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Dr. Bill Pezzaglia

I. Light & Spectra

Updated: 2006Sep18

Part II: Astrophysics

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I. Light and Spectra

A. Nature of Light

B. Black Body Radiation

C. Atomic Physics

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A. The Nature of LIght

1. The Speed of Light2. The colors in Light3. Wave Nature of Light4. Electromagnetic Waves

3 1. The Speed of Light• Ancient idea: light is emitted from the eye (instead

of being reflected into the eye from a source).

• 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.

• 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.

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Reference: http://en.wikipedia.org/wiki/Speed_of_light

a) Galileo couldn’t meaure it• 1629 Beeckman (friend of Descartes) proposes reflecting the

flash of a cannon off of a mirror.• 1638 Galileo proposes to flash a lantern at an assistant 1 mile

away, who will uncover his lantern when he sees the light reach him.

• 1667 The Accademia del Cimento of Florence states it was tried: "without any observable delay"

5 b). Olaf Roemer’s Experiment 6

• 1675 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: http://scienceworld.wolfram.com/biography/Roemer.html

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c). Christiaan Huygens(1629-1695)

• 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

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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.

d). James Bradley(1693 - 1762)

• 1680 Jean Picard observes positions of stars move during earth's orbit, but its NOT the parallax effect.

• 1728 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.

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e). Armand Fizeau (1819-1896) 9

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.

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 (1819-1868) 10

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 reflectedat a slight angle by a different face of the mirror. Knowing thedeflection 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.

f). Jean Foucault, Jean (1819-1868) 11

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 reflectedat a slight angle by a different face of the mirror. Knowing thedeflection 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.

•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.

2. The Components of Light

Early theories were that a prism createdcolor. White light goes in, colors come out.

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2a. The Components of Light 13

1672 Newton shows that the prism does not create color, it merely separates them.

The second prism does not create more colors.

2a. The Components of Light 14

1672 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• Note “violet” is a prismatic color• “Purple” is a mixture of red and blue.

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Referece: http://coolcosmos.ipac.caltech.edu/cosmic_classroom/classroom_activities/herschel_bio.html

2c. Infrared Light• 1800 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.

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2d. UltraViolet• Johann Wilhelm Ritter (1776-1810)

• 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.

• The sun puts out UV, we are protected by the ozone layer.

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Reference: http://coolcosmos.ipac.caltech.edu/

3a. Wave or Particle 18

• 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,around500 nm

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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”

193c. 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.

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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

• But there may be things out there that only produce Xrays or microwaves

21 3e. Wave Speed

c = f λ

c = speed of light (in vacuum)

f = frequency(in Hertz = cycles per second)

λ= wavelength (in meters)

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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 workwas doneby Newton

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B. Black Body Radiation

1. Stephan Boltzmann Law2. Wien’s Law3. Black Body Radiation

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1a. Temperature• 1851 Lord Kelvin’s temperature scale

• Conversion: 0 °K = -273 °C

• Temperature isa measure ofaverage energy

• 0K is absolutezero

30 1b. Josef Stefan’s Law 1879• Experimentally shows total output of

light of a hot dense (black) body is proportional to 4th power of the temperature (in Kelvin)

• Power (watts)=AσT4

• σ=5.67x10-8 Watts/(m2-K4)• A=surface area

• 1884 Ludwig Boltzmann (formerstudent of Stefan) derives formulafrom thermodynamics.

• I was a guest speaker (Sept 2005) at theJosef Stefan Institute in Slovenia.

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1c. Inverse Square Law• 1604 Kepler proposes

intensity of light drops of with square of distance (?)

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•Charles Soret measures solar flux to be about 1400 Watts/m2 at surface of the earth.

•Stefan uses this to estimatetemperature of sun to be 5700 K.

2a. Wien’s Displacement Law• 1893 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=6000ºK gives

λ=483 nm

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2b. Black Body Curve• Willhelm Wien gets

Nobel Prize 1911

• 1894 coins term“black body”

• The black body emitsall colors, but whereit peaks is describedby Wien’s law

34 2c. Color Indexing• 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.

• Standard Filters• U filter 370 nm• B filter 440 nm• V filter 550 nm

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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”).

36 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=nhfn=integer quantum numberf=frequency of oscillationh is “Planck’s Constanth=6.626x10-34 Joule-Sec

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3c. Planck Radiation Law 38

k = Boltzmann Constant (1.38 x 10-23 J/K)

•His theory exactly matched the experimental measurements of the black body radiation curve

3d. The Photon 39

•1905 Einstein proposes that its lightthat 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”

C. Atomic Physics

1. Discrete Spectra2. Kirchhoff’s Laws3. Model of Atom

45 1a. Dark Line Spectra• 1802 Wollastan sees lines in solar spectra

• 1814 Fraunhofer Labelsthem A, B, C, D

• Later measures over 500 lines!

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1b. Solar spectrum 47 1c. Bright Line Spectra• 1857 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

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2a. Kirchhoff’s Laws 49 2b. Gustav R Kirchhoff (1860)50

His three laws:1. A hot dense body will emit a

continuous spectrum2. A hot transparent gas will emit

emission line spectrum3. A cool transparent gas in front of a

source of continuous spectrum will produce absorption spectra.

2c. Spectral Analysis 51

•1861 Kirchhoff identifies elements in the sun from Fraunhofer lines

•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 !

The absorption lines match emission lines. Hence you can use them to identify elements in stars.

3a. Rydberg Formula 52

• 1885 Balmer comes up with formula that explains the Hydrogen lines (“Balmer Series”)

• 1888 Rydberg improves formula, where n1=2, n2={3,4,5}

•1895 Paschan Series discovered in IR, described by n1=3•1908 Lyman Series discovered in UV, described by n1=1

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3b. Atomic Theory 53

• 1808 Dalton’s theory of atoms• 1897 Thomson discovers electron• 1911 Rutherford’s experiment implies

dense core to atom (nucleus)

3c. Atomic Theory 54

• 1911 Rutherford’s suggest planetary model of atom, electrons orbit nucleus

• But, it would be unstable!

• Electrons wouldimmediatelyradiate and crashinto nucleus.

3d. Niels Bohr (Nobel Prize 1922)55

• 1913 Bohr proposes“quantized orbits” to atom.

3e. Emission and Absorption 56

3f. Emission & Absorption 57 3g. Spectral Series 58