Physics 116
Lecture 13
EM spectrum and speed of light
Oct 20, 2011
R. J. Wilkes
Email: [email protected]
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Announcements
•! JW will be away until 10/31
•! Guest lecturer today: Prof. Victor Polinger
•! Clicker quiz grades (up to and including quiz 4 on
10/18) are available on WebAssign.
•! Only your total score is shown: you got 3 pts for
each correct answer, 1 pt for each incorrect answer
(thank you for showing up and trying), and 0 pts for
no answer; max possible so far = 12 pts
•! Your total will NOT be updated after every quiz,
only every few weeks – will announce
10/20/11
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Lecture Schedule
(up to exam 2)
Today
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Light waves: visible E-M waves
•! First “modern” work by Newton, who
considered light to be corpuscular – a flow
of particles
•! Newton (via prisms) showed white light is
composed of all the colors of the rainbow
•! Newton’s Opticks (1704) was the first
significant treatment of the nature of light,
based on an empirical (experiment-based)
approach. (Book included the first
published description of calculus)
•! Despite some experimental evidence for a
wave nature to light, the weight of
Newton’s opinion on the matter damped
wave enthusiasts for 100 years
•! Thomas Young in England, A. Fresnel and
D. Arago in France, advocated wave theory
of light: proved it true via interference
demonstrations
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Electromagnetic spectrum
What we call EM waves depends upon their wavelength:
Name
Typical wavelength
AM radio band
100 m
FM radio / TV / CB bands
1m
Microwaves
1mm
Infrared (IR) radiation
1 micron (10-6 m)
Visible light
0.5 micron
Ultra-violet (UV) radiation
0.1 micron
X-rays
10-8
Gamma rays
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m (atom size)
“Ionizing radiation”:
Can disrupt atoms
(energy > 0.1 MeV)
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Speed of light measurements
•! Galileo, c.1600: “at least 10 times faster than sound”
–! men with shuttered lanterns, on hills 5 km apart
•! Ole Rømer, 1676: 2.4!108 m/s
–! Delay between apparent times Jupiter’s moon Io disappears
behind Jupiter, and predicted times, assuming Kepler’s laws
of planetary motion
•! Hippolyte Fizeau, 1849: 313,300 km/sec
–! first direct measurement, outside Paris (similar to Galileo’s
idea but with improved 19th C. technology)
•! Albert Michelson, 1926: 299,796 ± 4 km/sec
–! 1926 = last of many measurements by Michelson
•! Official value today: 299792.458 km/s exactly
–! we now define c to be this value! SI system of units uses c
as a fixed constant: "1 meter = distance travelled by light in
vacuum during a time interval of 1/299 792 458 of a
second." (http://physics.nist.gov/cuu/Units/current.html)
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Early ways to measure c
•! Rømer:
Fizeau:
Hidden behind Jupiter,
as viewed from earth,
between C and D
Io’s orbit
Period = 42.5 hr
around
when earth is at H
Jupiter
Predict disappearances:
•! Find: a bit later at L
•! Even later at K & F
•! Less delay at G
Earth’s
orbit
around
Sun
Light with which we see
Io go behind Jupiter takes
longer to reach us at K, F
Generate beam of light (he did NOT have a
light bulb!), send it to mirror a few km away
•! Spin a toothed disc to interrupt light beam
•! Adjust speed of wheel until reflected light
just meets next opening in wheel
•! Then: Round trip of light beam take time T
between notches in wheel
So c = (distance x2) / T
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A "remarkable coincidence"
•! "Electrical constants" !0 and "0 appear in Maxwell’s
equations:
–! We can measure !0 by measuring force between 2 charges
–! We get value of "0 by measuring force between 2 currents
•! Such measurements were available to Maxwell
–! Found that the c in his E&M equations ~ 3 x108 m/s
–! Same as contemporary measurements of speed of light
•! "We can scarcely avoid the inference that light consists
in the transverse undulations of the same medium which
is the cause of electric and magnetic phenomena.“
»! - Maxwell
•! Right (E-M/light connection), and wrong (medium)!
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How does a radio work?
•! Radio station sends electrical current to an antenna
–! Antenna radiates energy as electromagnetic waves:
•! AM radio ~ 1000 kHz (# ~ 100m), FM/TV ~ 100 MHz (# ~1m)
–! Broadcast signal consists of two parts:
•! “carrier wave” at station’s assigned frequency
•! “modulation” = information superimposed on carrier
–! Voice/music/picture signals (~ 1kHz) slightly vary carrier
–! AM means amplitude variation carries information content
–! FM means frequency is tweaked to model information content
»! Digital transmissions use pulse modulation (either AM or FM)
•! Your radio or TV picks up tiny
(microvolt) signals on its antenna
$! Filters out carrier wave
$! Amplifies audio/video signal
$! Sends reconstituted signals to
loudspeaker, earphone, or
screen
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How does your radio “tune in” a station?
•! Radio/TV “tuner” is another example of resonance
–! The combination of 2 simple electronic components makes a resonant
circuit: electrical equivalent of an organ pipe
Variable
capacitor
capacitor
inductor
(coil)
inductors
–! In 1930s radios, usually the inductor (coil) is fixed while the capacitor
is variable, attached to your tuning knob
–! Modern radios use “digital tuning”: capacitor is replaced with a silicon
chip that can have its resonant frequency digitally adjusted
In microwave (#=cm or mm) oven or radio equipment, the
resonant circuit may actually be a carefully shaped cavity,
just like an organ pipe
Cavity resonator from
microwave oven
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US Frequency Allocation – the FCC
“Radio” frequency-space is extremely valuable!
Here’s a sample: just the region from 300–600 MHz
!VHF TV
(300 MHz has a wavelength of 1 meter)
Phones!
Frequency allocation requires international diplomacy…
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Understanding radio wave behavior
•! Compare wavelength to sizes of features in environment
–! AM radio has long (# ~ 100m) wavelengths, “goes around” hills, etc
•! But iron bridge structure (e.g. University Bridge) looks solid to AM
–! Navy uses Extremely Low Frequency (ELF) to communicate with
submarines: wave with # ~ 100km penetrates (a bit) into ocean
–! “Shortwave” radio (# ~ 10m) bounces off ionized layers in upper
atmosphere: can go worldwide
–! FM radio (# ~ 1m), is blocked by hills, buildings
•! But iron bridge structure is transparent to it: gaps > wavelength
–! Super high frequency (GHz, #~ 1cm) for cell phones is line-of-sight
only, and blocked by any conducting material in buildings
•! Why use GHz? You can pack a lot of information onto its carrier
–! Modulation frequency must be << carrier frequency (many cycles/bit)
–! “Bandwidth”: carrier frequency is spread by modulation frequency
»! At 100 MHz, can only use <1 MHz modulation
»! At 2.5 GHz may have many MHz of modulation (many calls)
»! ELF: only a few bits - tell sub to surface and phone home!
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Energy and momentum of EM waves
•!
In 115 you learned about the energy density of E and B fields
•!
Maxwell’s equations relate the E and B fields in propagating waves, so
So E and B are proportional
•!
•!
What is the time-averaged energy density of a wave at some point in space?
•! The time-averaged amplitude of a sine wave is zero!
As with AC currents, must use RMS (root mean square) values to get a
meaningful time average of the energy carried by a wave :
•! average the square of the amplitude, and take its square root
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Examples
•! EM wave moving in +z direction has
•! What is B?
B must be oriented such that E x B = z axis, by RHR, so we must have
B
Bx
By %!
E
%!
Ey
Ex
•!
•!
Star moves away from us at 375 km/s - what is change in apparent
wavelengths of light from this star?
Light from a star that is moving away from Earth is Doppler-shifted to a longer
wavelength: it is red-shifted.
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So the yellow line at 587 nm emitted by
helium atoms in the star will be
observed on earth as 669 nm (red)
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Today’s quiz question
•! Which one of these is NOT a form of
electromagnetic radiation?
A.! Sonic boom when an airplane travels faster than
343 m/s
B.! X-rays used in hospitals
C.! AM radio (as opposed to FM radio)
D.! "Blacklight" illumination (ultraviolet light)
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