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:
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.
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!).
a.
Mirrors
also can be converging
(see figure) Demo: a
mirror
b.
Images can be formed in a similar way lenses are used.
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
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.
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
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.
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.