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Optics• Read Your Textbook: Foundations of Astronomy
Doppler Effect for Sound• Change in frequency of a wave due to relative motion
between source and observer.
Line of SightOnly
sensitive
to motion
between
source and
observer
ALONG
the line of
sight.
Radial Velocity ConventionTrue Velocity
RadialLine of Sight Component
Observer
No Doppler ShiftTransverse motion
Radial Velocity > 0Moving Away
Radial Velocity < 0Moving Toward
Doppler Effect• Light
Doppler Effect for Light Waves• Change in frequency of a wave due to relative motion
between source and observer.
• c = f speed of light = wavelength x frequency
c = 3 x 108 m/s
E = hf = hc/energy of a light wave, a photon
of frequency (f) or wavelength ( h = planck’s constant 6.63 x 10-34 J-sec
A light wave change in frequency is noticed as a change
in “color”.
Wavelength Doppler Shift0 = at rest (laboratory) wavelength
= measured (observed) wavelength
= 0
= difference between measured and laboratory wavelength
vr/c = 0
vr = (0)c radial velocity
Solar Spectrum Solar Radiation Output
The sun looks “yellow”
Wien's law relates the temperature T of an object to the wavelength maximum at which it emits the most radiation.
Mathematically, if we measure T in kelvins and the wavelength maximum () in nanometers, we find that*
max = 3,000,000/T
*3,000,000 is an approximation of the true value 2,900,000 (just like 300000000 m/s approximates the speed of light 299792458.
Wien’s Law
max = 3,000,000/T
Tsurface = 5800 K (solar surface temperature)
max = 3,000,000 / 5800 K
= 517 nm (Yellow-Green)
The atmosphere scatters most of the blue lightmaking the sun appear more yellow and the sky blue
Approximate Solar Peak
Light Waves
• Light is a wave that propagates at speed c.– c = 3 x 108 m/s in a vacuum
– velocity is slower in other media
• Like sound waves and other waves, light should exhibit the same properties seen for other waves. These are diffraction, reflection, and interference.
• In addition, light waves also exhibit refraction, dispersion and polarization.
Diffraction of Water Waves
• Diffraction: Waves ability to bend around corners
Ray Trace
A ray trace is meant to represent the direction of propagation
for a set of parallel waves called a “wave front.”
Diffraction
Constructive Interference• Waves combine without any phase difference• When they oscillate together (“in phase”)
Wave AdditionAmplitude ~ Intensity
Destructive Interference• Waves combine differing by multiples of 1/2 wavelength• They oscillate “out-of-phase”
Wave Subtraction
Two Slit Destructive Interference• Path Length Difference = multiples of 1/2
Two Slit Interference
Two Slit Interference• Slits are closer together, path length differences change
Light or Dark?• Path Length Differences =, Waves arrive in phase• Path Length Differences = 1/2 , Waves arrive out of phase
Light or Dark?
Light from the slits arrives at A. Path Lengthfrom slit 1 is 10,300 nm and from slit 2is 10,300 nm for a difference of 0 nm.
There is no path length difference so the waves from the two slits arrive at A oscillating in phase. They add constructively and produce a brighter area.
Light or Dark?
Light from the slits arrives at E. Path Lengthfrom slit 1 is 10,800 nm and from slit 2is 11,800 nm for a difference of 1000 nm.
This path length difference is exactlytwo wavelengths so the waves from the two slitsarrive at E oscillating in phase. They add constructivelyand produce a brighter area.
Light or Dark?
Light from the slits arrives at B. Path Lengthfrom slit 1 is 10,450 nm and from slit 2is 10,200 nm for a difference of 250 nm.
This path length difference is exactly1/2 a wavelength so the waves from the two slitsarrive at B oscillating out of phase. They add destructivelyand produce a dark area.
Newton’s Rings
Resolution
Resolving Power
Telescope diameter = D (cm)
Resolution = (arcminutes)
= 11.6/D
Larger D = smaller angular sizes resolved
Increasing Resolving Power
Magnification
Telescope diameter (D)
Focal Length (f)
f/# The focal length is # times the objective diameter
Magnification = focal length of objective/ focal length of eyepiece
f-number (f/#)The f/# refers to the ratio of the focal length to the diameter.
An f/10 optical system would have a focal length 10 Xbigger than its diameter.
The f/10 celestron C8 has a focal length of 80 inches.(8 inch aperture times 10)
Our 16 inch telescope in the newtonian f/4 configurationhas a focal length of 64 inches (16 x 4).
MagnificationMagnification depends on the ratio of the focal lengthsfor the primary aperture to the eyepiece.
M = focal length of objective / focal length of eyepiece = fo/fe
Therefore for the same eyepiece, in general, the telescopewith the longest focal length can achieve the greater magnification.
Magnification Isn’t EverythingMagnifying something spreads the light out into a largerand larger area. An object is only so bright and magnifying an image too much causes it to become so diffuse that it ceases to be visible.
Magnifying power for a telescope is not what you are looking for. Besides, increased magnification can be achieved bychanging eyepieces.