Transcript The Nature of Light (PowerPoint)

• The Electromagnetic Spectrum
• Polarization
• Measuring the Speed of Light
•The Wave Nature of Light
•The Particle Nature of Light
• Refractive Index
Photograph of a living fetus using fiber-optic photography
The Electromagnetic Spectrum
Electromagnetic Waves
When electric charge changes its motion (I.e. vibrates back and forth, as
in an electron in a transmitting ariel), it produces a changing electric field
over time. Because the electric field is changing, a changing magnetic
field is induced (according to Ampere’s Law) and this in turn further
generates a changing electric field (according to Faraday’s Law). Thus a
continually self generating wave consisting of varying electric and
magnetic fields (that are in phase but perpendicular to the direction of
motion) will travel through space away from the source in all directions
unless constrained, by cable. This self-generating wave is called an
electromagnetic wave. Think of a radio mast transmitting your favorite
radio show. There are electrons within the mast that are made to oscillate
back and forth by applying a alternating electrical voltage to the mast.
These vibrating electrons produce the radio waves (electromagnetic
waves) that are transmitted.
All waves in the electromagnetic spectrum consist of varying electric and magnetic fields. But what is the difference between a radio wave and an light
wave or an x-ray? Electromagnetic waves exist with an enormous range of frequencies. This continuous range of frequencies is known as the
electromagnetic spectrum. The entire range of the spectrum is often broken into specific regions. The subdividing of the entire spectrum into smaller
spectra is done mostly on the basis of how each region of electromagnetic waves interacts with matter. The longer wavelength, lower frequency regions
are located on the far left of the spectrum and the shorter wavelength, higher frequency regions are on the far right.
Polarization
Have you ever worn a pair of Polaroid sunglasses? If you haven’t then on your next visit to the mall try on a
pair and look at the shiny floor. What you should notice is that the sunglasses have somehow cut out all the
“glare”, which is the light reflected off the floor. Fishermen like to wear sunglasses made from polarizing
material (Polaroids) because they cut out the glare from the surface of the water and therefore help them
locate likely fish holding areas of the river. So how does this amazing optical material work?
First you must realize that electromagnetic waves are produced by vibrating electrons and that these
electrons are restricted in their motion to a plane of vibration. This means that the EM wave produced by
one electron is a transverse wave that moves in a plane. See diagram a. We call this plane polarized. A
vertically vibrating electron emits light that is vertically polarized while a horizontally vibrating electron emits
light that is horizontally polarized. See diagram b.
Diagram a. Vertically plane
polarized wave emitted by a
vibrating electron
For a common light source such as an incandescent light or the sun, the light is not polarized because the
vibrating electrons that produce the light vibrate in all directions. However when the light is reflected off say
the floor, the light becomes polarized in the horizontal direction. The floor effectively stops the vertical
component of the wave. Glare is thus horizontally polarized. The polarizing axis of Polaroid sunglasses is
vertical so that only the vertical component of EM waves gets through the material. Glare from a horizontal
surface therefore cannot get through the polarizer and is thus eliminated.
Diagram b. Vertical and
horizontal polarization
Diagram demonstrating how a Polaroid filter
works. For two filters placed over each other
with their axes aligned in the vertical
direction, light polarized in the vertical
direction can get through. If however the
filters are “crossed” with their axes
perpendicular to each other, light polarized
in the vertical plane by the first filter cannot
pass through the second filter (which only
passes light having a EM component in the
horizontal plane).
The Visible Light Spectrum
Though electromagnetic waves exist in a vast range of wavelengths, our eyes are sensitive to only a very narrow band. Since this narrow band of
wavelengths is the means by which humans see, we refer to it as the visible light spectrum. Normally when we use the term "light," we are
referring to a type of electromagnetic wave which stimulates the retina of our eyes. In this sense, we are referring to visible light, a small spectrum
of the range of frequencies of electromagnetic radiation. This visible light region consists of a spectrum of wavelengths, which range from
approximately 700 nanometers (abbreviated nm) to approximately 400 nm; that would be 7 x 10-7 m to 4 x 10-7 m. This narrow band of visible light
is affectionately known as ROYGBIV.
The Speed of Light
Early experiments to measure the speed of light failed because it was so high. Experimenters who
tried to measure how how it took light to travel to a mirror placed on a distant hillside and back
(Galileo) only managed to measure their own reaction time. Incidentally, it was mirrors placed on the
moon by the first “manned landing” missions that later led to increased accuracy about the speed of
light.
Roemer’s Method
So how did early physicists measure the speed of light? The first demonstration that light travels at a
finite speed was supplied by the Dutch astronomer Olaus Roemer about 1675. Roemer made very
careful measurements of the periods of Jupter’s moons. The innermost moon, Io, is visible through a
small telescope and was measured to revolve around Jupiter in 42.5 hours. Io disappears
periodically into Jupiter’s shadow, so this period could be measured with great precision. Roemer
was puzzled to find an irregularity in the measurements of Io’s observed period. He found that while
the earth is moving away from Jupiter, say from position B to C in the diagram opposite, the
measured periods of Io were all somewhat longer than average. When the earth was moving toward
Jupiter, say from position E to F, the measured periods were shorter than average. Roemer
estimated that the cumulative discrepancy between positions A and D amounted to about 22
minutes. (This time is known today to be about 17 minutes or 1000s). That is when the earth was at
position D, Io would pass into Jupiter’s shadow 22 minutes late compared with observations at
position A.
The Dutch physicist Christian Huygens correctly interpreted this discrepancy. When the earth was further away from Jupiter, it was the light that
was late, not the moon. Io passed into Jupiter’s shadow at the predicted time, but the light carrying the message did not reach Roemer until it had
traveled the extra distance across the diameter of the earth’s orbit.
speed of light = extra distance traveled = 300 000 000 km = 300 000 km /s
extra time measured
1000 s
Michelson’s Technique
The most famous experiment measuring the speed of light was performed by the American physicist Albert Michelson in 1880. The diagram
below shows that he rotated an octagonal mirror at such a rate so that light from a source would hit a mirror, travel to a distant mirror and be
reflected back. If the mirror was rotated such that the time taken for the light to go to the distant mirror and back was the same time for the mirror
to turn on-eighth of a rotation, the light would be reflected into the eyepiece. If too slow or too fast it wouldn’t enter the eyepiece.
Finding the total distance traveled by the light (from surveyed charts), and the time to travel, (judged accurately from the rotation rate of the
mirror), Michelson could determine the speed of light. Michelson’s experimental value for the speed of light was 299 920 km/s. which we round to
300 000 km/s.
Michelson received the 1907 Nobel Prize in physics for this experiment. He was the first American scientist to receive this prize.
Light is so fast that if a beam of light could travel around the earth, it would make 7.5 trips in one second. Light takes 8 minutes to travel from the
sun to earth, and 4 years from the next nearest star Alpha Centauri. The distance light travels in a year is called a light year.
The Wave Nature of Light
A Scottish physicist James Clerk Maxwell (1831 - 1879) produced a single theory of electromagnetism that predicted that light was an
electromagnetic wave that traveled at the same speed in a vacuum as other electromagnetic waves regardless of its wavelength. Other
scientists had previously showed that light exhibited properties of a wave. For example, Thomas Young showed in 1801 that light from two
coherent sources will interfere. But Maxwell proved that light of all wavelengths travel at the same speed in a vacuum and that its speed is the
same as all other electromagnetic waves. We can therefore say that:
Speed of a EM Wave = # Waves per second • length of a Wave
v

f
For light in a vacuum we call its speed c = 3 x 108 m/s. We can therefore write: c = f 
or
f=c/
or
=c/f
The Particle Nature of light
Before being shown that it was waves, scientists believed it was made of particles. Today it is known to be made of particles called photons and it
is also waves. The energy of a photon is proportional to its frequency and all the photons of a given frequency have the same amount of energy.
We can say:
Energy of a Photon = Planck’s Constant • # Waves per second
E
h
f
The constant h is known as Planck’s constant and is the same h used in describing angular momentum and spin on the atomic level. Its SI value is
6.63 x 10-34 Js.
Sample Practice Problem
What is a) the frequency of a 450 nm light wave? b) how much energy would each photon have and c) what color is this wavelength?
We know that:  = 450 x 10-9 m, c = 3 x 108 m/s and h = 6.63 x 10-34 Js
Therefore f = c / 
= 3 x 108 m/s / 450 x 10-9 m = 6.67 x 1014 s-1 (Hz)
E = h • f = 6.63 x 10-34 Js • 6.67 x 1014 s-1 = 4.42 x 10-19 J
The light has a small wavelength in the blue part of the spectrum
Electron-Volt
Light particles have small amounts of energy which can be expressed as electron-volts.
1 eV = 1.6 x 10-19 J
How much energy does a blue light particle carry in eV’s?
Eblue = 4.42 x 10-19 J (
1eV
)
1.6 x 10-19 J
Eblue = 2.76 eV
Photoelectric Effect
This effect made famous by Einstein in 1905 is used today in electronic sensory equipment from burglar alarms and garage door openers to
smoke detectors and light meters (photography).
When a light photon with enough energy strikes the thin metal sheet an electron is ejected from the surface of the metal and attracted towards
the positive plate. The electron then moves through the wires towards the positive side of the battery. As it moves through the ammeter (A), it
causes the needle to move, thus signifying an electric current. Note: another electron will also move from the negative side of the battery
through the wire to the metal plate to fill the hole vacated by the ejected electron. If light was a wave, then as the intensity of light (brightness) is
increased the number of ejected electrons would increase but the frequency of light would not be a factor in getting the ejected electrons to
move to the plate.
A
Photon
+
Electron ejected
Thin metal plate
+
-
Einstein found out that although increasing the light intensity did increase the current, the ability of an electron to leave the surface
of the metal depended on the frequency of light. He showed that the number of ejected electrons depended on the intensity of light
(which was proportional to the number of photons), but the kinetic energy of the emitted electrons depend on the frequency of the
light source (predicted by photon theory, E = h f)) and not the intensity of the light source (predicted by wave theory).
Kinetic Energy of Electron
If light is a particle (found experimentally)
If light is a wave (not found experimentally)
fo
frequency (Hz)
The graph above (solid line) shows that if light acts as a particle (photon) the kinetic energy of the electrons leaving the surface of the
metal will go up in proportion to the frequency.
A few photons of blue or violet light can eject a few electrons, but hordes or red or orange photons cannot eject a single electron.
Only high-frequency photons have the concentrated energy needed to pull loose an electron.
Einstein’s explanation for the photoelectric effect was verified 11 years later by American physicist Robert Millikan. Every aspect of
Einstein’s interpretation of the photoelectric effect was confirmed, including the direct proportionality of the photon energy to
frequency. It was for this that Einstein received his first Nobel Prize in Physics.
The Speed of Light in Transparent Materials and Refractive Index
Electrons in glass have a natural vibration frequency in the ultraviolet range. When ultraviolet light shines on glass, resonance occurs as the
wave builds and maintains a large vibration between the electron and the atomic nucleus, just as a large vibration is built when pushing
someone at the resonant frequency on a swing. The energy received by the atom can be passed on to neighboring atoms by collisions, or
reemitted as light.
If ultraviolet light interacts with an atom that has the same natural frequency, the vibration amplitude of its electrons becomes unusually large.
The atom typically holds on to its energy for quite a long time (about 1 million vibrations or 100 millionths of a second). During this time the atom
makes many collisions with other atoms and gives up its energy in the form of heat. That’s why glass is not transparent to ultraviolet.
But when the electromagnetic wave has a lower frequency than ultraviolet, as visible light does, the electrons are forced into vibration with
smaller amplitudes. The atom holds the energy for less time, with less chance of collision with neighboring atoms, and less energy is transferred
as heat. The energy of the vibrating electrons is reemitted as transmitted light. (see diagram below) Glass is transparent to all frequencies of
visible light. The frequency of the reemitted light passed from atom to atom is identical to that of the light that produced the vibration
to begin with. The main difference is a slight time delay between absorption and reemission.
The time delay results in a lower average speed of light through a transparent material as shown in the diagram below. Light travels at different
average speeds through different materials. In water light travels at about 75% of its speed in a vacuum, or 0.75c. In glass light travels at about
0.65c, depending on the type of glass. In a diamond light travels at only 0.40c, less than half its speed in a vacuum. When light emerges from
these materials into the air, it travels at its original speed, c.
The ratio of the speed of light in a vacuum to the speed v in a given material is called the index of refraction, n, of the material
n=c/v
Example
What is the approximate index of refraction of water?
nwater =
c / vwater = c / (0.75 c) = 1 / 0.75 = 1.33