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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