I. Light & Spectra. I. Light and Spectra. 1. The Speed of Light. A. The Nature of LIght. b). Olaf Roemer s Experiment. a) Galileo couldn t meaure it

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1 Part II: Astrophysics 1 I. Light and Spectra 2 Dr. Bill Pezzaglia A. Nature of Light I. Light & Spectra B. Black Body Radiation C. Atomic Physics Updated: 2011Feb24 A. The Nature of LIght 3 1. The Speed of Light 4 1. The Speed of Light Ancient idea: light is emitted from the eye (instead of being reflected into the eye from a source). 2. The colors in Light 3. Wave Nature of Light Heron of Alexandria advanced the argument that the speed of light must be infinite, since distant objects such as stars appear immediately when one opens one's eyes. 4. Electromagnetic Waves René Descartes argued that if the speed of light were finite, the Sun, Earth, and Moon would be noticeably out of alignment during a lunar eclipse. Since such misalignment had not been observed, Descartes concluded the speed of light is infinite. In fact, Descartes was convinced that if the speed of light were finite, his whole system of philosophy would be demolished. Reference: a) Galileo couldn t meaure it 5 b). Olaf Roemer s Experiment Beeckman (friend of Descartes) proposes reflecting the flash of a cannon off of a mirror Galileo proposes to flash a lantern at an assistant 1 mile away, who will uncover his lantern when he sees the light reach him finds that as distance to Jupiter changes (due to motion of earth and Jupiter) the times of eclipses of the moon Io can be late/early by several minutes. Calculates light travels 11 minutes per astronomical unit (AU). The actual value is 499 s, or 8 minutes, 19 s per AU. Reference: The Accademia del Cimento of Florence states it was tried: "without any observable delay" 1

2 c). Christiaan Huygens ( ) 1678 using Roemer s result (11 minutes/au), and a value for the Astronomical Unit, calculates speed of light 1678 he proposes light is a wave rather than a particle demolished Descartes' argument by pointing out, using Roemer's measurements, that light took (of the order of) seconds to get from moon to earth, maintaining both the co-linearity and a finite speed. 7 d). James Bradley ( ) 1680 Jean Picard observes positions of stars move during earth's orbit, but its NOT the parallax effect Bradley observes aberration of light (light appears to hit telescope at an angle because the earth is moving), gets deflection of 1/200 degree. gets value of c that is 185,000 miles/second. 8 e). Armand Fizeau ( ) In 1849, French physicist Armand Fizeau developed a device known as the Fizeau wheel in order to measure the speed of light. This instrument consists of a rotating toothed wheel through which a beam of light is passed. The light is then reflected by a distant mirror, which reflects it back to the wheel. When the rotation speed is low, the light beam returns quickly enough so as to pass through the same opening through which it was transmitted. As the rotation speed increases, the light is blocked because the wheel has advanced one-half the distance between openings. 9 f). Jean Foucault, Jean ( ) Used a rotating polygonal mirror and a distant mirror. As the light beam returned from its path to the distant mirror, the rotating mirror had advanced slightly and the beam was reflected at a slight angle by a different face of the mirror. Knowing the deflection angle, the distance to the fixed mirror, and the speed of rotation, he calculated the speed of light to be 298,000,000 meters per second, very close to the currently accepted value. 10 Further increasing the speed, the wheel advances the entire distance between openings, and the beam again passes through. Knowing all the dimensions involved and the speeds at which the light beam passed or didn't pass, Fizeau could calculate the speed of light. f). Jean Foucault, Jean ( ) Used a rotating polygonal mirror and a distant mirror. As the light beam returned from its path to the distant mirror, the rotating mirror had advanced slightly and the beam was reflected at a slight angle by a different face of the mirror. Knowing the deflection angle, the distance to the fixed mirror, and the speed of rotation, he calculated the speed of light to be 298,000,000 meters per second, very close to the currently accepted value The Components of Light 12 Foucault also measured the speed of light in water, and found it to be slower than in air, exactly as would be expected if light were composed of waves, but opposite the result expected if light were composed of particles. Early theories were that a prism created color. White light goes in, colors come out. 2

3 2a. The Components of Light 13 2a. The Components of Light Newton shows that the prism does not create color, it merely separates them. The second prism does not create more colors Newton further shows that a second prism can recombine colors to make white light. Hence white light is a mixture of all colors. 2b. The Visible Spectrum 15 2c. Infrared Light 16 Note violet is a prismatic color Purple is a mixture of red and blue Herschel discovers invisible calorific rays past the red that heats a thermometer Infrared (IR), meaning below the red Rattlesnakes can see IR. You sense IR as heat on your skin. Referece: 2d. UltraViolet Johann Wilhelm Ritter ( ) 1801 Experiments show silver chloride (i.e. film emulsion) breaks down slowly under red light, but faster as move to violet. Finds invisible chemical rays beyond the violet cause even faster reactions Ultraviolet (UV) means beyond violet. 17 3a. Wave or Particle Newton s corpuscular theory: light is a particle 1678 Huygens: light is a wave Foucault measures speed of light is slower in water (favors wave theory) 1801 Young s diffraction experiment proves it s a wave, and gives a way to measure its size Waves are very small, around 500 nm 18 The sun puts out UV, we are protected by the ozone layer. Reference: 3

4 3b. Electromagnetic Theory 1831 Michael Faraday proposes Electric and Magnetic Fields 1860 Maxwell shows changing electric field creates magnetic field, changing magnetic field creates electric. Derives wave solutions, with speed exactly c the speed of light. Proposes these waves are light 19 3c. The Electromagnetic Spectrum 1888 Hertz produces radio waves 1895 Rontgen produces X-rays 1900 Paul Villard discovers gamma rays They are all part of the electromagnetic spectrum, of which visible light is a small piece. 20 3d. Transparency of Atmosphere Other than visible light, only radio waves get through our atmosphere. In particular, the dangerous UV is blocked by the Ozone layer 21 3e. Wave Speed c = f λ c = speed of light (in vacuum) 22 f = frequency (in Hertz = cycles per second) But there may be things out there that only produce Xrays or microwaves λ= wavelength (in meters) 3f. Speed in Media In media (such as glass) the speed is slower. This causes refraction the bending of light. The speed usually depends upon the wavelength, called dispersion. This causes the colors to be spread out. This work was done by Newton 23 B. Black Body Radiation 1. Stephan Boltzmann Law 2. Wien s Law 3. Black Body Radiation 24 4

5 1a. Temperature 25 1b. Josef Stefan s Law Lord Kelvin s temperature scale Conversion: 0 K = -273 C Experimentally shows total output of light of a hot dense (black) body is proportional to 4 th power of the temperature (in Kelvin) Temperature is a measure of average energy Power (watts)=aσt 4 σ=5.67x10-8 Watts/(m 2 -K 4 ) A=surface area 0K is absolute zero 1884 Ludwig Boltzmann (former student of Stefan) derives formula from thermodynamics. I was a guest speaker (Sept 2005) at the Josef Stefan Institute in Slovenia. 1c. Inverse Square Law 27 2a. Wien s Displacement Law Kepler proposes intensity of light drops of with square of distance (?) Charles Soret measures solar flux to be about 1400 Watts/m 2 at surface of the earth shows that the color of black body is inversely proportional to temperature. λ=α/t Wien s constant α= 2,898,000 nm-k So T=6000 K gives λ=483 nm Stefan uses this to estimate temperature of sun to be 5700 K. 2b. Black Body Curve 29 2c. Color Indexing 30 Willhelm Wien gets Nobel Prize coins term black body If we can measure the color of a star, we can calculate its temperature Measure magnitude of star through color filters Color Index=C.I. = B-V is measure of temperature of star. The black body emits all colors, but where it peaks is described by Wien s law Standard Filters U filter 370 nm B filter 440 nm V filter 550 nm 5

6 3a. Black Body Theory Maxwell: hot atoms vibrate, acting like small antennas, radiating electromagnetic waves Wien tries to give theory to explain shape of curve, but it fails in IR Rayleigh (1900) & Jeans (1905) have another theory, but it fails in UV, blowing up to infinite energy (the ultraviolet catastrophe ). 31 3b. Max Planck s Theory 1900 Max Planck ad-hoc proposes that vibrations are quantized, i.e. come in steps of n=1, 2, 3, rather than continuous. Energy: E=nhf n=integer quantum number f=frequency of oscillation h is Planck s Constant h=6.626x10-34 Joule-Sec 32 3c. Planck Radiation Law 33 3d. The Photon 34 His theory exactly matched the experimental measurements of the black body radiation curve 1905 Einstein proposes that its light that is quantized. Proposes light is a particle, called the photon Energy of a single Photon: E = hf = hc/λ Uses idea to explain the photoelectric effect k = Boltzmann Constant (1.38 x J/K) C. Atomic Physics 1. Discrete Spectra 2. Kirchhoff s Laws 35 1a. Dark Line Spectra 1802 Wollastan sees lines in solar spectra 1814 Fraunhofer Labels them A, B, C, D Model of Atom Later measures over 500 lines! 6

7 1b. Solar spectrum 37 1c. Bright Line Spectra Bunsen s burner, a clean flame with no color 1859 Kirchhoff suggest using it to study spectra of elements in flame Each element has a unique set of bright line (emission) spectra 2a. Kirchhoff s Laws 39 2b. Gustav R Kirchhoff (1860) 40 His three laws: 1. A hot dense body will emit a continuous spectrum 2. A hot transparent gas will emit emission line spectrum 3. A cool transparent gas in front of a source of continuous spectrum will produce absorption spectra. 2c. Spectral Analysis The absorption lines match emission lines. Hence you can use them to identify elements in stars. 41 3a. Rydberg Formula Balmer comes up with formula that explains the Hydrogen lines ( Balmer Series ) 1861 Kirchhoff identifies elements in the sun from Fraunhofer lines 1888 Rydberg improves formula, where n 1 =2, n 2 ={3,4,5} 1868 Janssen finds a line that can t be identified during solar eclipse 1870 Lockyer & Frankland verify its an unknown element they name Helium. Helium is not discovered on the earth until 1895! 1895 Paschan Series discovered in IR, described by n 1 = Lyman Series discovered in UV, described by n 1 =1 7

8 3b. Atomic Theory 1808 Dalton s theory of atoms 1897 Thomson discovers electron 1911 Rutherford s experiment implies dense core to atom (nucleus) 43 3c. Atomic Theory 1911 Rutherford s suggest planetary model of atom, electrons orbit nucleus But, it would be unstable! Electrons would immediately radiate and crash into nucleus. 44 3d. Niels Bohr (Nobel Prize 1922) 1913 Bohr proposes quantized orbits to atom. 45 3e. Emission and Absorption 46 3f. Emission & Absorption 47 3g. Spectral Series 48 8