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Name: ___________________________
Introductory Exercise: Very Basics of Lights and Electromagnetic Waves
Basics: Electromagnetic (EM) waves are
traveling waves of electric and magnetic
fields moving through space. “Light” often
is used unofficially to refer to all EM
waves but what human eyes see as light is
only the “optical” or “visible” range of the
entire EM spectrum. The colors of
rainbows essentially are the visible light
spectrum perceived by human eyes and the wavelength is from about 400 nm (blue) to
about 700 nm (red).
(Explanation of waves - NASA: http://missionscience.nasa.gov/ems/02_anatomy.html )
(Credit: http://sob.nao-rozhen.org/content/green-flash-phenomenon)
Other examples of (non-electromagnetic) traveling waves are ripples, sound waves and
seismic waves of an earthquake.
Ripples, or Surface Waves
Sound Wave
http://imagine.gsfc.nasa.gov/YBA/M31-velocity/Doppler-shift-2.html
http://missionscience.nasa.gov/ems/02_anatomy.html
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Radio, infrared, visible, ultraviolet, x-ray and gamma-ray are other EM waves of
different spectrum range, that is, with different wavelength and frequency. Human eyes
cannot see these waves that are not in the optical (visible) range but sophisticated
detectors are built to observe in various frequencies.
Speed of Light, Frequency and Wavelength
Light or all EM waves travel at a constant speed. The speed of light is denoted by c and
its value is c = 300,000,000 m/s = 3 x 108 m/s (meters per second). The general relation
of the velocity (or speed), frequency and wavelength for any traveling wave is
c = f * l or velocity or speed = frequency * wavelength
where f = frequency = number of cycles repeated per unit time (second), and wavelength
l is the physical length or distance traveled per oscillating cycle (peak-to-peak distance
of the wave). The unit for frequency is “hertz”, which is 1/s, or cycle per second, and
the standard unit for wavelength is “meter”, of course.
Online information:
1. Frequency (Wikpedia) : http://en.wikipedia.org/wiki/Frequency
2. Read the section “Light and the Electromagnetic Spectrum” in the following:
http://elmhurst.edu/~ksagarin/color/discussion1.html
Practice 1) Red light has wavelength of about 700 nm (nanometer), what is it frequency
– that is, how many times does it oscillate or wiggle every second? Use c = f * l and
solve for f since c and l are known. Make you convert properly, such as nm to meter.
Practice 2) What is the speed of red light? Is it slower or faster than other lights in
general? How far does it travel in one second?
Practice 3) Compare red light to blue light? Which one is “longer” (wavelength)?
Which one has a “faster wiggle” (frequency)? Which one travels faster through space?
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Practice 4) Refer to the EM spectrum illustration. Can human eyes see Cosmic
“Microwave” Background Radiation that permeates the entire universe? What about the
radiations inside your tiny home “microwave” oven?
Light as Photons:
“Photon” is the modern language for light in the context of quantum mechanics, which
describes light as particles. Thus photons can be thought of as tiny “roundish objects of
pure energy” traveling through space. Each photon has energy that is directly
proportional to its frequency f :
E= h f
where h=6.626 x 10-34 m2kg/s is “Planck's constant”. The standard unit for energy is
Joule. For example, an x-ray photon has f = 1018 hertz (1/s), and the energy per x-ray
photon is E = h f = (6.626 x 10-34 m2kg/s ) (1018 hz)= 6.626 x 10-34+18 Joules = 6.626 x
10-16 J.
Neither the photon concept nor the above frequency-energy relation is known prior to
the advent of quantum mechanics in early 1900s and cannot be established using the
older “wave” formulation of electromagnetism. It is also worth noting that modern
optics experiments are capable of detecting lights of extreme low intensity to observe
individual photons.
Practice 5) Gamma rays are highly energetic with a typical frequency of 1020 hertz (1/s).
What is its wavelength? What is the energy carried by one gamma ray photon? Refer to
above example.
Practice 6) How much more energetic is a gamma ray photon compare to a red light
photon? Hint: Since energy is directly proportional to frequency (see above formula), as
h is a constant, then comparison of 2 energies simply requires a comparison of their
frequency without needing to compute energy. It is just a simple ratio (but of what?).
Still you can compute energy explicitly for practice.
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Practice 7) Does green light have longer or shorter wavelength than red light? Have
higher or lower frequency than red light? Does a green light photon have more or less
energy than a red light photon?
(Bonus: +1 ) Practice 8) Given a very common 40 watts lights bulb, let's estimate how
many photons it emits per second.
– A Watt, the standard unit of power measuring flow of energy per unit time, means
one Joule per second, J/s, so the question translates to “how many photons is
emitted per second so that the total is 40 joules of energy”?
– A common light bulb emits white light so it include all colors of light. But we
can ignore that and simply use red light (or any color) since the wavelengths are
relatively close. We are, after all, only making an estimate. Use previous
practice for the energy of a single red light photon, expressed in joule.
– Calculate “how many red light photos would total up to 40 joules?”
Practice 9) A very distant quasar is observed to have XXX Janskys (Incomplete...)
(Skip. This Question is to be completed for Spring, 2015)
Survey: On a scale of 0 to 5, how familiar are you with the exercise materials? Add
your thoughtful and constructive comment (for 1 extra pt):
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