Lecture #8: Thursday, Feb. 01

Note:

·        The due date of the second homework is Thursday, Feb. 1 at 23:59.

·        The third homework is due Tuesday, Feb. 6th at 23:59.

·        Exam #1 is Monday, Feb. 5.
It will cover chapters 1 to 5.
Most likely it will be 40 multiple-choice questions.
No materials to be used during exam.
Calculator can be used but is not needed

 

Topics:

  1. Review Kirchhoffs Laws
  2. Review Emission and Absorption of Photons

     III.            Telescopes

     IV.            Exam Review

 

         I.            Review: The 3 Kirchhoff’s Laws (Gustav Kirchhoff, 1859)

    1. Kirchoff's Laws describe the three types of radiation spectra.
      (Gustav Kirchhoff, 1859)

B.        Law 1: Continuous spectrum - all wavelengths are present

      1. Produced by solids, liquids, dense gas (interior of star)
      2. Wiens Law: hotter objects emit shorter wavelength (bluer) radiation
      3. Stephans Law: hotter objects emit more photons
        number of photons/second = Size times Temperature4

    1.  Law 2: Discrete or emission spectrum - only a few wavelengths are present

      1. Produced by excited or hot, thin gas
        (interstellar cloud, heated by a nearby star) 
      2. Emission spectrum is the "fingerprint" of an atom

    2.  Law 3: Absorption spectrum - only a few wavelengths are missing

      1. Examples: illuminated, cool, thin gas
        like sun's surface gas layer illuminated by interior
      2. Comes from atoms in a cool gas
        absorbing photons of only certain energies.
      3. Depends only on the atomic nature of the gas ("fingerprint")

  1. Review: Absorption and Emission of Photons

E.        Atoms exist only in certain energy states.
Definitions:

                                                               i.      ground state - lowest energy state

                                                              ii.      ionization - completely remove an electron

                                                            iii.      excited state - any higher energy state of an atom

                                                            iv.      transition - the jump of an electron between state

B.       Emisson: Electron falls to lower energy state and emits photon

C.       Absorption: Electrons jump to higher energy state and absorb photon

D.      Energy level diagram:

                

remember: visible photons range from 1.8 – 3.1 eV
example for “visible” transition: 13.06 eV – 10.2 eV = 2.86 eV

E.       Measurement of the spectra from an astronomical object can tell us what the object is made of.


     III.            Telescopes

A.      Basic principle: Lenses or mirrors can be used to collect light
from an object and focus it to a new location
(eg. To the film in a camera or the retina of our eyes).

B.       Lenses (made of glass or plastic)

                                                        a.            Use refraction to change direction of light
Origin of refraction: change of speed of light in glass
(Demo)

                                                       b.            Picture of the effect of a converging
lens and how an image is formed:

                                                        c.            The focal length of a lens is the distance from the lens
to where incoming parallel rays are focused. (see figure)

This is where the image of very distant objects is formed (Astronomy!).
  

C.       Mirrors

                                                        a.            Mirrors also can be converging
(see figure) Demo: a mirror

                                                        b.            Images can be formed in a similar way lenses are used.

D.      The basic telescope has two parts (see fig 3.4)

                                                        a.            objective lens (or mirror) - used to gather light and form an image.

                                                       b.            eyepiece - used to refocus and magnify the image from the objective,
for viewing with our eyes or an optical instrument.
DEMO: build a telescope

E.       Telescopes, which use a lens as the objective are called refractors.
Telescopes, which use mirrors are called reflectors.

F.       Basic Properties are:
Light gathering power, resolution, magnification  (see figure)

                                                        a.            L µ (diameter of objective)2 / (focal length)2.

                                                       b.            Example: compare to eye (0.5cm)
1cm lens: collects (1/0.5)2 = 22 = 4 times more light than our eyes.
   
Mt. Palomar 5 meter telescope:
collects (500/0.5)2 = 10002 = 1 million times more
light than our eyes.

G.      Resolving Power (or resolution)

                                                        a.            The smallest angular distance
that can be distinguished (see fig. 3.9).

                                                       b.            Eye: 3 arcmin resolution

                                                        c.            Diffraction Limit:
diffraction of light at edges of telescope
makes perfect dot appear as a blob (blurring)

resolving power (in degrees) =
  57.3° x (wavelength of light)/(diameter of the objective)

or for visible light:
resolving power (arcsec) = 10/(diameter of objective in cm)

for 5m Mount Palomar: 0.02 arcsec diffraction limit

                                                       d.            Atmospheric Blurring Limit:
The actual resolution (for earth based telescopes) is limited
by turbulence in the Earth’s atmosphere.
Astronomers referee to the amount of interference as seeing.
A good value for seeing is 1 arcsec. See fig. 3.12

Work arounds: space based, adaptive optics

H.      Magnification/ image size

                                                        a.            magnification = (focal length of objective/focal length of eyepiece)

                                                       b.            not so important as necessary magnification can be easily achieved

                                                        c.            Generally image has to be just large enough so that,
for example, 2 stars that one wants to resolve fall on
2 different pixels of the detecting device (retina, CCD chip, ...).
(see figure)

Example: 2 stars with 1 arcsec angular separation
(atmospheric limit) at the 5 m Mount Palomar telescope
are on the image seperated by 0.08 mm (16.76 m main focus).
CCD cameras: 0.01mm pixel size – OK

                                                       d.            Too much magnification reduces light gathering power
(larger focal length) and reduces field of view

                                                        e.            The practical limit of magnification is 10 times
the diameter of the objective in cm.

 
 
  
 

I.         Comparison of Reflecting and Refracting telescopes

                                                        a.            Refracting telescopes have chromatic aberrations
(since the bending of light depends on color).
Multiple lens systems can correct this, but the grinding
of these lenses is difficult. Light is lost at each interface.
A reflecting telescope does not have this problem because
 reflection does not depend on wavelength.
DEMO

                                                       b.            Weight.

                                                        c.            All lens surfaces must be perfect,
whereas only one surface of a mirror must be good.

                                                       d.            The largest practical limit to refracting telescopes is the
Yerkes Observatory 40 inch (1 meter) refractor.
The largest reflector is the Keck telescope in Hawaii at
10 meter diameter.

J.        Modern telescope features

                                                        a.            Segmented mirror telescopes (first was Mount Hopkins, Keck)
active optics adjusts segments several times per second to compensate
shifts, temperature changes etc. to keep focus.

                                                       b.            Multiple mirror telescopes (or multiple telescopes) can use
 interference to infer high resolution details.
The European Very Large Telescope (1999) will have
a resolution of 0.0024 arcsec for a 130 m baseline
 (4 x 8.2m telescopes with adaptive optics).

                                                        c.            Adaptive optics changes the shape of a smaller mirror in
response to the Earth’s atmosphere in real time to reduce
 atmospheric resolution limit. A bright natural or artificial
(LASER) guidance star serves as reference.

K.      Radio telescopes

                                                        a.            Much of the short-wave radio region of the sky can also
reach the surface of the Earth.
Day and night observation at any wheather are possible.

                                                       b.            Due to the large wavelength of radio-waves and
relatively small intensities a large telescope is needed.

                                                        c.            Large baseline arrays are used,
or large dishes like the Arecibo observatory.
or the Very Large Array VLA.
 

L.       Other wavelengths astronomy

                                                        a.            IR, UV, X-ray, gamma-ray

                                                       b.             different wavelength observations complement each other:

1.        Different sources visible (different Temperatures !)

2.        Different opaqueness of interstellar medium, dust clouds ...