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Light

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Title: Light


1
Light
  • Light Transmission
  • Thin Films Thin Films Interference
  • Luminosity
  • Polarized Light
  • Plancks Constant
  • Coherent Light
  • Lasers
  • Holograms
  • Luminous Flux
  • Illuminance
  • Luminous Intensity
  • Luminous Flux vs. Power
  • Luminous vs. Illuminated
  • Wave Vs. Particles
  • Electromagnetic Waves
  • Frequency and Wavelength
  • Michelson-Morely Experiment
  • Light Vs. Sound
  • Space Travel The Speed of Light
  • Why Objects Have Color
  • Primary and Secondary Colors
  • Light Colors Vs. Pigments
  • The Electromagnetic Spectrum
  • Parallax and Depth Perception

2
Light Introduction
For centuries the nature of light was disputed.
In the 17th century, Isaac Newton proposed the
corpuscular theory stating that light is
composed of particles. Other scientists, like
Robert Hooke and Christian Huygens, believed
light to be a wave. Today we know that light
behaves as both a wave and as a particle. Light
undergoes interference and diffraction, as all
waves do, but whenever light is emitted, it is
always done so in discreet of packets called
photons. These photons carry momentum, but not
mass.
Isaac Newton
Robert Hooke
Christian Huygens
3
Wave Vs. Particles
Light is an electromagnetic wave. As light
travels through space an electric field and a
magnetic field oscillate perpendicular to the
wave direction and perpendicular to each other.
Well learn more about these fields in later
units. A light wave is transverse rather than
longitudinal, since each field oscillates in a
plane perpendicular to the direction of the wave.
Unlike a pulse traveling down a length of rope,
nothing is physically moving in a light wave.
Light requires no medium! It can travel through
space that contains matter (such as air, glass,
or water) or through a vacuum.
If light did need a medium in order to propagate,
the earth would spend its days submerged in
darkness and the sun would not be visible.
4
Electromagnetic Waves
Electric and magnetic fields affect charges.
Light is an electric field coupled with a
magnetic field. The two fields oscillate
together but in different planes. To visualize
an electromagnetic wave, you must think in 3-D.
Lets put a light wave together one piece at a
time.
Above is a set of 3-D coordinate axes. The z
-axis is vertical, the y-axis is horizontal, and
the x -axis is coming out toward you.
5
Electromagnetic Waves (cont.)
The red wave represents an oscillating electric
field in the y-z plane. (Every point on this
curve has an x coordinate of zero.) It is a
snapshot in time. At the crests and troughs, the
electric field will exert the greatest force on a
charge, but in opposite directions. Charges
located at the y -intercepts will experience no
electric force (at this point in time).
6
Electromagnetic Waves (cont.)
In the top right picture, the blue wave
represents an oscillating magnetic field in the
x-y plane. (Every point on this curve has an z
coordinate of zero.) It is a snapshot in time.
Like the electric field, the magnetic field is
strongest at the crests and troughs.
Bottom right is shown an electric and a magnetic
field oscillating together. This is an
electro-magnetic wave (light). The fields travel
through space together. They have the same
period and wavelength, but they oscillate in two
different planes, which are perpendicular to each
other. The electric field, the magnetic field,
and the wave direction are all mutually
perpendicular. For some additional pictures,
check out these links below. Remember, what
youre seeing is just a snapshot in time (see
animation).
Wave Pic Light animation Propagation in matter
Oscillating charge animation
7
Frequency and Wavelength
The frequency of a light wave corresponds to the
color we see. The amplitude corresponds to
brightness. The frequency of visible light is
extremely high compared to that of audible sound.
Red light, for example, is the lowest frequency
of visible light, but even red light has a
frequency of over 400 trillion Hertz. This means
if youre looking at a red light, over 400
trillion full cycles of red light enter your eye
every second! The frequency of violet light is
even higherover 750 trillion Hz. Other types of
electromagnetic radiation, like X-rays, have even
higher frequencies, and some have lower
frequencies, like radio waves. Just as our ears
are only capable of hearing certain range of
sounds (20 20,000 Hz), our eyes can only see a
small range of frequencies.
Light Sound
Frequency Color Pitch
Amplitude Brightness Loudness
8
Frequency and Wavelength (cont.)
Because visible light waves have such high
frequencies, their wave-lengths are very short.
Recall the formula v ?f (wave speed
wavelength ? frequency). Since light of any
frequency always travels at the same speed in a
vacuum, v is a constant. Thus, the bigger f
is, the smaller ? must be. Red light, for
example, has a wavelength of only about 700 nm.
(1 nm 1 nanometer 10-9 m 1 billionth of a
meter.) Violet light has an even smaller
wavelength, since its frequency is higher.
X-rays have still smaller wavelengths. Radio
waves can have very long wavelengths (many
meters) since their frequencies are so low.
High Frequency ? Small Wavelength
Low Frequency ? Long Wavelength
Vacuum speed is constant.
9
Historical Background
  • Before Galileos time (around 1600), many people
    believe that light was infinitely fast. Its so
    fast that it seemed like it took no time to get
    from one place to another. Galileo and an
    assistant went to the Italian countryside, a mile
    apart, and tried to measure the speed of light by
    timing it. All they could determine was that
    light is much faster than sound.
  • Later that century (around 1667) a Danish
    astronomer named Ole Roemer made the first
    accurate measurement of the speed of light. He
    had been observing one of Jupiters moons, Io
    (which Galileo had discovered). As Io circled
    Jupiter, it would be eclipsed by Jupiter
    periodically. That is, Jupiter would block Ios
    view from Earth at regular intervals. Each time
    Io orbited Jupiter, an eclipse would occur. The
    time between the eclipses was the period of Ios
    orbit. Roemer noticed that the eclipses
    sometimes took a little longer, and sometimes
    they took a little less time. Ios period seemed
    to fluctuate first Io would be behind schedule
    then it would be ahead of schedule. This pattern
    repeated itself every year, which hinted to
    Roemer that the fluctuation had to do with
    Earths motion around the sun.

10
Historical Background (cont.)
Because Jupiter is farther from the sun, it moves
much slower around the sun (recall Keplers third
law). During the six-month period depicted
above, Earth is moving away from Jupiter.
Therefore, the light carrying the information of
the eclipse took a little longer to reach Earth,
since Earth was running away from that light.
At the end of the six months, the light from Io
had to travel an extra distance about equal to
the diameter of Earths orbit. Roemers observed
that Io eclipses were about 8 minutes behind
schedule after six months. Knowing approximately
Earths orbital diameter, Roemer calculated the
speed of light at around 125,000 miles per
second! Roemers speed, as great as it was, was
actually an underestimate. The true speed of
light is just a half a smidgeon under 3 108
m/s, which is about 186,300 miles per second! We
call this speed c. c 2.9979 ? 108 m/s ? 3
? 108 m/s
11
Historical Background (cont.)
  • Roemers main contribution was proving that the
    speed of light is finite. Since Roemer, several
    people contributed to determining the precise
    value for c. In 1849 Louis Fizeau found an
    excellent approximation for c without resorting
    to astronomical means. He used a rapidly
    rotating, toothed wheel. He shined a beam of
    light through one opening between the teeth,
    which reflected off a mirror over 5 miles away.
    When the wheel spun fairly slowly, the light
    could easily pass through the opening, reflect,
    and pass through it again in the other direction
    before its path was blocked by the next tooth of
    the wheel. By making the wheel spin faster and
    faster until the reflected beam of light was
    blocked, Fizeau was able to calculate c.
  • Jean-Bernard Foucault also made accurate
    measurements of c. He shined light at a
    rotating mirror, which reflected to a stationary
    mirror, back to the rotating mirror, and finally
    back toward the source. Because the rotating
    mirror turned slightly while the light was
    traveling to the stationary mirror and back, the
    rotating mirror reflected the light at a slight
    angle. This angle allowed him to calculate c.

12
Michelson-Morely Experiment
Albert Michelson is best known for an experiment
he did with Edward Morely in 1887. At the time it
wasnt understood that light needed no medium
through which to travel. It was proposed that
light traveled through an invisible ether in
space. The Michelson-Morely experiment was an
attempt to detect Earths motion through the
ether. Heres how it worked First imagine youre
standing still outside and there is a wind coming
from the north. If you run north, youll measure
a greater wind speed. If you run south, youll
measure it slower. Whether you run north or
south, though, youll still feel the wind coming
from the north. If you run east or west, however,
not only will the wind seem to change speed, so
will its direction.
Now imagine a race between two equally fast
swimmers. They each go the same distance in a
river, but one goes upstream and back while the
other goes directly across the river and back.
With no current the race would definitely be a
tie, since their speeds and distances are the
same. With a current, however, the cross-stream
swimmer will win. This is not obvious. You
should try to prove this. For a hint see the
river crossing--relative velocities slide from
the presentation on vectors. It involves the same
principle as Michelsons interferometer (but
without lasers). Michelson-Morely
Experiment
13
Michelson-Morely Experiment (cont.)
Michelson built something called an
interferometer to try to measure a change in the
speed of light in two different directions. The
Earth moving through the ether around the sun is
analogous to a wind or current. Instead of racing
two swimmers, Michelson raced beams of light.
Light was shone onto a mirror that allowed half
of it to pass through. Each beam traveled the
same distance before being reflected back and
allowed to recombine. Based on the interference
pattern of the combined waves, Michelson should
have been able to detect a winner. But no matter
how the experiment was done, the race was always
a tie. This eventually forced physicist to
abandon the ether theory. Einstein resolved the
problem in 1905 with his theory of special
relativity. In it he asserts that the speed of
light is the same no matter how fast or which way
an observer is moving.
Michelson
Einstein
14
Light Vs. Sound
It is important to emphasize just how fast light
is. Compared to light, sound is a snail. A wise
person once said, Light travels faster than
sound, which is why some people appear bright
until you hear them speak. Have you ever watched
a baseball game from a distance? You see the
batter make contact with the ball, but the sound
of the wallop is delayed. This is because,
although sound is really fast, light is
super-duper fast. For all practical purposes,
when you see something is when it happened (at
least for events here on Earth). You can
determine how far away a lightning strike is by
counting seconds from the time you see the
lightning until you hear the thunder. It takes
sound about 5 s to travel a mile, so if the
thunder lags behind the lightning by 2 or 3 s,
then the lightning strike occurred about half a
mile away. Problem You hear a thunder clap 6
s after you see the lightning. Assume the speed
of sound to be 343 m/s. How far away is the
lightning?
(Solution on next slide)
15
Light Vs. Sound (cont.)
Answer Ignoring the small amount of time light
needs to travel to you, we have d v t
(343 m/s) (6 s) 2058 m Problem Now lets do
the same problem without ignoring lights travel
time
Sound Waves
Light Waves
Solution on next slide ?
16
Light Vs. Sound (cont.)
Answer Let t time it takes the light to
reach you. In that time the sound of the thunder
only travels a short distance. Since you hear
the thunder 6 s after you see the lightning, the
sound travels for (6 s) t. The light and
sound each travel the same distance, so 343
(t 6) (3 108) t ? t
6.8600078 10-6 s ? d 2058.0024
m So, the lightning strike really occurred a
couple millimeters farther away than we had
calculated the first way. Note The difference
in results is meaningless here since we cant
know the time delay or the speed of sound to as
many significant digits as our answer has.
17
Space Travel The Speed of Light
We cant always ignore the time light takes to
travel. Whenever you look into the night sky, for
example, youre really looking back into time.
The stars you see are so far away that the light
they emit takes years to reach us. Nearby stars
are tens or hundreds light-years away. A
light-year is the distance light travels in one
year, almost 6 trillion miles. (Our sun is only
about 8 light-minutes away). Problem Schmedrick
is on a space journey heading toward Alpha
Centauri, the nearest star excluding the sun,
which is about 4.3 light-years away.
Schmedrick's rocket goes a constant 0.03 c (3
of the speed of light). As he passes Alpha
Centauri he sends a radio message back to Earth
and continues traveling away from Earth. The
Earthlings reply immediately. How long must
Schmedrick wait for his reply?
Solution on next slide ?
18
Space Travel The Speed of Light (cont.)
Answer Since we know a trip back and forth from
Alpha Centauri takes a total of 8.6 years, we can
set up our equation in the following way d vt
(c 1 in light years per year) 8.6 v
t c t ? 8.6 0.03 c t c t ? 8.6 0.03 t
t ? 8.6 0.97 t ? 8.6 / 0.97 8.87
Schmedrick will have to wait 8.87 years to
get a reply back from earth. Links Find out
more about Alpha Centauri here.
A. C.
S.
v t
4.3 ly
19
Why Objects Have Color
Visible light is a combination of many
wavelengths (colors), which give it a white
appearance. When light hits an object certain
wavelengths are reflected and others are
absorbed. The reflected wavelengths are the ones
we see and determine the color of an object.
In the first picture the tomato absorbs blue and
green wavelengths and reflects the red
wavelength. In the second picture red light is
shone upon the tomato. The tomato is still
reflecting the red wavelength and thus still
looks red. But in the 3rd picture blue light is
shone upon the tomato, and since the tomato
absorbs the blue wavelength the tomato appears to
be black.
Links Prism (light broken down in different
wavelengths.
20
Primary and Secondary Colors
The primary light colors are Red, Blue, and Green
(RGB). The secondary light colors are Yellow,
Cyan, and Magenta. Combining pigments in painting
is exactly the opposite The primary pigments
are Yellow, Cyan, Magenta. The secondary pigments
are Red, Blue and Green.
Animation
21
Light Colors Vs. Pigments
Primary colors in light are red, green, and blue
because when put together in the right
intensities they form white light. Televisions
use this idea to project pictures on the screen.
When lights these colors are combined in pairs
they form the secondary colors for
light. Pigment colors are seen by reflected
light. A primary pigment color is one that
absorbs only one primary light color and reflects
the other two primary colors. Thus yellow,
magenta, and cyan are the primary colors for
pigments. Yellow reflects red green, cyan
reflects green blue, and magenta reflects red
blue. Secondary pigments colors then are blue,
green, and red because they absorb two primary
light colors and reflect their own light color
back.
22
The Electromagnetic Spectrum
The electromagnetic spectrum covers a wide range
of wavelengths and photon energies. Visible light
ranges from 400 to 700 nanometers. About 550
nanometers, which is a yellowish green, is the
wavelength to which our eyes are most responsive.
Only a small portion of the electromagnetic
spectrum is visible to us. The smaller the
wavelength, the more energy each photons of the
light has.
23
Electromagnetic Spectrum (cont.)
Wavelengths other that visible light serve useful
purposes
Radio waves are very long (a few centimeters to 6
football fields) and can be used to send signals.
These signals are transmitted by radio stations.
They transmit information and music via amplitude
modulation (AM) and frequency modulation (FM).
Microwaves (a few millimeters long) are also used
in communications. Microwave ovens are great for
heating food since food is primarily water, and
microwaves have just the right frequency to get
water molecules vibrating.

Infrared (micrometers in length) are used in
remote controls to change the channel, and they
are also radiated by objects that are warmer than
their surrounding (like your body). They make
night vision equipment possible.
Ultraviolet light is harmful to our bodies
because its wavelength is so small. Short
wavelength mean high energy for photons. UV
causes our skin to tan and burn. Fortunately, the
ozone layer blocks most UV radiation, but
prolonged exposure to the sun should be avoided,
since UV rays can cause skin cancer. On the
positive side UV radiation helps people to
produce their own vitamin D.
24
Electromagnetic Spectrum (cont.)
X-rays are even more energetic, and hence more
dangerous, than UV rays, but luckily they cannot
penetrate our ozone layer. They are produced in
space and of course are used by doctors to get
pictures of your bones.
Gamma rays are the most energetic of the light
waves and little is known about them other than
they are very harmful to living cells and are
used by doctors to kill certain cells and for
other operations. They are produced in nuclear
explosions. Like other high energy rays, our
atmosphere protects us from gamma rays.
Astronomers have many different types of
telescopes at their disposal to observe the
universe in all parts of electromagnetic
spectrum. Some telescopes are ground-based
others are space-based
Arecibo Spitzer Hubble Keck Compton
25
Parallax and Depth Perception
Parallax is any alteration in the apparent
position of an object due to a change in the
position of the observer. A simple demonstration
of this effect can be seen by extending your
thumb at arms length. Then close one eye at a
time and note how your thumb appears to jump left
and right relative to the background. Now move
your thumb closer and note how the jump is
greater. This technique can be used in astronomy
to find a stars distance from Earth. For distant
objects like stars, astronomers must move their
eyes as far apart as possible. They accomplish
this by observing the apparent displacement of a
star against the background of more distant stars
resulting from the change of the Earths position
in orbit. The parallax angle is exaggerated in
the picture below.
?
?
? ?
26
Parallax and Depth Perception (cont.)
The picture is not to scale. The diameter of
Earths orbit is very small compared to the
distance of the star being measured, which in
turn is very small compared to the distance of
the background stars. For this reason the angular
displacement of points A and B, as seen from
Earth at any point in its orbit, is almost
exactly the same as the parallax angle.
Problem Back on Earth Schmedrick attempts to
figure out how far away a certain distant star
is. He figures out a 2 degree parallax angle from
two different observations made during the
earths period. How far away is the star? (Earth
93 million miles from the sun.)
Solution on next slide.
A
2o
B
27
Parallax and Depth Perception (cont.)
Answer Let R be the Earth-sun distance and x
the distance to the star in question. Thus,
tan (? / 2) R / x. With ? 2? and R 93
million miles, x ? 5.33 ? 109 miles The
Star Schmedrick is looking at is approximately 5
billion miles away. So, Schmed must have been
imagining this star, because its much too close
for any real life star (other than the sun).
R
2 o
x
28
Luminous vs. Illuminated
A luminous object is a body that produces its own
light such as the sun or a light bulb. An
illuminated object is a body that reflects light,
just like the moon, people, and buildings. Some
objects, like water and glass, transmit light to
some extent. In order to be seen, light must come
from an object one way or the other.
29
Luminosity Magnitude
Luminosity is the rate at which energy of all
types, and in all directions, is radiated by an
object. The luminosity of a star depends on its
size and its temperature L ? R 2 T 4. The sun is
a medium-sized star with a luminosity of 3.81026
J/s. The known luminosities of stable stars range
from about a millionth that of the sun for a
relatively cool white dwarf to about a million
times that of the sun for the hottest known
super-giant star. Astronomers assign stars
magnitudes based on how bright they are. Apparent
magnitude measures how bright a star appears to
be from Earth. Absolute magnitude measures its
true luminosity.
The brighter the star, the lower its luminosity.
Every 5 magnitudes corresponds to brightness
changing by a factor of 100. For example, a
magnitude 1 star is 10,000 times brighter than a
magnitude 11 star. Besides the sun, the brightest
star as seen from Earth is Sirius with an
apparent magnitude of -1.6.
30
Light Transmission
Transparent Materials, such as window glass,
through which light can travel easily and through
which other objects can clearly be
seen. Translucent Materials, such as glass
blocks, through which light can pass through but
no clear image can be seen. Opaque Materials
which absorb and reflect light. Objects cannot be
seen through the material. Most objects are
opaque.
31
Thin Films Thin Film Interference
The thin film effect refers to colors seen in
such things as soap bubbles and oil spills. It
occurs as a result of the constructive and
destructive interference of light waves, not
because of refraction as in a prism. When light
hits a bubble, some of it is reflected by the
outer (air-soap) interface (ray 1), while some
penetrates the bubble wall and is reflected by
the inner (soap-air) interface (ray 2). The two
reflected rays interfere with one another.
Typically, most wavelengths will be out of phase
since 2 has to travel a greater
Guinness Soap Bubble Records
distance than 1. However, one wavelength will be
in phase and this corresponds to the color
produced. The color depends on how great the
difference in distance is that the two rays
travel, and this distance depends on bubble
thickness. The variations in thickness (thinner
at the top, thicker at the bottom) are
responsible for the different colors.
incident ray
1
2
reflected rays
Continued on Next Slide
Soap Bubble Wall
32
Thin Films (cont.)
When light moving through the air encounters the
denser film the reflected ray is inverted, just
like a pulse traveling down a slinky is inverted
when it reflects at the connection point with a
heavier spring. The transmitted ray is not
inverted, which is also the situation with slinky
and spring. When the transmitted ray encounters
the soap-air interface at the inside of the
bubble, again some of it is reflected back. This
time, however, the wave is not inverted (just as
a pulse traveling on a heavy spring is not
inverted when it reflects at the connection point
with a slinky). The two reflected rays may or may
not be in phase it depends on how thick the film
is.Since white light is comprised of many
wavelengths, those that are nearly in phase after
reflecting off the bubble surfaces will be
reinforced (constructive interference). This is
the color that will appear on the bubble. The
other wavelengths are out of phase (destructive
interference) and are, at least partially,
cancelled out. Since gravity causes the bubble
to be thicker near the bottom, different
wavelengths are reinforced at different heights,
producing bands of colors. Interestingly, a
bubble on the space shuttle will not produce
bands of different colors. This is because the
shuttle is in free fall around Earth, which means
bubbles behavior as if theyre in a gravity-free
environment. Thus, bubbles are of uniform
thickness.
Continued on Next Slide
33
Thin Films (cont.)
So how do we determine which color will be
produced at a particular point on a bubble or
other thin film? Well, if the thickness of the
film is ?/4, then light of wavelength ? will be
reinforced. Heres why The then the round trip
in the film will be ?/2. This means the two waves
will be in phase, since one was inverted and one
wasnt.

Bubble Wall ? /4
Original Wave
Transmitted wave superimposed with upright wave
from 2nd reflection
Inverted wave from 1st reflection superimposed
with upright wave from 2nd reflection
air outside bubble
air inside bubble
34
Polarized Light
Electric Field Orientations
Light coming directly from the sun or other
sources is unpolarized, meaning the electric and
magnetic fields oscillate
Beam o Light
in many different planes. Polarized light refers
to light in which all waves have electric fields
oscillating in the same plane. Imagine trying to
pass a large piece of sheet metal through the
bars of a jail cell. To do this you would have to
orient the sheet vertically (or nearly so),
otherwise the bars would block the sheet. Here,
the bars are analogous to a polarizing filter,
and the sheet is analogous to the plane in which
the electric field is oscillating.
A polarizing filter is made of a material with
long molecules that allow electromagnetic waves
of one orientation through. If a wave has an
electric field with any other orientation, the
filter will only allow a component to pass
through, absorbing the rest. Note that only
transverse waves such as light can be polarized.
Much of the light we see is at least partially
polarized. For example, when light reflects off
of surfaces it is partially polarized. Some
sunglasses contain polarizing filters which helps
to block glare (such as the glare that is
noticeable when looking out over a lake on a
sunny day).
Polarized Light Glare Molecular View

Continued ?
35
Polarized Light (cont.)
Unpolarized light propagates in all orientations.
No particular orientation is preferred. When it
passes through a filter that only allows vertical
components of electric fields to pass, its
intensity is cut in half. This is because, on
average, the light is half horizontal and half
vertical in terms of electric field components.
All horizontal components are blocked, making the
resulting polarized light half as bright. Now,
imagine that you place another filter that is
perpendicular to the direction of the first one,
i.e., a filter that only allows the horizontal
components of electric fields to pass through.
This would completely block the remaining light.
Thus, any two perpendicular filters will block
all incoming light. Suppose now that the two
filters are offset by some angle ?. Regardless
of the angle, the first filter blocks half the
light. If ? 0, the second filter has no effect.
If ? 90?, the second filter blocks the other
half of the light. In gen-eral, when polarized
light with an electric field of amplitude E
passes through the second filter, the amplitude
will drop to E cos?. Furthermore, since the
energy a wave carries is proportional to the
square of its ampli-tude, the intensity of the
light will be the original intensity multiplied
by cos2?.
Blocking Light
Continued on Next Slide
36
Twisting of Light
We know that if ? 90? between two filters, then
no light will make it past the second one. At
other angles light will pass through both,
changing the orientation of its electric field
each time. So, what if we arranged several
polarizing filters so that the angle between any
two consecutive filters is less than 90?? The
answer is that light twists its way through the
filters, even if the angles between the filters
adds up to 90?. With each pass the light is
oriented in a new direction, and this new
orientation has a component parallel to the
orientation of the next filter.
Light Enters
Light Exits
Twisting Light
37
Quantum Mechanic--Background
Recall that a black body is an ideal absorber of
all incident radiation. A hot black body is also
a perfect emitter--radiation is the result of its
temperature, and since none of this is absorbed,
it is a perfect emitter of radiation. A black
body emits all wavelengths of light but not
equally there is always a wavelength in which
the radiation peaks. The hotter the black body,
the
smaller the peak wavelength. Objects around you
are cool, so their peak is in the infrared. The
sun is hot enough to peak in the visible spectrum
(all other wavelengths are emitted too but at
lower intensities). In the late 19th century
classical physics had predicted something
impossible as the temperature rises, the
intensity of the peak radiation approaches
infinity (red dashed line). The theory did match
experimental data for large wavelengths but
failed for small ones. This was known as the
ultraviolet catastrophe.
38
Plancks Constant
In 1900 Max Planck came up with a revolutionary
way to resolve the problem by assuming that
energy came in discrete amounts (quanta). This
was the beginning of quantum mechanics. Each
quantum of light is called a photon, and its
energy is given by E h f, where f is the
frequency of the radiation and h is the
constant of proportionality called Planks
constant. The formula states that higher
frequency light has proportionally more energy
per photon. Einstein lent credence to Planks
ideas by explaining the photoelectric effect in a
similar manner. Robert Millikan did a series of
experiments involving the photoelectric effect
and calculated the constant h 6.626 ? 10-34
J s.
Max Plank
Before Planck light was considered to be a wave.
Today we know it can be interpreted as either a
particle or a wave. As a wave, bright light can
be explained as a large amplitude in the electric
and magnetic fields. As a particle, bright light
would be explained by a large number of photons.
39
Coherent Light
Lamps, flashlights, etc all produce light. But
this light is released in many directions, and
the light is very weak and diffuse. In coherent
light the wavelength and frequency of the photons
emitted are the same. The amplitude may vary.
Such things as lasers and holograms are composed
of coherent light.
Incoherent
Coherent
40
Lasers
Laser stands for light amplification by
stimulated emission of radiation. A laser is a
device that creates and amplifies a narrow,
intense beam of coherent, monochromatic (one
wavelength) light. Heres how they work. There
are 2 primary states for an atom, an excited
state and a ground state. The ground state is the
lowest energy, most stable state. In the excited
state electrons are in a higher energy level. In
a laser, the atoms or molecules of a crystal
(such as ruby) or of a gas, liquid, or other
substance are excited in the laser cavity so that
more of them are at higher energy levels (excited
state) than are at lower energy levels. When an
excited electron drops back to a lower energy
level, a photon of a particular wavelength is
released. This photon stimulates other electrons
to emit photons. All these photons are in phase.
41
Holograms
As with any type of wave, light waves can
interfere with one another. The interference of
two or more waves will carry the whole
information about all the waves. It is on this
basis that holograms work. Holograms make use of
lasers and they work in the following fashion
(Explanation on next slide.)
Beam Splitter
Laser
Mirror
Reference Beam
Object Beam
Light wave interference
Beam Spreader
Film Plate
Object
42
Holograms (cont.)
As the laser hits the beam splitter, it is split
in two. The object beam heads towards the object
of interest, while the reference beam heads
toward a mirror. The beams are identical until
the object beam shines on the object. There some
of the light is absorbed some is reflected
toward the film. After reflecting off the mirror,
the reference beam is reunited with the object
beam on the film. Because one beam interacted
with the object and the other didnt, the two
beams will be out of phase and interfere with one
another. This interference pattern is imprinted
upon the holographic film plate, creating the
holographic image. This pattern records the
intensity distribution of the reflected light
just as an ordinary camera does. However, it also
records the phase distribution. This means that
it contains information about where the waves are
in their oscillating cycles as they strike the
film. To determine this the object beam must be
compared with the reference beam. This is
accomplished via the interference. Also unlike an
ordinary photo, a hologram contains all its
information in every piece of it. When viewed in
coherent light the object appears in 3-D and
viewing a hologram from different angles will
reveal the object from different angles.
43
Luminous Flux Illuminance
Luminous flux, ?, is the rate at which an object
emits visible light (adjusted to the
responsiveness of the human eye, which is most
sensitive to yellow-green). It is measured in
lumens. Imagine a light source in the center of a
sphere. Luminous flux is the quantity of light
that hits the surface of the sphere per unit
time. The size of the sphere is irrelevant. If
the sphere were larger, the same quantity of
light would reach the surface every second, so
the flux wouldnt change. However, this light
would be more spread out, so the illuminance of
the surface would be less than it was with the
same candle in the smaller sphere. Also called
illumination, the symbol for
illuminance is E, not to be confused with energy,
and is defined as luminous flux per unit of
surface area E ? / S. The SI unit for
illuminance is the lux, which is a lumen per
square meter. The illuminance of the sun is about
100,000 lx (lux) for the full moon its about
0.2 lx. A common, non-SI unit for illuminance is
the foot-candle, which is equivalent to about
10.8 lx.
44
Illuminance vs. Distance
A point source at P radiates light in all
directions. The pic below shows how light spreads
out as it radiates. If the illuminance on the
sheet 1 m from P is 1 unit, then the illuminance
on the sheet 2 m from P is four times less. This
is because doubling the distance increases the
area by a factor of four over which the light is
spread. Similarly, 3 m from P the illuminance is
nine times less, and 4 m from P its 16 times
less. Note the flux (amount of light) is not
changing, but the illuminance is because the same
amount is spread over different areas. In
general, E is proportional to ? and inversely
proportional to the square of the distance. This
is reminiscent of Newtons inverse square law for
gravitation.
45
Solid Angles
arc length 1 unit
angle 1 radian
We can measure ordinary, flat angles by the
ratio of arc length of a circle to the radius of
the circle. Imagine two radii shooting out from
the center, subtending part of the circumference.
By definition this ratio is the measure of the
angle between the radii in radians. There are 2 ?
radians in a circle since C 2 ? r. Now imagine
a sphere instead of a circle and a cone shooting
out from the center rather than a two radii (the
apex of the cone is at the center). Instead of
part of a circum-ference, the cone subtends part
of the surface area of the sphere. A solid angle
(measured in steradians) is defined as the ratio
of the subtended surface area of the of sphere to
the square of its radius. This definition applies
even if the subtended area is not circular. There
are 4 ? steradians in a sphere since S 4 ? r 2.
radius 1 unit
46
Luminous Intensity
Recall that illuminance is flux per unit area. A
related quantity is luminous intensity, I, which
is defined as flux per unit of solid angle. Thus,
I Ø / 4 ?, since there are 4 ? steradians in a
sphere. You can think of luminous intensity as
the amount of light contained within a cone whose
apex is at the source. The same amount of light
confined to a skinnier cone would mean a greater
intensity. Just as the flat angle is
independent of the size of the circle, the solid
angle is independent of the size of the sphere.
The intensity is the same at every sheet in the
pic below. In a sphere 7 m in radius, I is the
flux that falls on a 49 m2 surface on the sphere.
The SI unit for intensity is the candela, cd.
1 cd 1
lumen per steradian. A footcandle is the

illuminance one foot away from a 1 candela
source.
47
Efficiency of light sources
Light sources, like light bulbs, vary in
efficiency. This means that some bulbs, e.g.
fluorescent bulbs, will produce more light while
using less energy. (They can do this by producing
less waste heat.) The efficiency of a simple
machine is the work done by the machine divided
by the work put into it. In this context,
efficiency is the rate at which light is produced
by the bulb divided by the rate at which energy
is used to produce that light eff Ø / P, where
P is power. Note that both flux and power are
rates, so eff is really light over energy. It
is measured in lumens per watt. A typical candle
has an efficiency of about 0.1 lumen / W.
Incandescent bulbs are about 15 lumen / W, but a
fluorescent bulb is closer to 70 lumen / W. A
monochromatic source emitting light of around 555
nm in wavelength would be the ideal in terms of
efficiency, with all of its radiation being
visible to us instead of infrared (waste heat).
48
Credits
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49
Credits (cont.)
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ml
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