelvin. On its way to us at Earth, the sunlight passes through the Sun's atmosphere which is mostly hydrogen. Sketch the spectrum from the Sun--how does the Sun's spectrum differ from the spectrum of a light bulb? Shape? Location of max? Line absorption features?

    (21) Sodium is a relatively common element in the universe and the spectral signature of sodium is a useful diagnostic of the properties of stars and planets. Why do you think astronomers talk about sodium street lights being a major source of "light pollution?"

    Color

    Absorption occurs not just at narrow lines but also over broad regions of wavelengths. These very broadband absorptions cause objects to have color. Let's consider what happens when you illuminate an object with white light (e.g. a light bulb or sunlight). First let's sketch the spectrum of the incoming white light(with components Violet, Blue, Green, Yellow, Orange and Red):

    Now, let us sketch the spectrum of light reflected from a white object.

    Next, let us sketch the spectrum of light reflected from a red object--an object that absorbs most of light except the light in the red part of the spectrum.

    YOU sketch the spectrum of light reflected from a blue object.

    Here is the answer.

     

    Molecules

    The atmospheres of planets are generally made up of molecules, groups of 2 or more atoms, rather than single atoms. The spectra of molecules are more complex with many more lines than atoms. Look at the following figure, showing the emission of molecular hydrogen (a) versus atomic hydrogen (b).

    This is for hydrogen, one of the simplest molecules. For compounds of more complex molecules the number of lines oftens increases to the point where there broad regions of the spectrum that are absorbed or emit - rather than distinct, narrow lines.

    Spectral-Line Analysis

    Stars

    The spectra of stars are relatively simple. The dense, hot gas near the surface of the star produces a continuous spectrum of thermal emission. The light from the star passes through the star's atmosphere where gases absorb light at their characteristic wavelengths, producing absorption lines in the spectrum.

      (22a) What does the location of max tell us about the star?

      (b) What do the absorption lines tell us about the star's atmosphere?

    Planets

    Planetary spectra are more complex. Below is Jupiter's spectrum. First of all, there are two main components: (i) reflected sunlight and (ii) and the planets own thermal "glow." (Click on small 'thumbnail' picture below)

      (23a) In what regions of the electromagnetic spectrum are these two components?

      (23b) Furthermore, each component can have absorption lines or broad absorption bands. What do these absorption features tell us about the planet?

    Here are pictures of humans in reflected sunlight and in infrared "glow" - just like planets.
      (23c) Thinking first about the thermal radiation emitted by the planet, if the planet's atmosphere contains molecules (rather than single atoms), what kind of absorption features would you expect to see in the thermal component of a planet's spectrum? (Hint: Look at the figure of emission spectra above).

      (23d) Next, think about the sunlight hitting the planet. The sun is a star with an absorbing atmosphere of hydrogen with small quantities of metal atoms (like calcium, magnesium, iron). What kind of absorption features would you expect to see in the incident sunlight hitting the planet?

      (23e) Finally, think about the reflected sunlight component. There will be additional absorption features in the spectrum of the reflected sunlight. What kind of features do you expect if the planet

        (i) has a solid, icy surface (highly reflective - white) with little atmosphere (say like Europa)?

        (ii) has a thick atmosphere of molecular gases?

    The Earth's thermal emission

    Satellite measurements of the Earth's infrared thermal emission give us the spectrum below--the jagged profile shows the data and the smooth line is a theoretical spectrum of an object that has a temperature of 280 Kelvin.
      (24a) Convert this temperature to Centigrade and Fahrenheit.

      (b) Ozone and carbon monoxide are minor constituents of our atmosphere but notice the deep absorption features they carve out of the spectrum. This is how we monitor carbon dioxide and other anthropogenic (=human made) gases (i.e. pollutants). These molecules are absorbing the infrared radiation that is trying to escape the planet--what is going to happen to the atmosphere as a result of this absorption? Is the atmosphere going to get warmer or cooler? Much more about this later.(Click on small 'thumbnail' picture below)

    The solar spectrum hitting the Earth's surface

    Below is a plot of the solar spectrum that is observed above Earth's atmosphere and at sea level. Note the strong absorption bands of molecular water, carbon dioxide and ozone. In particular, look at the left hand end of the spectrum at the O3 absorption feature.

    (25) This O3 absorption feature is at what part of the spectrum? Why is this absorption feature extremely important for humans?(Click on small 'thumbnail' picture below)


    Model answers to the comprehension questions.