1445 Introductory Astronomy I

1
1445 Introductory Astronomy I

• Chapter 3
• Light and Telescopes
• R. S. Rubins
  Fall, 2008

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The Speed of Light 1

• Aristotle (ca. 360 BCE) thought the speed of
  light to be infinite, while Galileo (ca.1600)
  found it too fast to measure.
• In 1675, the Danish astronomer, Ole Roemer, used
  Newtons Laws to predict the eclipses of the
  moons of Jupiter. His predicted times were
  early when Jupiter was near conjunction, and late
  when near opposition.
• Believing Newtons Laws to be correct, he was
  able to calculate a value for the speed of light,
  which would have been accurate if the Sun-Jupiter
  distance had been known precisely at that time.
• Now known very precisely, the speed of light c in
  space has the approximate value,
• c 300,000 km/s ( 186,000 mi/s).

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The Speed of Light 2

• Roemers method (1675) compares the predicted
  eclipse times for one of Jupiters moons, based
  on Newtons Laws, with the measured times at
  opposition and near conjunction.

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The Speed of Light 3

• The terrestrial method (ca. 1920) measures the
  time for light to travel the 70 km round trip
  from Mt. Wilson to Mt. Baldy using the equation c
  x/t, where x is 70 km.

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Reflection of Light

• The angle of reflection r equals the angle of
  incidence i.

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Refraction of Light
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General Properties of Light

• A light ray is a very narrow beam of light.
• Reflection is the rebound of a light ray off a
  surface.
• Refraction is the bending of a light ray when
  passing from one transparent medium to another at
  an oblique angle.
• The denser the medium, the slower the speed of
  light thus, the speed of light is slower in
  glass than in air.
• Dispersion is the separation of light into its
  constituent colors.
• The color of light depends on its frequency (and
  wavelength).
• Monochromatic light is light of a single
  wavelength.
• Interference, diffraction and polarization are
  wave properties of light.

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Dispersion of White Light by a Prism

• The upper picture shows the variation of
  wavelength with color.
• The lower picture shows Newtons experimental
  proof that the glass changes the direction of a
  light-beam, but does not affect its color.

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Light Waves or Particles ?
There are two basic ways of transferring energy
in every-day life, either by particles or by
waves. In the 17th century, Newton considered
light to be particles, while the Dutch scientist,
Huygens, thought it to be waves. In 1801,
through the phenomenon of interference, Young
showed experimentally that light traveled as
waves. Wave properties of light Diffraction is
the bending of light behind an aperture or around
an obstacle. Interference is the combination of
two or more waves of the same type and wavelength
which meet at a point in space. Polarization is
the restriction of the vibration of a
(transverse) wave to a particular direction.
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Wave Motion

• The wavelength ? (in km) is the distance between
  neighboring points on the wave which have the
  same phase.
• The frequency f (in Hz) is the number of crests
  passing a given point per second.
• The speed of the wave is given by v f ?.
• For light, the speed c 300,000 km/s.

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Interference of Two Like Waves
Constructive interference occurs when the
two waves are in phase, so that their crests
coincide.
Destructive interference occurs when the
two waves are 180o out of phase, so that the
crest of one wave coincides with the trough of
the other.
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Double Slit Interference 5
smaller spacing
larger spacing
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Double Slit Interference 4

• Coming from the same source S0, the light passing
  through slits slits S1 and S2 is coherent, a
  requirement for interference.
• The interference of the diffracted waves from S1
  and S2 produces a set of interference fringes.

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Diffraction of Light

Diffraction, which is the bending of a wave
behind apertures and around obstacles, plays an
important role in double-slit interference.
The light passing through the narrow slit shown
in Fig (c) behaves as it does in double-slit
interference.
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Diffraction Grating 1

• A diffraction grating, which consists of
  thousands of equally spaced fine lines ruled on a
  small rectangular plastic slide, is used to give
  very sharp interference maxima.
• The figure shows how the spectra are sharpened
  when the number of slits is increased from 2 in
  Fig.(a) to 6 in Fig.(b).

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Grating Spectrometer

• The m 0 spectrum is observed when the telescope
  is lined up with the collimator (? 0).
• The m 1 spectra are observed by varying the
  angle ? in both directions.
• For the m 1 spectrum, the intensity maxima are
  given by
• ? d sin?.

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Dispersion by a Diffraction Grating
Emission line-spectrum
Continuous spectrum

• The m0 spectrum is not deviated.
• The diffracted spectra are denoted m 1 and m
  2.
• In the diffracted spectra, the red end (longer
  wavelengths) is more deviated from the m0 line
  than the blue.

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The Continuous Spectrum
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Emission Line-Spectrum of Sodium
The sharp spectral lines seen on the screen would
be observed only if the prism were replaced by a
grating.
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Emission Line-Spectra of some Elements
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Why The Sky is Blue

• Sunlight contains all the colors of the rainbow.
• The molecules of the Earths atmosphere scatter
  the incoming molecules in all directions. The
  blue (short wavelength) end of the spectrum is
  scattered more than the red (long wavelength)
  end. Thus, the sky looks blue, while the Sun
  appears yellow, which corresponds to white light
  minus the scattered blue.
• At sunrise or sunset, the Suns rays take a
  longer path through the atmosphere, so that more
  of the sunlight is scattered, making the Sun
  appear orange or red.

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The Electromagnetic Spectrum 1
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The Electromagnetic Spectrum 2
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The Electromagnetic Spectrum 3

• The EM spectrum extends from ?-ray wavelengths
  (shorter than 10-15 m) to radio waves (longer
  than 1000 km).
• All EM radiations travel through space at the
  speed of light c, differing only in their
  wavelengths ? (and frequencies f).
• While EM waves travel through space as waves,
  their interaction with matter is as tiny packets
  of energy, known as photons (Einstein, 1905).
• The energy E of a photon is given by E hf, where
  f is the frequency, or in practical units, by
• E 1240/? ,
• where E is in eV (electron-volts) and ? is
  in nm.
• Short wavelength (high frequency) photons have
  high energies, and vice-versa.

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Transparency of Earths Atmosphere

• Only visible light and radiowaves reach the
  ground at all their wavelengths, while all
  infrared rays reach high mountains.

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Refraction by a Converging Lens

• A converging (or convex) lens focuses light
  entering the lens parallel to the axis at the
  focal point F.
• Off-axis rays focus at a point in the focal
  plane.

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Focusing Light with a Converging Lens
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Chromatic Aberration 1

• Chromatic aberration in a lens causes blue end of
  the visible spectrum to have a shorter focal
  length than the red.
• Chromatic aberration does not occur in mirrors.

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Chromatic Aberration 2
An achromatic combination lens made with two
different types of glass can greatly reduce
chromatic aberration by correcting for two
colors.
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Spherical Aberration in a Lens

• Spherical aberration refers to the fact that
  the outermost rays striking a spherical lens or
  mirror come to focus earlier than the central
  rays.

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Spherical Aberration in a Mirror

• Spherical aberration occurs in a concave
  mirror with a spherical reflecting surface.

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Parabolic Mirror

• Spherical abberation does not occur in a
  mirror with a parabolic reflecting surface.

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Parallel Rays from a Distant Object
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Astronomical Telescope 1

• The magnification is given by M fo/fe , where
  fo and fe are the focal lengths of objective and
  eyepiece.
• The length of the instrument is L fo fe.

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Astronomical Telescope 2

• The final image seen by an observer looking
  through the eyepiece is inverted.

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Worlds Largest Refracting Telescope

• Built in the late 1800s, the telescope at the
  Yerkes Observatory, near Chicago, has an
  objective of diameter 40 inches.

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Astronomical Telescope 3

• Large objectives use parabolic mirrors because
• i. neither spherical aberration nor
  chromatic aberration occur
• ii. they weigh much less than large glass
  lenses
• iii. Unlike glass lenses, metal mirrors are
  structurally stable.

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Effect of Twinkling Star-Field from the Ground
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Effect of Twinkling View from the HST
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Adaptive Optics and Interferometry 1

• Adaptive optics is a ground-based method of
  compensating for atmospheric turbulence, which
  causes small shifts in the position of a stars
  image to occur, blurring the image and producing
  twinkling.
• In applying adaptive optics, a secondary mirror
  is made up of small segments, each of which is
  automatically adjustable, so that a reference
  star (or artificial image, produced by a laser
  beam) is kept in sharp focus.
• This allows the telescope to continue to work at
  its highest resolution, regardless of the
  turbulence.

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Proposed OWL 100m Reflecting Telescope
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Example of Adaptive Optics

• The Cats Eye Nebula taken from the same
  ground-based telescope, without (left) and with
  (right) adaptive optics.
• With adaptive optics, the proposed ground-based
  100 m OWL (overwhelmingly large) telescope would
  have a resolving power 40 times better than the
  HST.

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Radio Telescopes 1

• Prior to 1930, all astronomy was done with
  visible light.
• The largest single radio telescope dish in the
  world, in Arecibo, Puerto Rico, is 300 m in
  diameter, but its resolution is appreciably less
  than that of a large optical telescope.
• Very high resolution radio telescopes link
  individualtelescopes through a process known as
  interferometry.
• The Very Large Array (VLA), situated near
  Socorro, NM, contains 27 concave reflecting
  dishes, each 26 m in diameter, arranged along
  three arms.
• The Very Long Baseline Array (VLBA), uses
  radio telescopes thousands of miles apart, from
  Hawaii to New Hampshire.
• The downsides of such systems are their poor
  light-gathering ability (sensitivity) and their
  small fields-of-view.

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Keck Reflecting Telescopes, Hawaii

• While each telescope singly is equivalent to
  a 10 m reflecting telescope, when linked together
  they are equivalent to a single 85 m telescope.

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VLA 1
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VLA 2
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Radio Telescopes 2

• The new Green Bank Telescope (GBT) in West
  Virginia has a dish about 100 m in diameter, and
  is the worlds largest rotatable radio telescope.
  

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Optical and Radio Photos of Saturn

• To be displayed as a photo, the radio signal must
  be shown in false color.
• The most intense radio emission is red, followed
  by yellow and blue, while black means that there
  is no measurable signal.

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Radio Telescope at Cambridge U.

• With this detector strung together with 120
  miles of wire and cable, Jocelyn Bell in 1967
  discovered the pulsar.

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Telescopes at Other Wavelengths

• Water vapor is the main absorber of infrared
  radiation from space, so that surface IR
  telescopes must be placed in exceptionally dry
  locations, such as at the Summit of Mauna Kea in
  Hawaii.
• However, the best locations for IR , UV , X-ray
  and gamma-ray telescopes are on orbiting
  satellites.
• Normal methods of reflection do not work for X
  rays and gamma rays.
• X-rays, which can be reflected when grazing a
  surface, are focused with a grazing incidence
  X-ray telescope.
• High energy particle-physics techniques are used
  in building gamma ray instruments.