Transcript Lecture 7

Lecture 8
ASTR 111 – Section 002
Outline
• Quiz Discussion
• Light
– Suggested reading: Chapter 5.3-5.4 and 5.9
of textbook
• Optics and Telescopes
– Suggested reading: Chapter 6.1-6.4
The wavelength of a spectral line is affected by the
relative 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
Dl/lo = v/c
Dl = wavelength shift
lo = wavelength if source is not moving
v = velocity of source
c = speed of light
Blackbody Definition
• Does not reflect incoming radiation, only
absorbs
• Emits radiation, depending on temperature
• Temperature and emitted radiation intensity
follow a special relationship
One way of
creating a
blackbody
Photon enters
If hole is very small,
what is probability that
it exits?
• Blackbodies do not always appear
black!
–The sun is close to being a “perfect”
blackbody
–Blackbodies appear black only if
their temperature very low
Intensity
Special Relationship
For Intensity, think
photons/second on a
small area
Wavelength
Question
• Why is photon/second similar to
energy/second? How are they related?
Watt? Energy Flux?
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 StefanBoltzmann 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
Energy Flux Intensity
Special Relationship
For Intensity, think
photons/second on a
small area
Wavelength
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:
F ~T
4
Special Relationship
Energy Flux Intensity
Stefan-Boltzmann
Law tells us that if we
add up the energy
from all wavelengths,
then the total energy
Flux
F~T
Wavelength
4
Energy Flux Intensity
Special Relationship
Wien’s law tells us that
lmax depends on
temperature
Max intensity at lmax
lmax Wavelength
lmax
1
~
T
Energy Flux Intensity
Special Relationship
Sketch this curve for larger and
smaller T
Wavelength
Wavelength of peak
decreases as
temperature
increases
At high wavelengths,
intensity goes to zero
Overall amplitude
increases with
Temperature
As wavelength
goes to zero,
intensity goes to
zero
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 real
curve is a little flatter
near the peak
The Sun does not emit
radiation with intensities that
exactly follow the blackbody
curve
• If “white” was actually defined by the ideal
blackbody curve, we could add a little
green to white
So, what color is the sun in space?
Solid green
square
So, what color is the sun in space?
Add a little
green to
white
background
by making
solid green
square
mostly
transparent
• If “white” was actually defined by the ideal
blackbody curve, this would (sort of) make
sense.
• What we call white is actually not the ideal
blackbody curve. See
http://casa.colorado.edu/~ajsh/colour/Tspectrum.html
So, what color is the sun in space?
Left
side is
white
Right side is
(should be) a
little “pinker”
• http://casa.colorado.edu/~ajsh/colour/Tspectrum.html
If blue light has higher energy,
and energy is proportional to
temperature, why are my cold
spots blue?
Energy Flux
5
4
3
2
1
0
A
B
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?
• 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
• What is the intensity of curve B at 550
nm?
– Impossible to tell; 550 nm is not shown in this
figure
– Nearest 0.2
– Nearest 0.1
– Nearest 0.05
– Nearest 0.0
• 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
• 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
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?
T
side note: What is the difference between
optical and digital zoom?
Same amount of information
T
Practical note: What is the difference
between optical and digital zoom?
Much more information (detail)
T
Therefore
• 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
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?
Axle and wheel from
toy car or wagon
Sidewalk
Grass
• 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
Principle 3
• Light changes direction when it moves
from one media to another (refraction).
Use wheel analogy to remember which
direction
normal
Low index (e.g., air)
Higher index (e.g. water)
90o
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 diffracts and reflects
(you can see your reflection
in a lake and someone in lake
can see you)
These angles are equal
i
Low index (e.g., air)
Higher index (e.g. water)
r
What happens to each beam?
A
B
C
A
B
C
A
B
C
What happens?
zoom box
?
?
?
To figure
out path,
draw
normal
and unbent path.
zoom
zoombox
boxcontents
contents
nearly flat when
zoomed in
What happens?
?
?
?
zoom box
zoom box contents
What
happens
to the
beams
here?
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)
What happens?
?
?
Now we can explain
… rainbow color ordering
Sunlight
diffraction
reflection
Water droplet
diffraction
Sunlight
Observer sees red
higher in sky than blue
Now we can explain
… how an eye works
… how an eye works
Eye lens
Retina
Info from distant
object is concentrated
… how an eye works
Light from Sun
Light from a distant lighthouse
Eye lens
Retina
… how an eye works
m a distant lighthouse
ens
Retina
Sun appears lower
than lighthouse light
Now we can explain
… how telescopes work
Telescope principles
• Magnification is ratio of how big object
looks to naked eye (angular diameter) to
how big it looks through telescope
½o
10 o
Magnification is 10/0.5 = 20x
Telescope principles
• Although
telescopes
magnify, their
primary
purpose is to
gather light
Collector
Question
• 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
Collector
Reflecting telescope
• Previously I described a refracting
telescope. The principles of reflection
can be used to build a telescope too.
Solutions