tp://www.brightnightgallery.com/ ocation with little light pollution (+ some camera
Jan 21, 2016
http://www.brightnightgallery.com/
From a location with little light pollution (+ some camera tricks)
Lecture 8
ASTR 111 – Section 002
Mid-term evaluations/grades
• Required for Freshman and Sophomores
• Due by October 17th
• I entered mid-term grades for everyone
• Included everything before Quiz 6.
• Used 90% Exam 1 and 10% Quizzes
• If you missed Exam 1, used your Quiz ave.
Outline
• Quiz Discussion– Quiz solutions shown in class are now posted
online
• Light– Suggested reading: Chapter 5.3-5.4 and 5.9
of textbook
• Optics and Telescopes– Suggested reading: Chapter 6.1-6.4
Volume
2 meters
1 m
eter
3
3
4rVolume
Sphere Sphere
Increase r by a factor of 2 and Volume increases by 2x2x2 = 8
The radius changed from 0.5 to 1.0. Compute Volume using radius of 0.5 m and 1.0 m to see if you still get 8x the volume!
Area
2 meters
1 m
eter
2rArea
Disk Disk
Increase r by a factor of 2 and Surface Area increases by 2x2 = 4
The radius changed from 0.5 to 1.0. Compute Area using radius of 0.5 m and 1.0 m to see if you still get 4x the Area!
Doppler Effect
Doppler animations
• http://www.colorado.edu/physics/2000/applets/doppler2.html
• http://www.grc.nasa.gov/WWW/K-12/airplane/sndwave.html
The wavelength of a spectral line is affected by therelative motion between the source and the observer
Doppler Shifts• Red Shift: The object is moving away from the
observer• Blue Shift: The object is moving towards the
observer
/o = v/c
= wavelength shift
o = wavelength if source is not movingv = velocity of sourcec = speed of light
Finish line
cDistance between peaks
How often peakpasses finish line
How fast wave moves to right
Frequency and wavelength are intimately related for a wave.
Blackbody
Blackbody Definition• Does not reflect incoming radiation, only
absorbs• Emits radiation, depending on temperature• Temperature and emitted radiation
intensity follow a special relationship
Photon enters
If hole is very small, what is probability that it exits?
One way of creating a blackbody
• Blackbodies do not always appear black!
–The sun is close to being a “perfect” blackbody
–Blackbodies appear black only if their temperature is very low
Special Relationship
Wavelength
Inte
nsity
For Intensity, think photons/second on a small area
Question
• Why is photon/second similar to energy/second? How are they related?
Energy and electromagnetic radiation Planck’s law relates the
energy of a photon to its frequency or wavelength
E = energy of a photonh = Planck’s constantc = speed of light = wavelength of light
The value of the constant h in this equation, called Planck’s constant, has been shown in laboratory experiments to be
h = 6.625 x 10–34 J s
hc
E
Energy and electromagnetic radiation Planck’s law relates the
energy of a photon to its frequency or wavelength
E = energy of a photonh = Planck’s constantc = speed of light = wavelength of light
The value of the constant h in this equation, called Planck’s constant, has been shown in laboratory experiments to be
h = 6.625 x 10–34 J s
hc
E
hvE
vc
h
E
Watt? Energy Flux?
100 Watt light bulb
2000 Calories (unit of energy) over 24 hours is about 100 Watts
Watt? Energy Flux?
• A Watt is a unit of Energy [Joule] per time [second]. Joule is related to Calorie, which is a unit of energy we use for humans.
• For example, your electricity bill tells you how many kilowatt-hours you used. If you use 1 kilowatt for 100 hours then you used 100 kilowatt-hours
Watt? Energy Flux?
We also use Watts/(m^2). If you have a 1 meter square solar panel and it is being hit by 1 blue photon per second, you can compute the energy flow into the solar panel. Remember that a Watt is a Joule/second, and each photon has a certain amount of energy in Joules that is given by Plank’s law.
1 meter x 1 meter squareBlue photon
Flux
Flux is a measure of how much “stuff” crosses a small patch in a given amount of time. Can have flux of green photons, red photons, etc.
Blackbodies and Astronomy
Blackbody Laws• Stefan-Boltzmann Law – relates
energy output of a blackbody to its temperature
• Wein’s law – relates peak wavelength output by a blackbody to its temperature
Wien’s law and the Stefan-Boltzmann law are useful tools for
analyzing glowing objects like stars
• A blackbody is a hypothetical object that is a perfect absorber of electromagnetic radiation at all wavelengths
• Stars closely approximate the behavior of blackbodies, as do other hot, dense objects
• The intensities of radiation emitted at various wavelengths by a blackbody at a given temperature are shown by a blackbody curve
Special Relationship
Wavelength
Ene
rgy
Flu
x In
tens
ity For Intensity, think photons/second on a small area
Stefan-Boltzmann Law
• A blackbody radiates electromagnetic waves with a total energy flux F directly proportional to the fourth power of the Kelvin temperature T of the object:
4~ TF
Special Relationship
Wavelength
Stefan-Boltzmann Law tells us that if we add up the energy flux from all wavelengths, then the total energy Flux
4~ TF
Ene
rgy
Flu
x In
tens
ity
Think of total flux as related to area under this curve*. Add up contribution from each wavelength
* But not identical, so area does not scale by T4 . The area under a similar-looking curve does scale with T4
Special Relationship
Wavelengthmax
Wien’s law tells us that max depends on temperature
Max intensity at max
T
1~max
Ene
rgy
Flu
x In
tens
ity
Special Relationship
Wavelength
Sketch this curve for larger and smaller T
Ene
rgy
Flu
x In
tens
ity
T
1~max
4~ TF
Overall amplitude increases with Temperature
At high wavelengths, intensity goes to zero
As wavelength goes to zero, intensity goes to zero
Wavelength of peak decreases as temperature increases
Color and Temperature
What would this object look like at these three temperatures?
• Why does it glow white before blue?
• Can this figure help us explain?
• Can this figure help us explain?
Near this temperature, this special combination of intensities is what we call white. Also, the realcurve is a little flatter near the peak
The Sun does not emit radiation with intensities that exactly follow the blackbody curve
• http://www.shodor.org/refdesk/Resources/Models/BlackbodyRadiation/applet.html
http://casa.colorado.edu/~ajsh/colour/Tspectrum.html
Why do we associate blue with cold and red with hot?
• Lips turn blue when cold
• Ice takes on a blue-ish tint
• Face turns red when hot
• Red is the first thing you see when something is heated (usually don’t see much blue)
AB
C
Ene
rgy
Flu
x
1
2
3
4
5
0
One curve is ideal blackbody, one is measured above Earth’s atmosphere, one is measured at Earth’s surface.
• Which curve represents an ideal blackbody?– Curve A– Curve B– Curve C
• Which curve represents an ideal blackbody?– Curve A– Curve B– Curve C
• If the object in Figure 1 were increased in temperature, what would happen to curves A, B, and C?
• If the object in Figure 1 were increased in temperature, what would happen to curves A, B, and C?
All would increase in amplitude. Peak would shift to left. What would happen to the dips in C?
• Curve C is more jagged. The locations where the curve C is small correspond to– Spectral lines of a blackbody– Spectral lines of atmospheric molecules– Instrumentation error– Diffraction lines– Spectral lines of the lens used to the light into
colors
• Curve C is more jagged. The locations where the curve C is small correspond to– Spectral lines of a blackbody– Spectral lines of atmospheric
molecules– Instrumentation error– Diffraction lines– Spectral lines of the lens used
to the light into colors
Cloud of gas is like Earth’s atmosphere
• What is the intensity of curve B at 550 nm?– Impossible to tell; 550 nm is not shown in this
figure– Nearest 4– Nearest 3– Nearest 1– Nearest 0.5
• What is the intensity of curve B at 550 nm?– Impossible to tell; 550 nm is not shown in this
figure– Nearest 4– Nearest 3– Nearest 1– Nearest 0.5
3 ways to do it
1 m = 10-6 m so 0.55 m = 0.55x10-6 m = 5.5x10-7 m1 nm = 10-9 m so 550 nm = 550x10-9 = 5.5x10-7 m
Or use the method used for converting units
nm nm xnm xnm 10
10x
m10
1nmx
m
m10 x m0.55
9
6
9
6
5501055.01055.055.0 396
μ
nm mxm x100.55 m0.55 -6 55010550 9 or
• Venus has no atmosphere. If you measure the spectrum from its surface, – Curves B and C would not change– Curve C would look more like A– Curve C would look more like B– Curve B would look more like A– Curve B would look more like C
• Venus has no atmosphere. If you measure the spectrum from its surface, – Curves B and C would not change– Curve C would look more like A– Curve C would look more like B– Curve B would look more like A– Curve B would look more like C
• White light is composed of– Equal intensities of all colors of the rainbow– Unequal intensities of all colors of the rainbow– Equal number of photons of all colors of the
rainbow– Unequal number of photons of all colors of the
rainbow– Equal numbers of red, green, and blue
photons
• White light is composed of– Equal intensities of all colors of the rainbow– Unequal intensities of all colors of the rainbow– Equal number of photons of all colors of the
rainbow– Unequal number of photons of all colors of the
rainbow– Equal numbers of red, green, and blue
photons
• Does a blackbody have color?– Yes, and they all appear the color of the sun– No, you cannot see a blackbody– Yes, but its depends on its temperature– Maybe, it depends on if it is an ideal
blackbody
• Does a blackbody have color?– Yes, and they all appear the color of the sun– No, you cannot see a blackbody– Yes, but its depends on its temperature– Maybe, it depends on if it is an ideal
blackbody
• Why is the best reason for putting a telescope in orbit? – Closer to stars– Better view of celestial sphere– The speed of light is higher in space– Less atmospheric interference– Cost
• Why is the best reason for putting a telescope in orbit? – Closer to stars– Better view of celestial sphere– The speed of light is higher in space– Less atmospheric interference– Cost
Optics and Telescopes• Questions about blackbody curves
Key Words
• refraction/reflection
• converging/diverging lens
• focal point
• angular resolution
• magnification
• chromatic aberration
Key Questions
• Why are there so many telescopes in Hawaii?
• Why is our best most famous telescope orbiting Earth and not in Hawaii?
• What is the difference between optical and digital magnification (zoom)?
• How and when (but not why) does light (and other forms of electromagnetic radiation) bend?
• How does a telescope work?• What is the difference between magnification
and light-gathering power?
side note: What is the difference between optical and digital zoom?
side note: What is the difference between optical and digital zoom?
T
Same amount of information if I just expand the original
Practical note: What is the difference between optical and digital zoom?
T
Much more information (detail)
• You can create a digital zoom effect by taking a digital picture and expanding it (with photoshop, etc.)
• You can’t squeeze out more detail from the image (that is, increase the optical resolution), contrary to what you see on TV
Therefore
• How much larger is a raw image of 1600x1600 pixels than one with 800x800 pixels?
• 1600x1600 = 2,560,000 versus
• 800x800 = 640,0004x
1600
800
Can explain lots about telescopes and other
devices with only three optics principles
Principle 1
• Light rays from distant object are nearly parallel
Principle 1
• Light rays from distant object are nearly parallel
Collector
Principle 2
• Light reflects off a flat mirror in the same way a basket ball would bounce on the floor (angle of incidence, i = angle of reflection, r)
Principle 3 prep
What happens, a, b, or c?
• As a beam of light passes from one transparent medium into another—say, from air into glass, or from glass back into air—the direction of the light can change
• This phenomenon, called refraction, is caused by the change in the speed of light
Axle and wheel from toy car or wagon
Sidewalk
Grass
What happens, a, b, or c?
• As a beam of light passes from one transparent medium into another—say, from air into glass, or from glass back into air—the direction of the light can change
• This phenomenon, called refraction, is caused by the change in the speed of light
Axle and wheel from toy car or wagon
Sidewalk
Grass
Principle 3
• Light changes direction when it moves from one media to another (refraction). Use wheel analogy to remember which direction normal
90o
Low index (e.g., air)
Higher index (e.g. water)
Principle 3a
• Light changes direction when it moves from one media to another (refraction). Use wheel analogy to remember which direction normal
90o
Low index (e.g., air)
Higher index (e.g. water)
Principle 3b
• Same principle applies when going in opposite direction
normal
90o
Low index (e.g., air)
Higher index (e.g. water)
Principle 3c
• At interface light refracts and reflects (you can see your reflection
in a lake and someone in lake
can see you)
Low index (e.g., air)
Higher index (e.g. water)
These angles are equal
i r
What happens to each beam?
A
B
C
A
B
C
A
B
C
What happens?
?
?
?
zoom box
zoom box contents nearly flat whenzoomed inzoom box contents
zoom box contents
norm
al
90o
zoom box contents
To figure out path, draw normal and un-bent path.
zoom box contents nearly flat whenzoomed in
norm
al
90o
zoom box contents
Bends toward the normal.
What happens?
?
?
?zoom box
zoom box contents
zoom box contents
90o
zoom box contents
90o
The Lines Converge
Input parallel lines converge to focal point
F
F
What happens to the beams here?
And parallel lines go out when source at focal point
F
But you said different colors bend different amount!?
But you said different colors bend different amount!?
This is chromatic aberration
How I remember red bends less
How my optometrist remembers
Red light bends only a little
Red light has little energy (compared to blue)
But then you need to remember that red has big wavelength …
What happens?
?
?
Bend away fromthe normal
Now we can explain
… rainbow color ordering
Observer sees red higher in sky than blue
Sunlight
Sunlight diffractionreflection
refraction
Sunlight
Waterdroplets
Now we can explain
… how an eye works
… how an eye works
Retina
Info from distant object is concentrated on small area on retina
Eye lens
… how an eye works
RetinaEye lens
Light from Sun
Light from a distant lighthouse
Sunlight lower than lighthouse light
… how an eye works
RetinaEye lens
Light from a distant lighthouseSun appears lower than lighthouse light
Now we can explain
… how telescopes work
• Magnification is ratio of how big object looks to naked eye (angular diameter) to how big it looks through telescope
Telescope principles
½ o
10 o
Magnification is 10/0.5 = 20x
• Although telescopes magnify, their primary purpose is to gather light
Telescope principles
Collector
• How much more energy does a 1 cm radius circular collector absorb than a 4 cm radius collector?– Same– 2x– 4x– 16x– Need more info
Question
Collector
• How much more energy does a 1 cm radius circular collector absorb than a 4 cm radius collector?– Same– 2x– 4x– 16x– Need more info
Question
Area of circle is proportional to r2 A1 is proportional to (1 cm)2 = 1 cm2
A2 is proportional to (4 cm)2 = 16 cm2
What if I had asked what happens if the diameter changes from 1 cm to 4 cm?
Reflecting telescope
• Previously I described a refracting telescope. The principles of reflection can be used to build a telescope too.
Problem: head blocks light!
Solutions