Light and Continuous Spectra
Energy Production from the Sun:
The Sun dominates the energy ‘budget’ of the solar system
• How much energy does the Sun produce?
• How does the energy reach us?
• How does it produce that energy?
Light properties
•
•
•
•
•
•
Energy
Power
Intensity
Wavelength
Frequency
Speed
Which of the following is
NOT a unit of energy?
1.
2.
3.
4.
Joule
Kilowatt
Kilowatt-hour
Electron volt
Watt’s the difference between
energy and power?
• Consider the units: a Joule (J) is a unit of
energy, and a Watt (W) is a unit of power
• 1 W is defined as 1 J/s (Joule per second)
• Thus, power is a rate at which energy is
delivered
• Example: your “power” bill for electricity is
based on the number of kiloWatt-hours you
consume. So is the utility charging you for
power or for energy?
“Power” bills
• So when a utility charges you for a kW-hr:
• 1 kW = 1000 W; 1 hr = 3600 s
• A kW-hr can be converted into an equivalent
in Watt-seconds
• Recall that 1 W is defined as 1 J/s, so 1 J = 1
Ws
• In other words, your utility is charging you for
energy usage, not power. It’s not a power
company
Intensity
Intensity is a power density.
Units: W/m2 = W m-2
Pow
Intensity

Are
A
Solar Intensity
The Solar Energy Output is 4 x 1026 W.
How much of that hits us?
When the Sun is directly over head, it delivers the equivalent of
22 × 60 watt light bulbs over each square meter (m2) of
ground!!!
This amount, 1340 W m-2, is known as the solar constant
How is solar energy delivered from the Sun to
the Earth?
As light!!!!
Is the intensity of light reaching the surface
always 1340 W/m2?
1. Yes
2. No
Electromagnetic Wave
Electromagnetic Wave: propagating wave of electric and
magnetic fields that oscillate perpendicular to
each other and the direction of propagation
In a vacuum, wave propagates with speed = 3 x 108 m/s
(cosmic speed limit)
Electric field
Magnetic field
Wave Properties
speed (v): how much distance the wave moves per unit time
(for an EM wave v = c = 3 x 108 m/s)
frequency (f or ν (nu)): number of peaks that pass a location in a
given time (units: Hertz (Hz) = 1/s = s-1)
Wave Properties
wavelength (): distance between two consecutive peaks
(units: km, m, cm, mm, m, nm…)
amplitude: height of the wave (or depth of the trough); related to intensity
but we won’t use it
Wave Properties
speed (v): how much distance the wave moves per unit time
(for an EM wave v = c = 3 x 108 m/s)
frequency (f): number of peaks that pass a location is a
given time (units: Hertz (Hz) = 1/s = s-1)
wavelength (): distance between two consecutive peaks
(units: km, m, cm, mm, m, nm…)
These three properties are related:
f 
c

If wavelength is 10 m and frequency is 100 Hz (oscillations /
seconds), what would be the speed of the wave?
1.
2.
3.
4.
10 m/s
1 m/s
1000 m/s
100 m/s
If wavelength is 10 m and frequency is 100 Hz
(oscillations / second), what would be the speed of
the wave?
f 
v

v  f


 100s-1 10m
1000m/s
The Photon
Light behaves like both a particle and a wave!
Photon: smallest bundle of light energy
(i.e., a particle of light)
Photons carry light energy:
1. A photon’s energy is proportional to frequency
(Eph  f).
2. A photon’s energy is inversely proportional to wavelength (Eph 
-1).
hcPlank’s constant (h) = 6.602 x 10-34 Js
E
hf

ph

Matter actually a wave too!
• All matter exhibits particle and
wave properties (Louis de Broglie,
1921)
• For ordinary objects, the wave
nature of matter is much too small
to measure
– The wavelength of a baseball
moving at 80 mph would be
about 10-34 meters
• But for small particles, this is wave
Electron diffraction pattern
nature of matter is measurable
showing its wave nature
– The wavelength of an electron is
about 10-10 meters
The Visible Spectrum:
How is a difference in the frequency or wavelength of
light observed?
For visible wavelengths  COLOR
How does a prism work?
• Dispersion: Speed of light in
the prism (glass or plastic)
depends on the frequency
(color)
• Refraction: Change in speed
of light causes a change in its
direction
• Result: Blue changes
direction most since its
speed is the lowest inside the
prism. And red changes
direction least since its speed
is highest inside the prism.
Red
Orange
Yellow
Green
Blue
Indigo
Violet
R
O
Y
G
B
I
V
Herschel Thinks Outside the Box:
In 1800 William Herschel made a discovery when he tried to determine the
temperature of light.
• He noticed that a thermometer recorded
energy from the Sun`s spectrum even when
placed beyond the red end of the visible
rainbow.
•He called this emission Calorific Rays and
it was the first discovery that light had
colors invisible to the human eye.
•These rays are known today as infrared
light.
Herschel’s work  color is associated with a temperature
Visible light is just a small part of the electromagnetic (EM)
spectrum
Why are we spending so much time discussing the
electromagnetic spectrum?
Not easy to visit astrophysical objects (the
Sun, planets, other stars) and make direct
in situ measurements
We rely on remote sensing of EM radiation.
Tells us the temperature and composition
This gives us important clues to
the origins of these objects.
The Solar Spectrum:
When we look at the spectrum of the Sun, we see a distinct
distribution of colors.
Other stars have
similar patterns as
do most hot objects.
The main difference
is where the peak
color is.
Gustav Kirchoff (1862)
called this kind of
emitter a ‘blackbody’.
Ideal Blackbodies
Blackbody: an object that radiates energy into space in a manner that is
characteristic only of the temperature of the radiator.
Characteristics of Black Bodies
1. Characteristic I vs.  curve (shown left)
(all blackbodies radiate in more than one color)
2. Curve is related to T only
3. Increasing T, increases total intensity
4. As T increases, peak moves to lower 
5. Wavelength of peak intensity related only to T.
Wilhelm Wien (1893) describes the relationship
mathematically (now called Wien’s Law), where  is
measured in nanometers and T is measured in Kelvins:
lmax
Wavelength (nm)
2.9 ´ 10 6
=
T
Calculating The Sun’s
Temperature
So how well does this work?
Given Tsun = 6000 K
lmax
2.9 ´ 10 6
=
= 483 nm
6000
Which matches the
observed solar output
curve pretty well.
Ideal Blackbodies
Amount of light radiated by an object
is given by the Stefan-Boltzmann Law
(Josef Stefan, 1879; Ludwig
Boltzmann, 1884):
L =s T
4
Where L is the luminosity (power)
emitted by the object (in Watts), T is
its temperature (in Kelvins), and
 is the Stefan-Boltzmann constant,
which has the value 5.67 x 10-8
Wm2K4
Wavelength (nm)
Stars may be considered to act like blackbodies
UV
Visible
Infrared
If star A has a surface temperature of 9000 K and
star B has one of 3000 K, what is the ratio of the
power output of the stars (PowerA/PowerB)?
1.
2.
3.
4.
5.
81
2
9
3
16
Solution
If star A is 9000 K and star B is 3000 K, what is
the ratio of the power output of the stars
(PowerA/PowerB)?
PowerA
sT
=
PowerB
sT
4
A
4
B
æ TA ö
=ç
÷
è TB ø
4
æ 9000 ö
4
=ç
÷ = ( 3)
è 3000 ø
= 81
4
If star A has a surface temperature of
6000 K and star B has one of 3000 K,
which star has a longer peak wavelength
output?
1. Star A
2. Star B
Solution
If star A is 6000 K and star B is 3000 K, which star
has a longer peak wavelength output?
Since
lmax = 2, 900, 000 T
The colder star, star B, has the longer wavelength.