Light
What is light?
1. How does light “behave”?
2. What produces light?
3. What type of light is emitted?
4. What information do you get from
that light?
Methods in Astronomy
• Photometry
– Measure total amount of light within a certain filter – Study distribution and extent of object
• Spectroscopy
– Slit up light into its wavelength components – Study particular absorption and emission lines
Need to understand astrophysical radiation processes
Understand some of the relevant physics
Be able to interpret the measured light information
Today’s Overview and Concepts
1) What is Light? Properties?
2) Analyze Black Body Radiation and understand correlations between:
– color
– dominant wavelength – surface temperature – flux
– luminosity – magnitude – radius
2) How can you determine those properties of stars?
3) The Hertzsprung-Russel Diagram
Electromagnetic Radiation
Newton: Beam of light separated into rainbow colors
The spectrum has a much wider range; ranging from Gamma to Radio Waves
The "visual" part is only a small fraction of the entire
electromagnetic spectrum.
Visual: 4000 to 7000 Å (1 Å = 10-10 m)
This is also in your toolkit.
Infra-Red Radiation
night animals
How do Waves behave?
Ocean Waves Interference Pattern
Does light also show an Interference Pattern??
How do we know that light is
wave?
“It behaves like waves”
What happens when two waves are
interfering?
Demo of Joung’s Double Slit Experiment
Light – waves in what??
• Medium? ---- Ether?
• Light is electromagnetic radiation. What is that?
• It is a self-perpetuation wave, where the electric field gives rise to a magnetic field which in turn gives rise to an electric field…
• What is propagating?
• Space around an electric charge may be characterized by an
electric field, E, which manifests itself as a force on a test charge placed nearby. If an electromagnetic wave encounters such a test charge, that charge will oscillate. Maxwell’s equations say that a time varying electric field produced a perpendicular time-varying magnetic field B. This disturbance in B then gives rise to a time varying E, which in turn… this therefore is a self-propagating wave of electric and magnetic fields in a vacuum.
Waves
Wavelength is the distance from crest to crest
Frequency is the number of crests passing per second
Velocity of light is 300,000 km/sec
ν
λ ⋅
=
c
How do we know that light is wave?
“It behaves like waves”
= λ
πx h
h o 2
sin
Light Waves
Light is electromagnetic radiation. It is a self-perpetuation disturbance, where the electric field gives rise to a magnetic field which in turn gives rise to an electric field…
( )
( )
−
=
−
=
ct y
B B
ct x
E E
o o
λπ λπ sin 2
sin 2
But…..
• How do you get shadows with waves???
• How do you get photos?
• (do waves make photos?)
• Is light a particle?
The
Photoelectric
Effect
Light is a
Particle
called
"Photon"
The Photoelectric Effect
In 1905 Einstein made 4 main discoveries:
• Brownian motion
• Photo-electric effect
• Special Relativity
• E=mc
2He got the Nobel prize for the Photo-Electric Effect.
Einstein showed that:
• light is a particle, called "Photon"
• light is quantized (more later)
• the energy of a photon is related to the frequency of light
ν
h
E =
Energy
frequency
Frequency of light = ν Wavelength of light = λ Energy of light = E
Planck’s constant = h Speed of light = c
ν h λ c
h
E = =
More Energy
Shorter Wavelength
Faster rate of waves passing
ν
λ ⋅
=
c
Relationship between the velocity of light, its wavelength and its frequency is:
Paradox?
• Can Proof that Light is a Wave
• Can Proof that Light is a Particle
Which is correct?
A Particle with a Wavelength???
(What type of animal is that?)
Paradox?
How, then, do we know what is really true in Life?
How, then, do we know what is really true in Life?
• The experiment shows that light has a wave character
• The experiment shows that light has a particle character Which statement is correct?
• We determine reality by experimenting.
• The experiment itself determines reality.
The experiments give contradictory results
Energy and Intensity of Light
ν h λ c
h
E = =
What produces light?
• hot bodies Today: Experiment & Theory
• hot gases Today: Experiment only
• shocks and friction
• electric fields
• magnetic fields
• chemical reactions
• nuclear reactions
The Light Bulb
Radiation from a dense body, i.e., from the Iron Wire
inside the bulb
To be compared later to the and
What is a Black Body?
“A Perfect Absorber”
– no Reflection
“Perfect Emitter”
Def: A black body is an object that absorbs
ALL
radiationthat is incident upon it.
this makes it “black”
The Spectrum of a Light bulb
Less light More light Red light disappears
Blue light disappears Less light
The Black Body Spectrum
Less light Most light
Blue light disappears Less light
Red light disappears
Black Bodies emit Light with a characteristic Spectrum
This shape is meant by that
The Black Body Spectrum
Black Bodies emit Light with a characteristic Spectrum
Empirical formula
−
=
−
=
1 1 2
1 1 2
2 3 5
2
kT h
kT hc
c e I h
e I hc
ν ν
λ λ
ν λ
The Light-bulb experiment
Decrease electricity supply
total amount of light decreases
color gets redder (relatively less blue light)
temperature gets colder
Have a relationship between:
Color, Temperature & Brightness
1) Hotter Bodies emit more light
2) Hotter bodies emit bluer light
Temp
4∝ Flux
This is Stefan-Bolzman’s law
Temp ∝ 1/wavelength
This is Wien’s law
Experimental Findings for Black Body
T
0029
.
0
max
=
λ
T
4F = σ
Hotter bodies emit bluer light
Temp ∝ 1/wavelength
[Inverse relationship]
This is Wien’s law
Graphical Illustration
T
0029
.
0
max
=
λ
Total Flux
Total energy density radiated at all wavelengths
Area under the curve
Integrate over all wavelengths
λ
∫
∞λ
=
0
)
( d
F
Flux
4
4
0
1 5 4
0
1 5 2
3 4
4
0
5 2
0 5 2 0
5 2
1 15 1
2
1 2
1 2
1 1 2
T F
e x Tables dx from
Integral T
e x
dx c
h k
hc x kT
Substitute hc
kT hc e
kT
hc d kT hc
hc by kT Multiply e
hc d d
F F
Integrate e
F hc
x x
kT hc
kT hc kT
hc
σ
π λ
λ
λ λ λ λ
λ
λ λ λ
λ λ
=
⇒
=
−
−
=
=
−
=
−
=
=
−
=
∫
∫
∫
∫
∫
∞
∞
∞
∞
∞
Stars
have
colors
HST image of Quintuplet Cluster
- almost real colors
Stars are “roughly” black bodies
Do not see this light
Bolometric correction
λ
∫ λ
=
A
A
V
F d
L
7000
4000
)
(
Since know the shape of the a Black Body Curve know how much light missing
Apply so-called bolometric correction
V A
Bol A m
d F
d F
m
L m L
m
+
=
=
−
∫
∫
∞ 0 7000
4000 2 1 1
2
) (
) ( log
5 . 2
log 5 . 2
λ λ
λ λ
Determining the Temperature
Method 1: “By Eye”
Figure out the colors;
Get λ
max;
Use Wien’s law to get temperature.
How do you determine the dominant wavelength?
Betelgeuse: color red λmax Rigel: color blue λmax
Rigel: λmax is around
4000Å – this is in the blue part of the spectrum
Betelgeuse: λmax is around 7000Å – this is in the red part of the spectrum.
Which star is hotter? By how much?
Betelgeuse: color red λmax = 7000Å Rigel: color blueish λmax = 4000Å
Recall Wien's law:
But watch out for UNITS
Temperature has to be in Kelvin
Wavelength in meters (e.g. 7000Å = 7000 x 10-10 m = 7 x 10 -7 m)
max
0029
.
0
= λ
T
Temperature scale
In Astronomy we always use the Kelvin Scale.
Why? Absolute Zero corresponds to Zero Energy Absolute Zero
Recall Wien's law:
First convert units:
Betelgeuse: color red λmax = 7000Å = 7 x 10-7m Rigel: color blueish λmax = 4000Å = 4 x 10-7m
Betelgeuse
Rigel
Betelgeuse is 4/7 times as hot as Rigel
max
0029 .
0
= λ T
( ) m K
T
B
B 4000
10 7
0029 .
0 0029
. 0
7 max
× ≈
=
= −
λ
( ) m K
T
R
R 7000
10 4
0029 .
0 0029
. 0
7 max
× ≈
=
= −
λ
( ) ( )
( )( ) 70004000 74
0029 .
0
0029 .
0
max max
max
max = = =
= o
o
B R
R B R
B
A A T
T
λ λ λ
Calculation easier in ratios λ
Temperature?
About 37o Celsius.
37 + 273 = 310 Kelvin
K m T
6
max 9.4 10
310 0029 .
0 0029
.
0 −
×
=
= λ =
Quiz Question 1: Hot Human Bodies
Humans emit at ~ 9µm Humans emit light at
INFRA RED wavelengths
meters micro
meters 4
. 9
10 4 . 9
max
6 max
=
×
= −
λ λ
Temperature?
About 0o Celsius = 273 Kelvin
K m T
6
max 10.6 10
273 0029 .
0 0029
.
0 −
×
=
= λ =
Quiz Question 2: Ice & Cold Dust
Dust has temp of ~30-300 K And thus emits at ~ 10-100µm
Which is at near to far IR wavelengths Ice emit light at “near” INFRA
RED wavelengths
meters micro
meters 4
. 10
10 4 . 10
max
6 max
=
×
= −
λ λ
Other objects
Filters & Experiments with Pictures
(Photometry Lab)
Determining the "color index“ – Quantitative Method
a) Measure the magnitudes using filters, e.g., B & V
b) Determine the color index (B-V)
c) Then use Wien’s law to get Temperature
First Look at the Spectra of Stars
Then look at the entire Electromagnetic Spectrum in your Toolkit
The Visual Part of the Spectrum is marked in the picture below Spectrum (a): We see relatively more red light
Spectrum (c): We see relatively more blue light Correlating Colors and Dominant Wavelengths
Spectrum (a): Dominant Wavelength is at Long Wavelengths – here in the IR Spectrum (c): Dominant Wavelength is at Short Wavelengths – here in the UV
Red yellow blue
λmax in IR λmax in Visual λmax in UV
How do your "measure" colors?
Use filters, take black and white pictures (not color), then
measure magnitude in each filter
HST image of Quintuplet Cluster
-- almost real colors
Horsehead Nebula
Nebulosity in Sagittarius
How do your "measure" colors?
Use filters & take (black and white ) pictures, then measure magnitude in each filter;
Then calculate the Difference in Magnitude in two Filter Bands.
Blue star:
• much light in blue filter
• relatively less light in red filter
Red star:
• less red light than blue star
• but relatively more light in red filter than blue star
Color
=
−
∫ ∫
λ λ λ
λ λ λ
d R
Flux
d R
V Flux B
B V
) ( ) (
) ( ) log (
5 . 2
V T
B 8540
865 .
0 +
−
=
−
Color index = B-V = Magnitude
in B– Magnitude
in VEmpirical relationship for solar like stars:
The Hertzsprung Russel Diagram
• For all stars can determine their absolute magnitudes and color
• Make a plot of absolute and color
MV
B-V Luminosity
Temperature
The Hertzsprung Russel Diagram
• For all stars can determine their Luminosities and their Temperatures
• Make a plot of Stellar Luminosity and Temperature
Luminosity MV
Temperature or B-V
The Hertzsprung
Russel Diagram
(HRD)
Plot of Luminosity and Temperature
Most stars are so-called
“main-sequence” stars
Color and Temperature
Wien’s law
T
0029
.
0
max
=
λ
Color is the same Temperature is the same
Temperature and Flux
Temperature is the same Flux is the same
Stefan-Bolzman’s law Flux = σ Temp
4If both stars have the same color…
Luminosity and Size
BIG Star
The Flux – the amount of light
passing through the green square is the SAME.
Which star is more luminous?
The larger or smaller?
SMALL Star
Which star is more
luminous?
Recall Definitions
Luminosity:
Luminosity is an intrinsic quantity of the star. It is the energy per second
emitted from the entire star.
Units: Watts (or Joules/sec)
Flux:
The energy per second passing through a certain area. It is the energy per
second per square meter.
Units: Watts/m2 (or Joules/sec/m2 )
This quantity is the flux
Luminosity and Size
The Luminosity of a star is the
total amount of light emitted
from its surface.
Thus the luminosity is obtained
by multiplying the flux by the
area of the star.
Area
Flux
Luminosity = ×
Luminosity
4
Area
Flux
Luminosity = × ⇒ L = F ⋅
π
R2T
4F = σ
4 2
2
4
4 R F R T
L = π ⋅ = π ⋅ σ
4
4 R
2T
L = πσ
The Luminosity of a star depends on its Radius and its Temperature Recall Stefan-Bolzman's law:
Insert the value for Flux into the above equation:
Recall:
redder stars are cooler
Wien’s lawcooler stars emit less flux
Stephan Bolzman’s lawget more light from bigger stars
For Stars: Have a relationship between:
Temperature, Luminosity, & Size
Determining the Radii of Stars
Can figure out radius of a star if know luminosity and temperature.
4
4 R2T L = πσ
2 4 2
4 2
4 2
4 2 4
2 4 2
4 4
⋅
=
⋅
=
=
=
=
T T L
L R
R
or
T T R
R L
L
T T R
R T
R T R T
R T R L
L
sun sun
sun
sun sun
sun
sun sun
sun sun sun
sun
sun πσ
πσ
For easier calculations you can use these
Aside: In general always compare the stars. Stick to SOLAR units. Why? The sun is a meaningful star for us -- so compare other stars to the sun…
What about the size of a Star?
Can you use the small angle formula?
206,265"
angle distance
star of
size = ⋅
Distance to the star
size of star Angle
If the angle is measured in arc seconds
Example: Betelgeuse
Betelgeuse is 100,000 times as luminous as the sun.
Betelgeuse’s color is red, the suns, color is yellow.
Red color Temp ~ 3000K
Yellow colors Temp ~ 6000K
Could put the values of the luminosities and temperatures into these formulae:
But there is an easier method…. Again use ratios….
4
4 Sun2 Sun
Sun R T
L = πσ LBetel = 4πσ RBetel2TBetel4
Sun 5
Betelgeuse 10 L
L = ×
Example: Calculation
4
4 Sun2 Sun
Sun R T
L = πσ
4
4 Betel2 Betel
Betel R T
L = πσ
Procedure (on right):
Write down both formulae;
Add two lines to turn this into ratios;
Cancel constants.
4 2
⋅
=
sun Betel sun
Betel sun
Betel
T T R
R L
L
K K 6000 3000
105
2 4 5
6000
10 3000
⋅
=
K K R
R
sun Betel
sun Betel
sun Betel
sun Betel
sun Betel
R R
R R
R R
R R
1300
1300 16
10
16 10
16 10 1
5 5 2
2 5
=
=
⋅
=
⋅
=
⋅
= 12 161
4
=
=
So Betelgeuse is 1300 times bigger than the sun.
How big is that? The Earth – Sun distance is 1AU 1300Rsun ~ 6AU
Betelgeuse is 6 times as big as the Earth – Sun distance.
Betelgeuse is a Red Supergiant!
The Hertzsprung
Russel Diagram
(HRD)
• Betelgeuse has a red color (T~3000K)
and is very luminous LB=105Lsun.
This puts Betelgeuse into the top right in the HRD
Betelgeuse is much bigger than the sun
Big stars are in the top RH Small stars are in the
bottom LH
Radius increases
from bottom left
to top right
BIG
SMALL
Mass increases
along main
sequence from
bottom right to
top left
Frequencies of Stars
• Most are Main
Sequence Stars
• Smaller Main
sequence stars are
much more
numerous than
luminous m.s. stars
Next: What are Spectral Types?
1) Hotter Bodies emit more light
Temp
4∝ Flux
This is Stefan-Bolzman’s law
2) Hotter bodies emit bluer light
Temp ∝ 1/wavelength
This is Wien’s law
3) Luminosity of a star is light emitted from its surface.
Lum ∝ Temp
4and R
2Summary of Rules:
T
0029
.
0
max
=
λ
T
4F = σ
4
