Download Light and other electromagnetic radiation Goals-

Light and other electromagnetic radiation
Goals--we want to understand:
1. the bizarre, dual nature of light
2. the structure of atoms
3. how we use light to gain information on objects that
we cannot touch
4. what determines how bright an object actually is and
how bright it appears to us
Just what IS light, anyway?
Does it consist of waves of electromagnetic energy? (Huygens)
-orDoes it consist of particles (photons)? (Newton)
-YES-
You can devise an experiment that will prove conclusively that either
of the above cases is true.
• When light propagates, it is best described as a wave.
• When light interacts with matter, it is best described as photons.
This is the clearest example of a concept in quantum mechanics called
wave-particle duality.
• On small scales, all things show some behaviour that is “wavelike,” and some that is “particle-like.”
Light as a wave
A light wave consists of an electric field, and a magnetic field, both of
which are oscillating.
• As the electric field changes, it causes the magnetic field to change,
and vice-versa.
• This way, electromagnetic waves are able to propagate through
space all by themselves.
– Other waves need some medium through which they can
propagate (sounds waves through air, for example).
If we draw only the electric field, then the light wave looks more
familiar:
Wavelength, λ
We describe waves by their:
•Wavelength (λ): The distance between identical points on the wave.
•Frequency (f): The number of wavelengths that pass by each second.
Wavelength and frequency are related by:
λf = c
C = speed of light. The same for all electromagnetic waves.
Question:
A difference between electromagnetic waves and either sound or
water waves is:
a) Electromagnetic waves all have shorter wavelengths.
b) Electromagnetic waves can travel in a vacuum.
c)
Electromagnetic waves all have the same amplitude.
d) Electromagnetic waves can travel from place to place
instantaneously.
Units:
Wavelength:
• Angstrom (Å): 10-10 meters
• Nanometers (nm): 10-9 meters
• Microns (µm): 10-6 meters
• Millimeters (mm): 10-3 meters
• Meters (m): about three feet
Frequency:
• Hertz: 1 cycle per second
• Megahertz (MHz): 106 cycles per second
• Kilohertz (kHz): 103 cycles per second
Our eyes are sensitive to a very small part of the electromagnetic
spectrum.
Name:
Typical wavelengths
Frequencies
X-rays
< 10 Å
> 3x1017 Hz
Ultraviolet
(sunburn)
30-3000 Å
9x1014-1017 Hz
Visible light
4000-8000 Å
Infrared
(heat)
1-100 µm
4-8x1014 Hz
3x1012-3x1014 Hz
100 µm - few mm
about 3x1011 Hz
FM Radio
2.8 - 3.4 m
88 - 108 MHz
AM Radio
188 - 556 m
540 - 1600 kHz
Microwaves
Diffraction and interference are explained if light is a wave: the twoslit experiment shows both of these at work.
Bright lines are seen on the screen
where the difference in the path
lengths from the two slits to the
screen is an integer number of
wavelengths.
Dark lines are seen where the
difference is an odd half number of
wavelengths.
Incoming parallel
wave crests
Screen with
two slits
Viewing screen
When the paths from the two slits to the screen differ by λ, 2λ…, the two
waves add. This is called constructive interference.
+
=
When the path are l/2, 3l/2… different, the waves cancel. This is
called destructive interference.
+
=
Doppler Shift
The change in the observed color of light because the source and the
observer are either approaching or moving away from each other.
Static light source: color looks the same to all observers.
Circles are crests of
waves moving away
from light source
Moving light source: light waves expand around where the source
was when they were emitted.
1
1
2
1
2
3
Sees a
redshift
Sees a blueshift
Sees no shift
Question:
In which of the following situations would the light that we see from a star
show a blueshift?
a) The star is moving away from us.
b) The star is moving across our field of view.
c) The star is moving towards us.
Light as particles
We also think of light as coming in discrete particles, called photons.
• Each photon has a wavelength associated with it, the same as the
wavelength of the color light it represents.
• Each photon has an energy given by its wavelength (or,
equivalently, its frequency) as:
E = hf
This view of light was introduced by Einstein to explain the
photoelectric effect.
electrons
photons
metal
Types of Spectra
•
•
•
Continuous spectrum
– All colors present to some degree.
– From a hot solid, liquid, or very
dense gas.
Emission-line spectrum
– Only light at certain, very
specific wavelengths is present.
– From a hot gas.
Absorption-line spectrum
– All colors are present, except at
certain wavelengths.
– From a cool gas in front of a
continuous source.
Continuous Spectra
Most sources of continuous spectra emit Planck (or “blackbody”)
spectra.
energy
wavelength
The wavelength where the spectrum peaks depends upon the
temperature of the source, according to Wien’s Law.
λ peak
1
∝
T
The total amount of electromagnetic energy emitted by a continuous
source increases very rapidly with its temperature, as described by
Stefan’s Law.
F∝Τ
•
•
•
4
F is the flux. It is the amount of energy emitted by every unit area
of the surface of the light source.
For example, a star that is twice as hot as the Sun (but the same
size) would be 16 times brighter.
Because of this, it is the rare hot stars that dominate the light that
we see from most galaxies.
By looking at continuous spectra from multiple sources, we see both
Stefan’s and Wien’s Laws in action
The total amount of light emitted by an object (the luminosity) also
increases with the total amount of emitting area. For a star, this
means that:
2
source
L∝R
•
•
R is the radius of the emitting object (NOT the distance to it).
A star with twice the radius of the Sun (but the same temperature)
would emit four times more light.
€
Questions:
Two stars have the same radii. One is blue and the other is red. The red
star appears to be twice as bright as the blue star when you see them
in the sky.
Which star is emitting more light?
a) The red star.
b) The blue star
Which star is hotter?
a) The red star.
b) The blue star.
Which star is further away?
a) The red star.
b) The blue star.
Emission and Absorption Spectra
“Fingerprints of the atoms”
We can think of atoms as looking like miniature Solar Systems.
One or more negatively-charged electrons orbit around a nucleus that
consists of positively-charged protons and neutral neutrons.
+
ordinary
hydrogen
+
deuterium
0
-
-
+
0
-
0
+
helium
-
Unlike the Solar System, the electrons can only exist in certain orbits,
called energy levels.
Higher energy
+
-
The lowest possible energy level, where the electron likes to be, is
called the ground state.
When a photon of the right energy hits an atom, the electron can use
the energy of the photon to move to a higher energy level.
The photon is absorbed in the process, resulting in an absorption-line
spectrum.
before
after
Wrong energy
Right energy
In reverse, an electron that is in a high energy level will spontaneously
“jump” to a lower level. The energy that it loses is emitted as a
photon. The result is an emission-line spectrum.
before
after
The atoms of each element have unique arrangements of energy levels,
and so each elements has a unique absorption and emission-line
spectrum. By examining an absorption or emission-line spectrum, we
can therefore determine the chemical makeup of the emitting object.
Another inverse-square law
The apparent brightness of an object (a star, a candle, a flashlight…)
decreases with the square of distance, like gravity.
Imagine two spheres centered on a light source.
The same photons pass through both spheres. The area of a sphere:
A = 4πR
2
R1
R2
The apparent brightness is
total light
1
∝ 2
area
R
This means, for example, that sunlight is 900 times fainter at Neptune
than at Earth.
Question:
Which of the following characteristics of light are associated with the wave
nature of light?
a) Constructive interference and diffraction.
b) The Doppler effect and the formation of spectral lines.
c)
Formation of spectral lines and the photoelectric effect.
d) Diffraction and the photoelectric effect.