Physics 116 Lecture 13 EM spectrum and speed of light Oct 20, 2011 - - PowerPoint PPT Presentation

• R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Lecture 13

EM spectrum and speed of light

Oct 20, 2011

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• 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.

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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

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• nly every few weeks – will announce

Announcements

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Today

Lecture Schedule

(up to exam 2)

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Light waves: visible E-M waves

• First “modern” work by Newton, who

considered light to be corpuscular – a flow

• f 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
• f light: proved it true via interference

demonstrations

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Electromagnetic spectrum

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What we call EM waves depends upon their wavelength:

Name Typical wavelength AM radio band 100 m FM radio / TV / CB bands 1 m 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 m (atom size) Gamma rays (energy > 0.1 MeV)

“Ionizing radiation”: Can disrupt atoms

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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: 2.4108 m/s

– Delay between apparent times Jupiter’s moon Io disappears behind Jupiter, and predicted times, assuming Kepler’s laws

• f 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:

Earth’s

• rbit

around Sun Io’s orbit around Jupiter Hidden behind Jupiter, as viewed from earth, between C and D Period = 42.5 hr when earth is at H Predict disappearances:

• Find: a bit later at L
• Even later at K & F
• Less delay at G

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 Light with which we see Io go behind Jupiter takes longer to reach us at K, F

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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 – 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 capacitor inductor (coil) inductors

In microwave (#=cm or mm) oven or radio equipment, the resonant circuit may actually be a carefully shaped cavity, just like an organ pipe

Variable capacitor

Cavity resonator from microwave oven

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US Frequency Allocation – the FCC

VHF TV (300 MHz has a wavelength of 1 meter) Phones

“Radio” frequency-space is extremely valuable! Here’s a sample: just the region from 300–600 MHz 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

• nly, 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!

• 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

Energy and momentum of EM waves

• 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

So E and B are proportional

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• 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

Examples

• 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. B

So the yellow line at 587 nm emitted by helium atoms in the star will be

• bserved on earth as 669 nm (red)

E

Ex Ey By Bx

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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)