Astronomy 162: Introduction to Stars, Galaxies, and Cosmology
Kris Stanek
Department of Astronomy
The Ohio State University
Lecture 2: Light
Review from 161. See relevant sections in Textbook.
Key Ideas
- Light is Electromagnetic Radiation
- Light as Waves and Photons
- Electromagnetic Spectrum
- Sequence of photon energies
- Luminosity vs. Apparent Brightness
- Inverse Square Law of Brightness
- Doppler Effect
- Due to relative motion between source & observer
- Way to measure speeds at a distance
Key Equations
c = λ ν
E = h ν
f = L / (4 π D2)
(λobserved - λemitted)/λemitted = V/c
Electromagnetic Radiation
Light is Electromagnetic Radiation, a self-propagating
Electromagnetic disturbance that moves at the speed of light
Light can be treated as either Electromagnetic Waves
or Photons (particles of light).
We will find the latter
characterization useful when we think of light interacting
with atoms.
Wave Nature of Light
Can treat light as an Electromagnetic Wave
- Periodic fluctuation in the intensity of coupled electric and
magnetic fields.
- Wave travels through a vacuum at the speed of light.
- Doesn't need a medium to "wave" in.
The speed of light (c) is the same for all light waves:
c = 299,792.458 km/sec ~ 3.0x105 km/s
This speed is independent of the wavelength or frequency of the
light!
Like other waves, light waves have a frequency, wavelength, and amplitude,
usually symbolized with ν, λ, and A, respectively.
The wavelength and frequency of light waves are connected by
c = λ ν
Particle Nature of Light
We can also treat light as particles or Photons.
Photon:
- Massless particles that carry energy at the speed of light.
Photons are characterized by their Energy, which is
proportional to their Frequency, ν.
Photon Energy:
E = h ν
where: ν = frequency of the light, and h = Planck's
Constant.
In words: Higher Frequencies mean Higher Energies
The Electromagnetic Spectrum
The sequence of photon energies running from low energy to high
energy is called the Electromagnetic Spectrum
low energy = low frequency = long wavelength
- Examples:
- Radio Waves, Infrared
Radio telescopes often observe radiation from
galaxies with a wavelength of λ=20 cm.
Using the formula c = λ ν, this
wavelength corresponds to ν=1.5x109 waves/s.
high energy = high frequency = short wavelength
- Examples:
- Ultraviolet, X-rays, Gamma Rays
Even though individual gamma rays have much higher
frequency and much higher energy than radio waves,
they still all travel at the same speed, c.
Major Divisions of the Electromagnetic Spectrum
| Type of Radiation | Wavelength Range |
| Gamma Rays | <0.01 nm |
| X-Rays | 0.01-10 nm |
| Ultraviolet | 10-400 nm |
| Visible Light | 400-700 nm |
| Infrared | 700-105 nm (0.1 mm) |
| Microwaves | 0.1-10mm |
| Radio | >1 cm |
The Visible Spectrum
This is all forms of light we can see with our eyes.
- Wavelengths: 400 - 700 nanometers (nm)
- Frequencies: 7.5x1014 - 4.3x1014 waves/second
We sense visible light of different energies as different colors.
The basic colors of the visible spectrum are defined roughly as follows,
in order of increasing photon energy:
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| Color Name |
Red |
Orange |
Yellow |
Green |
Blue |
Indigo |
Violet |
Approximate
Wavelength |
700nm |
650nm |
600nm |
550nm |
500nm |
450nm |
400nm |
You can remember the order of these colors from lowest to highest
energy using : ROY G. BIV
Note: The wavelengths given in the table above are only approximate.
How "Bright" is a Light Source?
We need to quantify how bright a light source is. The most convenient
way is using the photon picture for light:
- "Brightness" measures the number of photons per second emitted by the
light source
There are two ways to quantify this:
- Luminosity (L):
- Measure of the total energy output:
- L is measured in Power Units (energy/sec) like Watts
- L is independent of distance
- Luminosity is an intrinsic property of the light source.
- Apparent Brightness:
- Measures how bright an object appears to be as seen from
a distance
- Brightness is measured in Flux Units (energy/sec/area)
- Brightness depends on the distance to the source
- Brightness is what we actually measure (an observable property).
Luminosity and Brightness are related through the Inverse Square Law
of Brightness:
f = L / (4 π D2)
where D is the distance to the light source.
In words:
- Apparent Brightness is inversely proportional to the
square of the distance to the source
Implications:
- If the source is 2x closer, it appears 4x brighter.
- If the source is 2x farther away, it appears 4x fainter.
This law is extremely important to us in astronomy.
If we measure the brightness and we know the distance, we
can then derive the luminosity, the energy emitted by the
source:
L = 4 π D2 f
The Doppler Effect
Change in observed wavelength of a wave when the source of the
waves and observer are moving relative to each other.
Examples:
- Sound Waves (Siren, Train Horn, Passing Racecar)
- Light Waves
The amount of the shift and its sign depends on
- relative speed of the source & observer
- direction of motion (together or apart)
Doppler Effect in Sound
Imagine an ambulence at rest at a stoplight, its siren blaring.
It emits sound waves that move out spherically, in all directions.
Now imagine it moving toward you. The waves moving in your
direction are scrunched together because of the motion of the
ambulence. As it passes you, the sound waves you hear become
spread out.
As it's coming toward you, you hear sound of shorter wavelength (scrunched),
higher frequencies. As it's moving away, you hear longer wavelengths (spread
out), lower frequencies.
Doppler Effect in Light
The Doppler Effect in light works the same way as it does for sound:
- Moving away from the observer, wavelength gets longer:
REDSHIFT (longer wavelength, smaller frequency)
- Moving towards the observer, wavelength gets shorter:
BLUESHIFT (shorter wavelength, larger frequency)
A Way to Measure Speeds
Observe the wavelength
λobserved of a
light source with a known emitted wavelength
λemitted.
The difference between the observed and emitted wavelengths is
directly proportional to the speed of the source towards or away from
you (V), given by the
Doppler Formula:
(λobserved - λemitted)/λemitted = V/c
Here c is the speed of light.
- The size of the shift gives the speed of the source
- The color of the shift (Red or Blue) gives the direction of motion
(away or towards you).
The Doppler Effect in Practice
The Doppler Effect in light is used by astronomers to measure the speeds
of objects moving towards or away from the Earth.
But, we also use the Doppler Effect in light in everyday settings. Some
examples:
- Traffic Radar Guns:
- Radar gun bounces a pulse of microwaves (or infrared laser light)
of a known wavelength off a car or truck, measure the wavelength
reflected back. The Doppler shift gives the vehicle's speed.
- Doppler Weather Radar:
- Similar principle, bounce microwave radar signals of known
wavelength off of clouds, measure the wavelength reflected back. The
Doppler shift and its sign (blue or red) gives the speed and direction
of the clouds. The strength of the returned signal also gives the
amount of rain or snow falling.
The properties of light give us a way to bridge the vast distances
between us and astronomical objects.
The light "encodes" important information about the source of the light.
In particular,
- the luminosity measures how much energy the object emits in the
form of light.
- the Doppler Shift tells us how fast it is moving towards or away from us
To learn more from light, however, we need to understand how light and
matter interact, which is the subject of the next lecture.