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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
Light Gathering Power
Light Gathering Power
Telescope diameter (D)
Light Gathering Power (LGP) is proportional to area.
LGP = p (D/2)2
D = diameter
Light Gathering Power
Light Gathering Power
Telescope diameter (D)
Light Gathering Power (LGP) is proportional to area.
LGP = p (D/2)2
D = diameter
A 16 inch telescope has 4 X the LGP of an 8 inch.
LGP 16 inch = p (16/2)2
LGP 8 inch = p (8/2)2
LGP16/LGP8 = 4
A 16 inch telescope has 2800 X the LGP of the eye.
LGP 16 inch/LGP eye (0.3inch) = (16/0.3)2 = 2844
More Light
Types of Waves
• Compression wave
oscillations are in the
direction of motion
• Transverse Wave
oscillations are transverse
to the direction of
motion
Wave Parameters
Wavelength (l)
Amplitude (A)
Frequency (f)
length
height
repetition
Amplitude:
Size of wave (perpendicular to direction of propagation)
Proportional to Intensity(Sound loudness, Light brightness)
Wavelength:
l 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=lf
Frequency increases
Energy increases
Wavelength decreases
Frequency decreases
Energy decreases
Wavelength increases
An Electromagnetic Wave (a.k.a. Light)
Light travels at a velocity c = l f
(3x108 m/s)
E-M Frequency and Wavelength
Electromagnetic Spectrum
Electromagnetic Spectrum Uses
The Visible Spectrum
COLOR
FREQUENCY (10-14 Hz) WAVELENGTH (nm)
•
•
•
•
•
•
4.0-4.8
4.8-5.1
5.1-5.4
5.4-6.1
6.1-6.7
6.7-7.5
R
O
Y
G
B
V
750-630
630-590
590-560
560-490
490-450
450-400
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 = l f
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 = l f
l = 3 x 108/94.1 x 106
= 3.2 meters
Doppler Effect
Change 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
Doppler Effect for Sound
• Change in frequency of a wave due to relative motion
between source and observer.
Line of Sight
Only
sensitive
to motion
between
source and
observer
ALONG
the line of
sight.
Radial Velocity Convention
True Velocity
Radial = Line of Sight Component
Observer
Radial Velocity > 0
Moving Away
No Doppler Shift
Transverse motion
Radial Velocity < 0
Moving Toward
Doppler Effect
• Light
Doppler Effect for Light Waves
• Change in frequency of a wave due to relative motion
between source and observer.
• c=lf
E = hf = hc/l
speed of light = wavelength x frequency
c = 3 x 108 m/s
energy of a light wave, a photon
of frequency (f) or wavelength (l)
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 Shift
l0 = at rest (laboratory) wavelength
l = measured (observed) wavelength
Dl = l - l0
= difference between measured and laboratory wavelength
vr/c = Dl/l0
vr = (Dl/l0)c
radial velocity
Solar Spectrum
Solar Radiation Output
The sun looks “yellow”
Wien’s Law
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 (l) in nanometers, we find that*
lmax = 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.
Approximate Solar Peak
lmax = 3,000,000/T
Tsurface = 5800 K (solar surface temperature)
lmax = 3,000,000 / 5800 K
= 517 nm
(Yellow-Green)
The atmosphere scatters most of the blue light
making the sun appear more yellow and the sky blue
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 Addition
Amplitude ~ 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 l
Two Slit Interference
Two Slit Interference
• Slits are closer together, path length differences change
Light or Dark?
• Path Length Differences = l, Waves arrive in phase
• Path Length Differences = 1/2 l, Waves arrive out of phase
Light or Dark?
Light from the slits arrives at A. Path Length
from slit 1 is 10,300 nm and from slit 2
is 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 Length
from slit 1 is 10,800 nm and from slit 2
is 11,800 nm for a difference of 1000 nm.
This path length difference is exactly
two wavelengths so the waves from the two slits
arrive at E oscillating in phase. They add constructively
and produce a brighter area.
Light or Dark?
Light from the slits arrives at B. Path Length
from slit 1 is 10,450 nm and from slit 2
is 10,200 nm for a difference of 250 nm.
This path length difference is exactly
1/2 a wavelength so the waves from the two slits
arrive at B oscillating out of phase. They add destructively
and produce a dark area.
Newton’s Rings
Resolution
Resolving Power
Telescope diameter = D (cm)
Resolution = a (arcminutes)
a = 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 X
bigger 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 configuration
has a focal length of 64 inches (16 x 4).
Magnification
Magnification depends on the ratio of the focal lengths
for 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 telescope
with the longest focal length can achieve the greater
magnification.
Magnification Isn’t Everything
Magnifying something spreads the light out into a larger
and 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 by
changing eyepieces.
What do you want in a telescope?
Resolving Power
Telescope diameter = D (cm)
Resolution = a (arcminutes)
a = 11.6/D
Larger D = smaller angular sizes resolved
The Principle of Reflection
The Angle of Incidence = The Angle of Reflection
Reflection
Optical Mirrors
Reflection
Telescope Configurations
Imaging
Interactive Demonstrations On The WEB
• Simple Geometric Optics
http://pls.atu.edu/physci/physics/people/trantham/Applets/lenses/javalens.html
• Wave Addition
http://pls.atu.edu/physci/physics/people/trantham/Applets/waveaddition/waveapplet.htm
l
• Two-slit Interference
http://pls.atu.edu/physci/physics/people/trantham/Applets/youngslit/javayoungslit.html
• Doppler Shift
http://pls.atu.edu/physci/physics/people/trantham/Applets/Doppler/javadoppler.html
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.
Refraction is Dispersive
Light of different frequencies is refracted by different amounts
Beach Party
Pavement
Sand
Beach Party
Pavement
Sand
Beach Party
Pavement
Sand
Beach Party
Pavement
Sand
Beach Party
Pavement
Sand
Refraction
Light waves, like people wave fronts can slow down also.
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.
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
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/v
Note:
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
Indices of Refraction
transparent medium
vacuum
air
water
ice
salt
Pyrex glass
quartz
glycerine
acrylic
diamond
index of refraction
1.0000000
1.00029
1.33
1.31
1.54
1.50
1.46
1.47
1.70
1.24
Light Speed
What is the speed of light waves traveling through acrylic?
nacrylic = c / v
Light Speed
What is the speed of light waves traveling through acrylic?
nacrylic = c / v
1.7 = 3x108/v
V = 3x108/1.7
= 1.76x108 m/s
Light Speed
What is the index of refraction for a substance in which the
speed of light is only 2.0x108 m/s?
nunknown = c / v
= 3x108/2x108
= 1.5
This substance is, or most resembles….glass.
Glass has an index of refraction of 1.50
Refracting and Reflecting Telescopes
Lenses
Refraction
The Beauty of Dispersion and Refraction
Rainbows
Chromatic Aberration
Formation of Images
Hubble Space Telescope
Hubble’s Innards
Repairs and Instrument Upgrades
New Instruments
Hubble Images
a-Ground based image
b-Hubble before repair image
c-Hubble before repair (image processing) image
d-Hubble fixed image
Instrumentation
CCD Cameras
Lasers
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.