Chapter 6: Light
In our day to day lives, we learn about the world by seeing, hearing,
touching, tasting, and smelling
Generally, we cannot hear, touch, taste, or smell the
cosmos. But,
we can see it!
Light as We See It
Light is a form of energy (radiative energy)
Energy/time = power
Power units = watt = 1 Joule/sec
Light can be
emitted by an object (example = the Sun)
absorbed by an object (example = black board)
transmitted through an object (example = eye glasses)
reflected by an object (example = mirror)
White light is actually a combination of all colors of the rainbow
prism
Most objects emit, absorb, transmit & reflect some colors
better than others
We see the color of the light that enters our eyes,
So, we see the colors emitted, transmitted, & reflected
example
window is "transparent"
opposite of "transparent" = "opaque"
mirror reflection:
angle of incidence = angle of reflection
other objects reflect light in many directions,
called "scattering"
But, what IS light??
Humans exploring light is like blind people exploring an elephant
One thinks the elephant is a wall, another thinks it is a spear, etc.
(Saxe poem)
Humans think light is similar to a particle and similar to a wave
Particle: light is made of individual photons
that fly through space and bounce of things,
just like balls (particles) do
Wave: light carries energy, but not material,
just like a wave does
A wave passing through water causes the water to
rise and fall. Example
Similarly, as a light wave passes by, its magnetic and
electric fields increase and decrease
(Magnetic field is familar: it causes certain objects to move)
(Electric field causes charged objects to move)
Electromagnetic wave
Light has wavelength, frequency, speed, as do waves
Wavelength: distance between peaks
Frequency: number of peaks that pass by per second
Speed: speed that light wave propagates
speed = wavelength * frequency
Speed of light (in vacuum) = 300,000 km/sec = 3.0 x 108 m/s
(light travels slower when going through stuff)
Different colors of light have different wavelenghts
and different energies (shorter wavelenghts -> more energy)
Energy = frequency * h
h = Planck's constant
h = 6.626 x 10-34 Joule * sec
h = 4.136 x 10-15 eV * sec
Problem
In Ch 4, we learned about electrons in atoms changing levels
We talked about the transition from 12.1 eV to 10.2 eV
What is the frequency of the light produced ?
Energy = frequency * h
frequency = Energy / h
frequency = (12.1 eV - 10.2 eV) / 4.136 x 10-15 eV * sec
frequency = 4.6 x 1014 * (1/sec)
= 4.6 x 1014 Hertz
What is the wavelength of the light produced ?
speed = frequency * wavelength
wavelength = speed / frequency
wavelength = (3 x 108 m/s ) / 4.6 x 1014 * (1/sec)
wavelength = 6.5 x 10-7 m
= 650 nanometers
= 6500 Angstroms
(there has been some rounding, true answer = 6563 Angstroms)
This light is red in color
The "visible spectrum" is just a small part of the whole spectrum
whole spectrum
Note that radio waves, are really a form of light
Problem:
Does this make sense? yes or no
Because of their higher energies, X-rays must travel
through space faster than radio waves. Yes or no?
Spectra from Space
Photons care whether they are dealing with a low density cloud of gas (Earth clouds, gas between the stars, between the galaxies) or a high density material (solid objects, the Sun, stars)
Low density ("optically thin") case:
This is like what we have talked about, but scaled up
Excited atoms can emit photons of particular energies
and absorb photons of the same particular energies
Hydrogen atom example
When do we see emission versus absorption?
Heat up atoms -> more collisions -> more excitations
-> more emission
Cool down atoms -> less emission
A cloud is always emitting some light
however, if the cloud is between you and a
bright light source, then you notice the cloud absorb light
Or, if the cloud is off your line of sight, can see reflection
(scattering)
Each type of atom (element) has its own set of photon energies,
called
Different elements -> "different emission line spectra"
Different ionization levels (having lost or gained electrons)
-> different emission line spectra
Molecules: can rotate and vibrate, but at particular rates,
so can have transitions between these rotational and vibrational
energy levels. And, can have electronic transitions. So, can
make/absorb light of many colors
Use spectra from space to figure out what is going on:
chemical composition, ionization (assoc. with temperature)
Example: nebula = cloud in space and
the Orion nebula's ultraviolet spectrum
Question:
A familar example of the emission line spectra we've just talked about is a red neon lightbulb (used to advertise businesses). Other examples are
sodium lightbulbs (yellowish, used in some street lamps) and fluorescent lightbulbs.
If you looked critically at a rainbow colored tie-dyed T shirt under these lightbulbs, would you see the normal rainbow? Why / Why not?
Break down this question: do these lights emit all colors (like a rainbow), or particular colors and not other colors?
When the red neon light photons bounce off the green in the shirt, what happens?
In order for you to see the green of the shirt, what color has to be in
the "incident" light ? Is it ?
"Scale up" your answer to deal with the fluorescent lightbulb.
Opaque ("optically thick") case:
Example = Sun.
An atom deep in the sun only emits photons of particular colors
Many atoms between the first and the surface. The original photons
cannot leave without being aborbed by something in their path.
Absorption -> excites electron(s) in absorbing atoms
Atoms emit photons
Repeat many, many times before photons can leave
The departing photons usually have different energy than original
Scale-up: start with many atoms that emit only particular colors
end up emitting a rainbow of photon energies
called "continuous spectrum"
Stellar spectra
The degree to which an object is optically thin or thick depends on
the degree of this rainbow-isation effect
This is called "thermal radiation" or "blackbody radiation"
"thermal" because the temperature is important
1.) Hotter objects emit more energy/(surface area)
(energy radiated) / (time * surface area) is proportional to T4
E/(time*area) = s * T4 (Stephan - Boltzman Law)
s = 5.7 x 10-8 watt / (m2 K4)
2.) The brightest part of the rainbow shifts to shorter
wavelengths as the temperature increases
lamdamax= 2,900,000 nanometers / T (K) (Wien's Law)
Examples:
Fire poker
Spectrum versus temperature
Animated version
Human
Something for you to consider:
This is the spectrum of a planet.
There are 3 wavelength regions of absorption and 2 of emission
in this spectrum.
Which regions are "line emission" from optically thin gas?
Which are blackbody emission from an opaque object?
Think about the fact that we are looking at a planet --
what part of a planet is opaque (ground, atmosphere, ...)
and what part is optically thin?
What color does this planet look to the eye?
Is the planet cool-ish or hot-ish?
Any guesses on which planet this is?
Announcements:
My office moved to room 306 A
The first midterm is Feb. 16
Now, back to our regularly scheduled program
The Doppler Effect
The Doppler Effect works on both light and sound because both are waves
Sound: pitch is due to frequency of sound waves
high frequency => high pitch
speed = frequency * wavelength
so, short wavelength => high pitch
Light: color is associated with frequency (and wavelength)
blue has higher frequency (shorter wavelength) than red
Think about a loudspeaker and a person, both stationary
If the person walked toward the loudspeaker, then she/he crosses
some waves, so perceives higher pitch
If the person walked toward a lightbulb, would see shorter wavelength
Example: Train
Examples in astronomy:
Most stars are moving relative to us,
so we see their spectra shifted in wavelength
Can measure the velocity along the line of sight (radial velocity)
(radial velocity)/(speed of light)
= (observed wavelength - rest wavelength)/(rest wavelength)
Example:
The rest wavelength of the red hydrogen line is 656.285 Angstroms,
but when we look at the star Vega, we see this line at
656.255 Angstroms, what is Vega's radial velocity
(relative to us)?
656.255 < 656.285, so the line is blue shifted, Vega and us
are moving toward each other.
radial velocity =
(speed of light)*((obs. wavel. - rest wavel.)/(rest wavel.))
= 300,000 km/s *
((656.255 - 656.285) Angstroms / 656.285 Angstroms)
= -13.7 km/s
Radial velocity versus tangential (transverse) velocity
A star in an elliptical orbit
A rotating star
Animations for Students to Use
Doppler animation A
Doppler animation B
Question: Does this make sense, yes or no?
If a distant galaxy has a substantial redshift (as viewed from our,
galaxy then anyone living in that galaxy would see a substantial
redshift in a spectrum of the Milky Way galaxy.
Yes or No ?
