### Lecture5

```Astronomy 1 – Fall 2014
Lecture 5; October 16, 2014
Previously on Astro-1
• The Nature of Light
–
–
–
–
Relation of speed to wavelength and frequency
Wavelength dependence of scattering
Doppler effect and Doppler formula
– Describes the spectrum of light emitted by opaque sources
– The temperature of the blackbody determines
• The spectrum (Wien’s Law)
• The energy flux (Stefan-Boltzman Law)
• Kirchoff’s Laws
– A hot body produces a continuous spectrum
– A hot transparent gas produces emission lines
– Cool transparent gas in front of a hot body produces absorption lines
Today on Astro-1
• Light can have particle-light properties.
– The particles of light are called photons.
–
–
Planck’s Law: E = h = hc/
Atoms absorb & emit photons at discrete energies
• Spectroscopy and the composition of objects
• Geometrical Optics
– Reflection/Mirrors
– Refraction/Lenses
• Telescopes
– Optical
– Other wavelengths
CLM - Fall 2014
Kirchoff’s Laws
1. A hot, dense object such as a blackbody emits a continuous
spectrum covering all wavelengths.
2. A hot, transparent gas produces a spectrum that contains bright
(emission) lines.
3. A cool, transparent gas in front of a light source that itself has
a continuous spectrum produces dark (absorption) lines in the
continuous spectrum.
CLM - Fall 2014
CLM - Fall 2014
CLM - Fall 2014
What causes spectral lines?
The structure of atoms
CLM - Fall 2014
Rutherford’s Experiment
CLM - Fall 2014
Rutherford’s
model of the atom.
Today we know
this is not exactly
correct – electrons
do not orbit the
nucleus, but the
basic idea is right - protons and
neutrons exist in
the nucleus, and
electrons are
outside of it.
CLM - Fall 2014
Planck’s Law
“Light is also a Particle”
E=
hc
l
or E = hv
E = Energy of a photon
h = Planck’s constant = 6.625×10-34 J s
c = speed of light
λ = wavelength of light
ν = frequency of light
CLM - Fall 2014
What is the Energy of a Photon?
Example: DNA molecules are easily broken when hit
with ultraviolet light at 260 nm. How much energy
does a single photon at this wavelength have?
A.
B.
C.
D.
E.
7.6 x 10-19 J
7.6 x 10-17 J
7.6 J
5.7 x 10-49 J
7.6 x 1019 J
(6.625 ´10-34 Js)(3.00 ´10 8 m /s)
-19
E=
=
=
7.64
´10
J
-7
l
2.60 ´10 m
hc
CLM - Fall 2014
Niels Bohr
1885-1962
The Bohr model
of the atom
Was a postdoc with Rutherford.
In 1912, to explain discrete
nature of spectral lines,
hypothesized that electron orbits
are quantized (quantum
mechanics!).
CLM - Fall 2014
Bohr and Einstein, 1925
The quantum nature of light is related to the quantum nature of
atoms!
CLM - Fall 2014
In 1885 Swiss schoolteacher Johann Jakob Balmer, by trial and error,
created a formula that can predict where lines of hydrogen fall in the
spectrum of a star.
We still call these Balmer lines.
æ1 1 ö
= Rç - 2 ÷
è4 n ø
l
1
R = Rydberg constant = 1.097×107 m-1
n = any integer greater than 2
CLM - Fall 2014
æ 1 1 ö The Balmer series and fomula. 7 -1
= Rç - 2 ÷ R = Rydberg constant = 1.097×10 m
è4 n ø
l
1
Bohr figured out the physical
explanation for Balmer’s
formula – the spectra from
stars depends on the
structure of atoms!
æ 1
1ö
= Rç 2 - 2 ÷
èN
l
n ø
1
N = lower orbital
n = higher orbital
Electron Transitions in the Hydrogen Atom
The same wavelength occurs whether a photon is emitted or absorbed.
CLM - Fall 2014
CLM - Fall 2014
Every Element Has a Unique Set of
Spectral Lines
Atomic number is the number of protons in an atom.
CLM - Fall 2014
CLM - Fall 2014
Nitrogen & Sulpher
Hydrogen & Oxygen
Spectroscopy Reveals the Chemical
Composition of Celestial Objects
CLM - Fall 2014
Light is a wave… it is affected by motion too.
Bottom line: you can tell how fast something is moving
from its spectrum… sort of
Extra-solar planets: most have
been discovered using Doppler
shift measurements of their
parent stars (since 1995)
Spectral Lines
(iclicker Question)
Professor Martin used a spectrograph on the Keck telescope
to observe a distant galaxy. She detected 2 absorption lines
from sodium atoms. The wavelengths she measured were
0.22 nm bluer than the wavelengths of 589.0 and 589.6 nm
where she expected to find the lines. What should she
conclude?
A. There are cool clouds between the observer and the
galaxy.
B. There gas between the galaxy and the observer is
hotter than the galaxy.
C. The gas clouds are moving away from the galaxy
towards the observer.
D. The gas clouds are falling into the galaxy.
E. Both A and C
Structure of Atoms
(icliker Question)
•Most of the mass of ordinary matter resides in the
•A) electrons and nuclei, shared equally
•B) nuclei of atoms
•C) electrons around the nuclei of atoms
•D) energy stored within the atom in electromagnetic
forces
•E) Atoms have no mass.
CLM - Fall 2014
Geometrical Optics
The Light Rays from Distant
Objects are Parallel
Light from Every Point on an Extended Object
Passes through Every Point in the Lens
…and creates
extended images.
Refraction Demo:
Change in Direction of a Light Ray
Refraction
Which Way Does the Path Bend?
Demo:
Law of Reflection
Importance of the telescope
‘Three great events stand at the threshold
of the modern age and determine its
character: 1) the discovery of America; 2)
the Reformation; 3) the invention of the
telescope and the development of a new
science that considers the nature of the
Earth from the viewpoint of the universe’
(Hannah Arendt, ‘The Human Condition’)
Galileo’s Telescope
The Keplerian Telescope
Telescope Demo
(iclicker Question)
The objective lens of our telescope demo has a
focal length of 500 mm. Suppose we replace the
250 mm eyepiece with a 50 mm eyepiece. How
will the magnification of the meter stick change?
A.
B.
C.
D.
E.
Increase 5x
Increase to 10x
Decrease to 50x
Increase to 50x
The magnification does not change.
Telescope Demo
(iclicker Question)
The objective lens of our telescope demo has a focal
length of 500 mm. Suppose we replace the 250 mm
eyepiece with a 50 mm eyepiece. How should we move
the objective lens?
A.
B.
C.
D.
E.
Move the objective lens closer to the eyepiece.
Move the objective lens further from the eyepiece.
Move the objective lens away from the optical axis.
There is no need to refocus the telescope.
Back and forth by trial and error; it cannot be
predicted.
Telescope Demo
(iclicker Question)
Suppose the professor covers the bottom half of the objective
lens. What will the lass see through the telescope on the sceen?
A. The top of the ruler, and this image will be inverted left to
right.
B. The bottom of the ruler because the image is inverted, and
this image will be inverted left to right.
C. The top of the ruler, and this image will NOT be inverted left
to right.
D. The bottom of the ruler because the image is inverted, and
this image will NOT be inverted left to right.
E. The same image we saw previously.
Name some shortcomings of lenses
Newtonian Reflector
Telescopes:
Light gathering power
Light gathering power depends on size
of objective lens or primary mirror
How Do You Make a Lightweight
10m Diameter Mirror?
How much more light gathering
power does a 10m telescope have
than an 0.5 m telescope?
Answer: The light gathering power is proportional to the
square of the mirror’s diameter.
(10m)2/(0.5m)2 = 100m / 0.25m = 400
So you can see objects about 400 times fainter with the
10m telescope in the same amount of time.
Reflection Telescopes
The Secondary Mirror Does
Not Cause a Hole in the
Image
This illustration shows how
even a small portion of the
primary (objective) mirror of
a reflecting telescope can
make a complete image of
the Moon. Thus, the
secondary mirror does not
cause a black spot or hole in
the image. (It does, however,
make the image a bit dimmer
by reducing the total amount
of light that reaches the
primary mirror.)
Reflecting Telescopes
This view of the Gemini North
telescope shows its 8.1-meter
objective mirror (1). Light
incident on this mirror is reflected
toward the 1.0-meter secondary
mirror (2), then through the hole
in the objective mirror (3) to the
Cassegrain focus
Angular Resolution
Angular resolution of the telescope
Limited by:
•Blurring effects of the atmosphere (“seeing”), i.e. the twinking of
stars
•The quality of the optics and detector on the telescope.
•The size of the telescope – the “diffraction limit.”
The diffraction limit
l
q = 2.5 ´10
D
5
θ= diffraction-limited angular resolution of the
telescope, in arcseconds
λ= wavelength of light, in meters
D = diameter of telescope objective, in meters
Example: What is the diffraction limit for red light
(640nm=6.4×10-7m) for a telescope with with a 0.5m
objective/primary.
l
-7
6.4
´10
m
q = 2.5 ´10 5 = 2.5 ´10 5
= 0.32"
D
0.5m
So even if you had a perfect atmosphere and perfect optics, you
couldn’t resolve details finer than 0.32” with a 0.5m telescope.
Today
astronomers build
telescopes at the
best sites in the
world, then travel
to the telescope to
observe, or have
someone else onsite observe for
them, or observe
remotely over the
internet.
Mauna Kea, an extinct volcano in Hawaii that reaches 13,400 feet, is
the best site in the world for optical and infrared telescopes. It has
mostly clear, dark skies, little atmospheric turbulence, and is above
most of the water vapor in the Earth’s atmosphere. Notice the snow and
lack of vegetation.
Adaptive Optics Help Telescopes on Earth Remove
the Blurring Caused by the Atmosphere
Laser Beacon Makes an Artificial Star
Astronomy Uses the Entire EM Spectrum
The percentage of radiation that can penetrate the Earth’s atmosphere at
different wavelengths. Regions in which the curve is high are called
“windows,” because the atmosphere is relatively transparent at those
wavelengths. There are also three wavelength ranges in which the
atmosphere is opaque and the curve is near zero: at wavelengths less than
about 290 nm, which are absorbed by atmospheric oxygen and nitrogen;
between the optical and radio windows, due to absorption by water vapor
and carbon dioxide; and at wavelengths longer than about 20 m, which are
reflected back into space by ionized gases in the upper atmosphere.
Hubble Space Telescope
James Webb Space Telescope
(see movie on class website)
Saturn Reflects the Sun’s Light;
And It Also Emits Light as Do All Blackbodies
Orion
Discovery
Enabled by
Year
The heavens are not perfect and
unchanging; (ultimately) the Earth
is not the center of the universe.
The telescope and Galileo’s observations.
~1609
The sun and stars are giant balls of
hydrogen undergoing fusion.
Fraunhofer’s invention of the spectrograph.
1814
Our galaxy is not the center of the
universe, and the universe is
expanding.
Edwin Hubble and the giant Palomar 200inch and large-format photographic plates.
1929
The universe started as a hot “Big
Bang”
Penzias and Wilson using a radio
“telescope,” confirmed by satellites.
1965
Planets are common in the universe. Modern charge-couple-device detectors
(CCD); Iodine cell for spectrograph.
1995
Dark Energy dominates the
universe.
1998
Large-format CCD detectors; 10m Keck
telescope.
And there are many more involving infrared,
x-ray, ultraviolet and gamma-ray discoveries.
Summary
• Light can have particle-light properties.
• Particle energy: E = h = hc/
• Every element (even every ion) has a unique spectral
fingerprint.
• Spectroscopy reveals the composition of distant objects
• Geometrical optics
– Reflection & Refraction
– Focus, Spherical aberration, Chromatic aberration
• Telescopes
– Light gathering power
– Magnification
– Resolving power
Homework (Due Monday 10/20)
• On your own: answer all the review questions
in chapter 5 & 6.s
• To TAs: answer questions,
– 5.34 (Note that Io’s surface temperature is -150o C
and not 2150o C),
– 5.37, 5.43, 5.44
– 6.34, 6.36, 6.40, 6.41
```