Download How is Light Made?

Review: Electromagnetic (EM) Radiation
• EM radiation: regularly varying electric & magnetic fields
– can transport energy over vast distances.
How is Light Made?
• “Wave-Particle Duality” of EM radiation:
– Can be considered as EITHER particles (photons) or as waves
• Depends on how it is measured
• Includes all of “classes” of light
Deducing Temperatures and
Luminosities of Stars
(and other objects…
objects…)
– ONLY distinction between X-rays and radio waves is wavelength λ
Increasing energy
G
10-15 m
)
ys
Ra
UV
t(
10-9 m
10-6 m
a
m
am
ht (IR)
ig
s iole le L red
y
v
a
b
Ra ra
si Infr
X Ult
Vi
10-4 m
M
w
ro
ic
es
av
o
di
Ra
10-2 m
w
es
av
103 m
Increasing wavelength
Electromagnetic Fields
Sinusoidal Fields
• BOTH the electric field E and the magnetic
field B have “sinusoidal” shape
Direction
of “Travel”
Wavelength λ
Frequency ν
λ
time
z Distance between two identical points on wave
1 unit of time
(e.g., 1 second)
z number of wave cycles per unit time
registered at given point in space
z inversely proportional to wavelength
1
Wavelength and Frequency
λ = v/ν = c /ν (in vacuum)
z Proportional to Velocity v
z Inversely proportional to temporal frequency ν
z Example:
z AM radio wave at ν = 1000 kHz = 106 Hz
z λ = c/ν = 3 × 108 m/s / 106 Hz = 300 m
z λ for AM radio is long because frequency is small
Light as a Particle: Photons
z Photons: little “packets” of energy
z Energy is proportional to frequency
“Units”
Units” of Frequency
⎡ meters ⎤
c⎢
⎣ second ⎥⎦ = ν ⎡ cycles ⎤
⎢⎣ second ⎥⎦
⎡ meters ⎤
λ⎢
⎥
⎣ cycle ⎦
⎡ cycle ⎤
= 1 "Hertz" (Hz)
1⎢
⎣ second ⎥⎦
Generating Light
• Light is generated by converting one class
of energy to electromagnetic energy
– Heat
– Explosions
E = hν
Energy = (Planck’s constant) × (frequency of photon)
h ≈ 6.625 × 10-34 Joule-seconds = 6.625 × 10-27 Erg-seconds
Converting Heat to Light
The Planck Function
• Every opaque object (a human, a planet, a star)
radiates a characteristic spectrum of EM radiation
– Spectrum: Distribution of intensity as function of wavelength
– Distribution depends only on object’s temperature T
Planck’
Planck’s Radiation Law
• Wavelength of MAXIMUM emission λmax
is characteristic of temperature T
• Wavelength λmax ↓ as T ↑
• Blackbody radiation
ultraviolet
visible
infrared
radio
As T ↑, λmax ↓
Intensity
(W/m2)
0.1
1.0
10
100
1000
10000
λmax
http://scienceworld.wolfram.com/physics/PlanckLaw.html
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Temperature dependence
of blackbody radiation
Sidebar: The Actual Equation
B (T ) =
•
2hc 2
λ
1
5
e
hc
λ kT
As object’s temperature T increases:
1.
−1
2.
Wavelength of maximum of blackbody spectrum (Planck
function) becomes shorter (photons have higher energies)
Each unit surface area of object emits more energy (more
photons) at all wavelengths
• Derived in Solid State Physics
• Complicated!!!! (and you don’t need to know it!)
h = Planck’s constant = 6.63 ×10-34 Joule - seconds
k = Boltzmann’s constant = 1.38 ×10-23 Joules per Kelvin
c = velocity of light = 3 ×10+8 meter - second-1
Shape of Planck Curve
Planck Curve for T = 70007000-K
http://csep10.phys.utk.edu/guidry/java/planck/planck.html
http://csep10.phys.utk.edu/guidry/java/planck/planck.html
• “Normalized” Planck curve for T = 5700K
– Maximum Intensity set to 1
• Note that maximum intensity occurs in visible region of
spectrum for T = 5700K
Two Planck Functions
Displayed on Logarithmic Scale
• This graph is also “normalized” to 1 at maximum
• Maximum intensity occurs at shorter wavelength λ
– boundary of ultraviolet (UV) and visible
Features of Graph of Planck Law
T1 < T2 (e.g., T1 = 5700K, T2 = 7000K)
• Maximum of curve for higher temperature
occurs at SHORTER wavelength λ:
– λmax(T = T1) > λmax(T = T2) if T1 < T2
• Curve for higher temperature is higher at ALL
WAVELENGTHS λ
http://csep10.phys.utk.edu/guidry/java/planck/planck.html
• Graphs for T = 5700K and 7000K displayed on
same logarithmic scale without normalizing
⇒ More light emitted at all λ if T is larger
– Not apparent from normalized curves, must
examine “unnormalized” curves, usually on
logarithmic scale
– Note that curve for T = 7000K is “higher” and its peak is
farther “to the left”
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Wavelength of Maximum Emission
Wien’
Wien’s Displacement Law
Colors of Stars
• Star “Color” is related to temperature
• Obtained by evaluating derivative of Planck
Law over temperature T
2.898 ×10−3
λmax [ meters] =
T [K]
Human vision range
400 nm = 0.4 µm ≤ λ ≤ 700 nm = 0.7 µm
(1 µm = 10-6 m)
Colors of Stars
– If star’s temperature is T = 5000K, the wavelength
of the maximum of the spectrum is:
λmax =
2.898 × 10 −3
m ≅ 0.579µm = 579nm
5000
(in the visible region of the spectrum, green)
Blackbody Curve for T=3000K
• If T << 5000 K (say, 2000 K), the wavelength of
the maximum of the spectrum is:
λ max =
2.898 × 10 −3
m ≅ 0.966 µm ≅ 966nm
3000
(in the “near infrared” region of the spectrum)
• The visible light from this star appears “reddish”
• In visible region, more light at long λ
⇒ Visible light from star with T=3000K appears “reddish”
– Why?
Colors of Stars
• If T << 5000 K (say, 2000 K), the wavelength of
the maximum of the spectrum is:
λmax =
2.898 × 10 −3
m ≅ 1.449 µm ≅ 1450nm
2000
(peaks in the “near infrared” region of the spectrum)
Colors of Stars
• Color of star indicates its temperature
– If star is much cooler than 5,000K, the
maximum of its spectrum is in the infrared and
the star looks “reddish”
• It gives off more red light than blue light
– If star is much hotter than 15,000K, its spectrum
peaks in the UV, and it looks “bluish”
• It gives off more blue light than red light
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Planck Curves for
Rigel and Betelgeuse
Betelguese and Rigel in Orion
Betelgeuse: 3,000 K
(a red supergiant)
RIgel
Betelgeuse
Rigel: 30,000 K
(a blue supergiant)
Plotted on Log-Log Scale to “compress” range of data
Luminosities of stars
• Sum of all light emitted over all wavelengths
is the luminosity
– A measure of “power” (watts)
– Measures the intrinsic brightness instead of
apparent brightness that we see from Earth
• Hotter stars emit more light at all wavelengths
through each unit area of its surface
– luminosity is proportional to T4 ⇒ small increase in
temperature makes a big increase in luminosity
Consider 2 stars with same
diameter and different T’
T’s
Luminosities of stars
• Stefan-Boltzmann Law
L = σT 4
L = Power emitted per unit surface area
σ = Stefan-Boltzmann Constant
≈ 5.67 × 10-8 Watts / (m2 K4)
• Obtained by integrating Planck’s Law over λ
• Luminosity is proportional to T4
⇒ small increase in temperature produces big
increase in luminosity
What about large & small stars
with same temperature T?
• Surface Area of Sphere ∝ R2
– R is radius of star
• Two stars with same T, different
luminosities
– the more luminous star must be larger to
emit more light
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How do we know that Betelgeuse
is much, much bigger than Rigel?
Rigel?
• Rigel is about 10 times hotter than
Betelgeuse (T = 30,000K vs. 3,000K)
– Rigel gives off 104 (=10,000) times more
energy per unit surface area than Betelgeuse
• But these two stars have approximately
equal total luminosity
– therefore diameter of Betelguese must be
about 102 = 100 times larger than Rigel
So far we haven’
haven’t considered
stellar distances...
distances...
• Two otherwise identical stars (same
radius, same temperature ⇒ same
luminosity) will still appear vastly different
in brightness if at different distances from
Earth
• Reason: intensity of light inversely
proportional to the square of the distance
the light has to travel
– Light wave fronts from point sources are like
the surfaces of expanding spheres
Use Stellar Brightness Difference
The HertzsprungHertzsprung-Russell Diagram
• If one can somehow determine that brightnesses
of 2 stars are identical, then use their relative
brightnesses to find their relative distances
• Example: the Sun and α Cen (alpha Centauri)
– spectra look very similar
⇒ temperatures are almost identical (from Planck
function)
• diameters are also almost equal
• deduced by other methods
⇒ luminosities about equal
• difference in apparent magnitudes ⇒ difference
in relative distance
– Check using parallax distance to α Cen
HertzsprungHertzsprung-Russell (“
(“H-R”) Diagram
• Graphical Plot of Intrinsic
Brightness as function of Surface
Temperature
• 1911 by Hertzsprung (Dane)
• 1913 by Henry Norris Russell
• Stars Tend to “Cluster” in Certain
Regions of Plot
Star Types
O B
A
F
G K M
– “Main Sequence”
– “Red Giants” and “Supergiants”
– “White Dwarfs”
• Star “Types” based on
Temperature
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