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Studying for the Exam
• Relevant chapters: E, 1, 2 & 3
• To prepare for the exam it is helpful to …
– review readings
– review lecture notes online (esp. concept
– revisit homework
– look over the activities
Studying for the Exam
• Filter out the relevant information, don’t
focus on details
• Properties of relevant information:
– Information appears repeatedly in course
materials (readings, slides, homework,…)
– It is not an isolated fact, but can be “reasoned
– It is an important concept (e.g. daily &
monthly motion, scientific method)
Exam Questions
• About 30 multiple choice questions
• A few short answer problems
• Types of questions NOT on the exam:
What’s Galileo’s birth year?
What is the frequency of yellow light?
What is the distance of the Earth to the Sun?
What is the mathematical formula for the
Hydrogen energy levels?
Exam Questions
• Types of questions that could be on the exam:
– Why isn’t there a lunar eclipse every full moon?
– It is noon in Westerville. Is it earlier/ later/different
day/different season in Paris, France?
– What is the difference between a sidereal and a solar
– How high above the horizon is the polar star at noon if
you are at 23 degrees northern latitude?
– Given the wavelength of yellow light, what is its
Doppler Shift
• From Wikipedia
Doppler Shift
• Can use the Doppler shift to
determine radial velocity of
distant objects relative to us
• Transverse velocity can be
measured from the motion of
stars with respect to background over a period of years
Homework: Doppler Shift of
Hydrogen spectrum
• The discrepancy between the wavelength of
a line measured in the lab versus measured
on an object is proportional to the velocity
of the object
• Apparent/ true wavelength = 1+ velocity/c
• Example:
– Observed(or apparent): 698 nm
– Actual(or true or lab) wavelength: 656.3nm
– velocity = (698nm/656.3nm -1) c = 19100 km/s
Atomic Energy Levels
• For Hydrogen, the energies of the atomic levels are
given by a simple formula that just depends on the
(excitation) number n of the orbit: En = – Ry / n2
where Ry = 13.6 eV = 2.179 x 10-18J  E1, E2=¼ E1, E3=1/9 E1,…
• Electrons in higher levels will cascade down,
producing many different spectral lines
• Formula can be converted to frequency, wavelength
Light hits Matter: Refraction
• Light travels at different speeds in vacuum, air,
and other substances
• When light hits the material at an angle, part of it
slows down while the rest continues at the original
speed – results in a change of direction
– Different colors bend different amounts – prism,
Application for Refraction
• Lenses use refraction to focus light to a
single spot
Light hits Matter (II): Reflection
• Light that hits a mirror is
reflected at the same
angle it was incident
• Proper design of a mirror
(the shape of a parabola)
can focus all rays
incident on the mirror to
a single place
Application for Reflection
• Curved mirrors use reflection to focus light
to a single spot
• From Galileo to Hubble
• Light collectors
• Two types:
– Reflectors
– Refractors
• Magnification:
– ratio of focal
lengths of
objective and
– M = fobj/feye
– Example:
telescope with
40mm eyepiece:
Reflecting Telescopes
Problems with Refractors
• Different colors (wavelengths) bent by
different amounts – chromatic aberration
• Other forms of aberration
• Deform under their own weight
• Absorption of light
• Have two surfaces that must be optically
Telescope Size
• A larger telescope gathers more light (more
collecting area)
• Angular resolution is limited by diffraction
of light waves; this also improves with
larger telescope size
Resolving Power of Telescopes
Andromeda Galaxy
Telescope 1
Telescope 2 of double size
Resolving Power of Telescopes (II)
(a) 10’
(b) 1’
(c) 5”
(d) 1”
• The magnification of a telescope can easily
be changed by plugging in a different
eyepiece with a different focal length
• M= focal length of main lens or mirror
focal length of eyepiece
Example: F= 2000mm, f = 40 mm  M= 50
Atmospheric Limitations
Atmospheric Limitations
Optical Window
Radio Window IR Window
Largest Earth-Based Telescopes
• Hobby-Eberly Telescope,
Davis Mountains, TX
– 11 m diameter
– Cannot see all parts of the
• Keck I and II, Mauna Kea,
– 36  1.8 m hexagonal
equivalent to 10 m
– Above most of atmosphere
(almost 14,000 ft ASL)
– Operating since 1993
Other Techniques
• Put telescopes on
– Hubble Space
Telescope: 2.4 m,
since 1990
• Use computers to
correct optics during
light gathering:
adaptive and active
• Interferometry
• Radio astronomy
Other Wavelengths
• Must be carried out on satellites (or rockets,
balloons, etc.) due to strong absorption in the
• Infrared astronomy
• High-energy (UV, X-ray, gamma-ray) astronomy
• Radio
• Infrared
Each region of the
• Visible
spectrum gives us
valuable information
about the universe
• X-Ray
(only these frequency bands can
be observed with groundbased telescopes)
• Gamma