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 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

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 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?

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 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 from all wavelengths, then the total energy Flux

4~ TF

Ene

rgy

Flu

x In

tens

ity

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

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

• 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 makingsolid 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?

• http://casa.colorado.edu/~ajsh/colour/Tspectrum.html

Right side is (should be) alittle “pinker”

Left side is white

If blue light has higher energy, and energy is proportional to temperature, why are my cold spots blue?

AB

C

Ene

rgy

Flu

x

1

2

3

4

5

0

• 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?

T

Same amount of information

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

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

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 diffracts 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 in

norm

al

90o

zoom box contents

To figure out path, draw normal and un-bent path.

What happens?

?

?

?zoom box

zoom box contents

F

What happens to the beams here?

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

Observer sees red higher in sky than blue

Sunlight

Sunlight diffractionreflection

diffraction

Water droplet

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

Reflecting telescope

• Previously I described a refracting telescope. The principles of reflection can be used to build a telescope too.

Solutions