optics read your textbook: foundations of astronomy –chapter 6, 7 homework problems chapter 6...
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Optics• Read Your Textbook: Foundations of Astronomy
– Chapter 6, 7
• Homework Problems Chapter 6– Review Questions: 1,2 5-7– Review Problems: 1-3, 8– Web Inquiries: 2
• Homework Problems Chapter 7– Review Questions:1, 2, 4, 5, 7, 10-12– Review Problems: 1-4, 9– Web Inquiries: 1
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Light Gathering PowerTelescope diameter (D)Light Gathering Power (LGP) is proportional to area.
LGP = (D/2)2 D = diameter
Light Gathering Power
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Light Gathering PowerTelescope diameter (D)Light Gathering Power (LGP) is proportional to area.
LGP = (D/2)2 D = diameter
A 16 inch telescope has 4 X the LGP of an 8 inch.
LGP 16 inch = (16/2)2 LGP16/LGP8 = 4LGP 8 inch = (8/2)2
A 16 inch telescope has 2800 X the LGP of the eye.LGP 16 inch/LGP eye (0.3inch) = (16/0.3)2 = 2844
Light Gathering Power
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More Light
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Types of Waves• Compression wave
oscillations are in the
direction of motion
• Transverse Waveoscillations are transverse
to the direction of
motion
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Wave ParametersWavelength () length
Amplitude (A) height
Frequency (f) repetition
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Amplitude: Size of wave (perpendicular to direction of propagation) Proportional to Intensity(Sound loudness, Light brightness)
Wavelength: Size of wave (in the direction of propagation)
Frequency: Number of waves passing a fixed position per second f (cycles/second, Hertz)
Wave Speed: v = f
Frequency increases Frequency decreasesEnergy increases Energy decreases Wavelength decreases Wavelength increases
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An Electromagnetic Wave (a.k.a. Light)
Light travels at a velocity c = f (3x108 m/s)
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E-M Frequency and Wavelength
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Electromagnetic Spectrum
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Electromagnetic Spectrum Uses
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The Visible Spectrum
COLOR FREQUENCY (10-14 Hz) WAVELENGTH (nm)
• R 4.0-4.8 750-630• O 4.8-5.1 630-590• Y 5.1-5.4 590-560• G 5.4-6.1 560-490• B 6.1-6.7 490-450• V 6.7-7.5 450-400
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Radio (Light) Wave
94.1 THE POINT, broadcasts at a frequency of
94.1 MHz (106 Hz).
What is the wavelength of its carrier wave?
A radio wave is a light wave, c = f
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Radio (Light) Wave
94.1 THE POINT, broadcasts at a frequency of
94.1 MHz (106 Hz).
What is the wavelength of its carrier wave?
A radio wave is a light wave, c = f
= 3 x 108/94.1 x 106
= 3.2 meters
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Doppler EffectChange in frequency of a wave due to relative motion between
source and observer.
A sound wave frequency change is noticed as a change in pitch.
http://pls.atu.edu/physci/physics/people/trantham/applets/doppler/javadoppler.html
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Doppler Effect for Sound• Change in frequency of a wave due to relative motion
between source and observer.
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Line of SightOnly
sensitive
to motion
between
source and
observer
ALONG
the line of
sight.
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Radial Velocity ConventionTrue Velocity
RadialLine of Sight Component
Observer
No Doppler ShiftTransverse motion
Radial Velocity > 0Moving Away
Radial Velocity < 0Moving Toward
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Doppler Effect• Light
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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”.
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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
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Solar Spectrum Solar Radiation Output
The sun looks “yellow”
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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
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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
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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.
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Diffraction of Water Waves
• Diffraction: Waves ability to bend around corners
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Ray Trace
A ray trace is meant to represent the direction of propagation
for a set of parallel waves called a “wave front.”
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Diffraction
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Constructive Interference• Waves combine without any phase difference• When they oscillate together (“in phase”)
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Wave AdditionAmplitude ~ Intensity
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Destructive Interference• Waves combine differing by multiples of 1/2 wavelength• They oscillate “out-of-phase”
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Wave Subtraction
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Two Slit Destructive Interference• Path Length Difference = multiples of 1/2
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Two Slit Interference
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Two Slit Interference• Slits are closer together, path length differences change
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Light or Dark?• Path Length Differences =, Waves arrive in phase• Path Length Differences = 1/2 , Waves arrive out of phase
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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.
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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.
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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.
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Newton’s Rings
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Resolution
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Resolving Power
Telescope diameter = D (cm)
Resolution = (arcminutes)
= 11.6/D
Larger D = smaller angular sizes resolved
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Increasing Resolving Power
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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
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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).
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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.
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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.
What do you want in a telescope?
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Telescope diameter = D (cm)
Resolution = (arcminutes)
= 11.6/D
Larger D = smaller angular sizes resolved
Resolving Power
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The Principle of Reflection
The Angle of Incidence = The Angle of Reflection
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Reflection
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Optical Mirrors
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Reflection
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Telescope Configurations
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Imaging
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Interactive Demonstrations On The WEB
• Simple Geometric Opticshttp://pls.atu.edu/physci/physics/people/trantham/Applets/lenses/javalens.html
• Wave Additionhttp://pls.atu.edu/physci/physics/people/trantham/Applets/waveaddition/waveapplet
.html
• Two-slit Interferencehttp://pls.atu.edu/physci/physics/people/trantham/Applets/youngslit/javayoungslit.html
• Doppler Shifthttp://pls.atu.edu/physci/physics/people/trantham/Applets/Doppler/javadoppler.html
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Refraction
Refraction: The bending of light upon entering a medium with
with a different density.
A light wave will speed up or slow down in response to
a changing medium.
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Refraction is Dispersive
Light of different frequencies is refracted by different amounts
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Beach Party
Pavement
Sand
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Beach Party
Pavement
Sand
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Beach Party
Pavement
Sand
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Beach Party
Pavement
Sand
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Beach Party
Pavement
Sand
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Refraction
Light waves, like people wave fronts can slow down also.
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Bending Because of Velocity
Principle of Refraction:
A light wave will slow down upon entering a denser medium. The refracted light will be bent toward the normal to the surface in this case.
A light wave will speed up upon entering a less dense medium. The refracted light will be bent away from the normal to the surface in this case.
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Refraction
Velocity slows down and is bent toward the normal to the surface, then speeds up upon exiting the glass and is bent away.
Air
Glass
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Index of Refraction
To characterize the change in velocity of a light wave in a
transparence medium, we use the index of refraction (n). It is
the ratio of the speed of light in a vacuum (c) compared to the
speed of light in the medium (v).
n = c / vNote:
since c = 3x108 m/s is the speed limit for light, v for any
other medium is less than c.
Therefore, the index of refraction is always > 1.0
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Indices of Refraction
transparent medium index of refraction
vacuum 1.0000000
air 1.00029
water 1.33
ice 1.31
salt 1.54
Pyrex glass 1.50
quartz 1.46
glycerine 1.47
acrylic 1.70
diamond 1.24
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Light Speed
What is the speed of light waves traveling through acrylic?
nacrylic = c / v
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Light Speed
What is the speed of light waves traveling through acrylic?
V = 3x108/1.7
= 1.76x108 m/s
nacrylic = c / v
1.7 = 3x108/v
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Light Speed
What is the index of refraction for a substance in which the
speed of light is only 2.0x108 m/s?
This substance is, or most resembles….glass.
Glass has an index of refraction of 1.50
nunknown = c / v
= 3x108/2x108
= 1.5
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Refracting and Reflecting Telescopes
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Lenses
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Refraction
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The Beauty of Dispersion and Refraction
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Rainbows
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Chromatic Aberration
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Formation of Images
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Hubble Space Telescope
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Hubble’s Innards
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Repairs and Instrument Upgrades
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New Instruments
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Hubble Images a-Ground based image b-Hubble before repair image
c-Hubble before repair (image processing) image d-Hubble fixed image
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Instrumentation
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CCD Cameras
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Lasers
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Clock Drive
Last but NOT least.
You and telescopes
are on the moving
observatory we call
earth.
A clock drive is
required to counter
earth’s rotation and
provide tracking
for telescopes and
cameras.