Physics 116 Lecture 13 EM spectrum and speed of light Oct 20, 2011 R. J. Wilkes Email: ph116@u.washington.edu 10/20/11 1
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 2
Lecture Schedule (up to exam 2) Today 10/20/11 3
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 10/20/11 4 4
Electromagnetic spectrum 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 “Ionizing radiation”: X-rays 10 -8 m (atom size) Can disrupt atoms Gamma rays (energy > 0.1 MeV) 10/20/11 5
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 � 10 8 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 19 th 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) 6
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 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 Earth’s just meets next opening in wheel orbit • � Then: Round trip of light beam take time T Light with which we see around between notches in wheel Io go behind Jupiter takes Sun So c = (distance x2) / T longer to reach us at K, F 7
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 x10 8 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)! 8
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 9
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 inductors Variable inductor capacitor (coil) capacitor – � 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 10
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… 11
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! 12
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 10/20/11 13
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 x B E % � B y % � E y E x • � 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. So the yellow line at 587 nm emitted by helium atoms in the star will be observed on earth as 669 nm (red) 10/20/11 14
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) 15
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