Transcript I. Light & Spectra

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Part II: Astrophysics
Dr. Bill Pezzaglia
I. Light & Spectra
Updated: 2006Sep18
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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.
2.
3.
4.
The Speed of Light
The colors in Light
Wave Nature of Light
Electromagnetic Waves
1. The Speed of Light
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Ancient idea: light is emitted from the eye (instead
of being reflected into the eye from a source).
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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.
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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: http://en.wikipedia.org/wiki/Speed_of_light
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a) Galileo couldn’t meaure it
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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"
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b). Olaf Roemer’s Experiment
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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
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.
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d). James Bradley
(1693 - 1762)
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• 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.
e). Armand Fizeau (1819-1896)
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.
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f). Jean Foucault, Jean (1819-1868)
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.
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f). Jean Foucault, Jean (1819-1868)
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.
•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.
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2. The Components of Light
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Early theories were that a prism created
color. White light goes in, colors come out.
2a. The Components of Light
1672 Newton shows that the prism does not
create color, it merely separates them.
The second prism does not create more colors.
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2a. The Components of Light
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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
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Note “violet” is a prismatic color
“Purple” is a mixture of red and blue.
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2c. Infrared Light
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1800 Herschel discovers
invisible “calorific rays”
past the red that heats a
thermometer
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Infrared (IR), meaning
“below” the red
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Rattlesnakes can “see” IR.
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You sense IR as “heat” on
your skin.
Referece: http://coolcosmos.ipac.caltech.edu/cosmic_classroom/classroom_activities/herschel_bio.html
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2d. UltraViolet
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Johann Wilhelm Ritter (1776-1810)
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1801 Experiments show silver chloride
(i.e. film emulsion) breaks down slowly
under red light, but faster as move to
violet.
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Finds invisible “chemical rays” beyond
the violet cause even faster reactions
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Ultraviolet (UV) means beyond violet.
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The sun puts out UV, we are protected
by the ozone layer.
Reference: http://coolcosmos.ipac.caltech.edu/
3a. Wave or Particle
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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
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3b. Electromagnetic Theory
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1831 Michael Faraday proposes Electric and Magnetic
Fields
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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.
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Proposes these waves are “light”
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3c. The Electromagnetic Spectrum
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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
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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
3e. Wave Speed
c=f
c = speed of light (in vacuum)
f = frequency
(in Hertz = cycles per second)
= wavelength (in meters)
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3f. Speed in Media
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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
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B. Black Body Radiation
1. Stephan Boltzmann Law
2. Wien’s Law
3. Black Body Radiation
1a. Temperature
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1851 Lord Kelvin’s temperature scale
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Conversion: 0 °K = -273 °C
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Temperature is
a measure of
average energy
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0K is absolute
zero
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1b. Josef Stefan’s Law 1879
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Experimentally shows total output of
light of a hot dense (black) body is
proportional to 4th power of the
temperature (in Kelvin)
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Power (watts)=AT4
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=5.67x10-8 Watts/(m2-K4)
A=surface area
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1884 Ludwig Boltzmann (former
student of Stefan) derives formula
from thermodynamics.
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I was a guest speaker (Sept 2005) at the
Josef Stefan Institute in Slovenia.
1c. Inverse Square Law
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1604 Kepler proposes
intensity of light drops
of with square of
distance (?)
•Charles Soret measures solar flux
to be about 1400 Watts/m2 at
surface of the earth.
•Stefan uses this to estimate
temperature of sun to be 5700 K.
2a. Wien’s Displacement Law
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1893 shows that the “color” of black
body is inversely proportional to
temperature.
 = /T
Wien’s constant
= 2,898,000 nm-K
So T=6000ºK gives
=483 nm
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2b. Black Body Curve
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Willhelm Wien gets
Nobel Prize 1911
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1894 coins term
“black body”
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The black body emits
all colors, but where
it peaks is described
by Wien’s law
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2c. Color Indexing
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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
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Maxwell: hot atoms vibrate, acting
like small antennas, radiating
electromagnetic waves
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Wien tries to give theory to explain
shape of curve, but it fails in IR
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Rayleigh (1900) & Jeans (1905)
have another theory, but it fails in
UV, blowing up to infinite energy
(the “ultraviolet catastrophe”).
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3b. Max Planck’s Theory
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1900 Max Planck ad-hoc proposes
that vibrations are “quantized”, i.e.
come in steps of n=1, 2, 3, rather than
continuous.
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Energy: E=nhf
n=integer quantum number
f=frequency of oscillation
h is “Planck’s Constant
h=6.626x10-34 Joule-Sec
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3c. Planck Radiation Law
•His theory exactly matched the experimental
measurements of the black body radiation curve
k = Boltzmann Constant (1.38 x 10-23 J/K)
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3d. The Photon
•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/
•Uses idea to explain the
“photoelectric effect”
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C. Atomic Physics
1. Discrete Spectra
2. Kirchhoff’s Laws
3. Model of Atom
1a. Dark Line Spectra
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1802 Wollastan sees lines in solar spectra
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1814 Fraunhofer Labels
them A, B, C, D
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Later measures over 500 lines!
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1b. Solar spectrum
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1c. Bright Line Spectra
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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
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2b. Gustav R Kirchhoff (1860)
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.
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2c. Spectral Analysis
The absorption lines match emission lines. Hence
you can use them to identify elements in stars.
•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 !
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3a. Rydberg Formula
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1885 Balmer comes up with formula that
explains the Hydrogen lines (“Balmer Series”)
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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
3b. Atomic Theory
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1808 Dalton’s theory of atoms
1897 Thomson discovers electron
1911 Rutherford’s experiment implies
dense core to atom (nucleus)
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3c. Atomic Theory
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1911 Rutherford’s suggest planetary model
of atom, electrons orbit nucleus
But, it would be unstable!
Electrons would
immediately
radiate and crash
into nucleus.
3d. Niels Bohr (Nobel Prize 1922)
• 1913 Bohr proposes
“quantized orbits” to atom.
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3e. Emission and Absorption
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3f. Emission & Absorption
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3g. Spectral Series
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