Light
•Wave Vs. Particles •Light Transmission
•Electromagnetic Waves •Thin Films & Thin Films
Interference
•Frequency and Wavelength
•Michelson-Morely Experiment •Luminosity
•Light Vs. Sound •Polarized Light
•Space Travel & The Speed of •Planck’s Constant
Light •Coherent Light
•Why Objects Have Color •Lasers
•Primary and Secondary Colors •Holograms
•Light Colors Vs. Pigments •Luminous Flux
•The Electromagnetic Spectrum •Illuminance
•Parallax and Depth Perception •Luminous Intensity
•Luminous Flux vs. Power
•Luminous vs. Illuminated
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.
Robert Hooke Christian Huygens Isaac Newton
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. We’ll 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.
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. Let’s 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.
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).
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 Wave Pic Light animation
additional pictures, check out these
links below. Remember, what Propagation in matter
you’re seeing is just a snapshot in
time (see animation). Oscillating charge animation
Frequency and Wavelength
The frequency of a light wave corresponds to the color we see. The
amplitude corresponds to brightness.
Light Sound
Frequency Color Pitch
Amplitude Brightness Loudness
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 you’re 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 higher—over 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.
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.
Historical Background
• Before Galileo’s time (around 1600), many people believe that
light was infinitely fast. It’s 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 Jupiter’s moons, Io (which
Galileo had discovered). As Io circled Jupiter, it would be eclipsed
by Jupiter periodically. That is, Jupiter would block Io’s view from
Earth at regular intervals. Each time Io orbited Jupiter, an eclipse
would occur. The time between the eclipses was the period of Io’s
orbit. Roemer noticed that the eclipses sometimes took a little
longer, and sometimes they took a little less time. Io’s 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
Earth’s motion around the sun.
Historical Background (cont.)
Because Jupiter is farther from the sun, it moves much slower
around the sun (recall Kepler’s 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 Earth’s orbit.
Roemer’s observed that Io eclipses were about 8 minutes behind
schedule after six months. Knowing approximately Earth’s orbital
diameter, Roemer calculated the speed of light at around 125,000
miles per second! Roemer’s 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
Historical Background (cont.)
• Roemer’s 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.
Michelson-Morely Experiment
Albert Michelson is best known for an experiment he did with Edward Morely
in 1887. At the time it wasn’t 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 Earth’s
motion through the ether. Here’s how it worked: First imagine you’re standing
still outside and there is a wind coming from the north. If you run north, you’ll
measure a greater wind speed. If you run south, you’ll measure it slower.
Whether you run north or south, though, you’ll 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 Michelson’s interferometer (but without lasers).
Michelson-Morely Experiment
Michelson-Morely Experiment (cont.)
Michelson built something called an interferometer Michelson
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 Einstein
which way an observer is moving.
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)
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 let’s do the same problem without ignoring light’s travel
time:
Light Waves Sound Waves
Solution on next slide
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 can’t know
the time delay or the speed of sound to as many significant
digits as our answer has.
Space Travel & The Speed of Light
We can’t always ignore the time light takes to travel. Whenever you
look into the night sky, for example, you’re 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
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 A. C.
8.6 = 0.97 t S.
8.6 / 0.97 = 8.87
vt
4.3 ly
Schmedrick will have to wait 8.87 years to get a reply back
from earth.
Links: Find out more about Alpha Centauri here.
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.
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
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.
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.
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.
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
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 arm’s 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 star’s 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 Earth’s position in orbit. The
parallax angle is exaggerated in the picture below.
Parallax and Depth Perception (cont.)
The picture is not to scale. The diameter of Earth’s 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 earth’s
period. How far away is the star? (Earth 93 million miles from the
sun.) Solution on next slide.
A
2o
B
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 it’s
much too close for any real life star (other than the sun).
R
2o
x
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.
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 3.8×1026 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.
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.
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
Guinness Soap Bubble Records
phase since #2 has to travel a greater
distance than #1. However, one wavelength will be in
incident ray phase and this corresponds to the color produced.
The color depends on how great the difference in
#1 distance is that the two rays travel, and this distance
#2 depends on bubble thickness. The variations in
reflected thickness (thinner at the top, thicker at the bottom)
rays are responsible for the different colors.
Soap Bubble Wall Continued on Next Slide
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 they’re in a gravity-free environment.
Thus, bubbles are of uniform thickness.
Continued on Next Slide
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. Here’s 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 wasn’t.
Bubble Wall
/4
Original Wave
Transmitted
wave
superimposed
with upright
wave from 2nd
Inverted wave reflection
from 1st reflection
superimposed
with upright wave
from 2nd reflection
air outside bubble air inside bubble
Polarized Light
Light coming directly from the sun or Electric Field
other sources is unpolarized, meaning Orientations
the electric and magnetic fields oscillate
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
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
“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
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.”
Planck’s 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 Plank’s constant. The formula states
that higher frequency light has proportionally more energy
per photon. Einstein lent credence to Plank’s ideas by
explaining the photoelectric effect in a similar manner.
Robert Millikan did a series of experiments involving the
Max Plank photoelectric effect and calculated the constant:
h = 6.626 10-34 J s.
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.
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
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.
Here’s 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.
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.)
Laser Beam Splitter
Mirror
Reference Beam
Object Beam
Light wave
Beam Spreader
interference
Film Plate
Object
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 didn’t,
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.
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 wouldn’t
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 it’s about 0.2 lx. A common, non-SI
unit for illuminance is the foot-candle,
which is equivalent to about 10.8 lx.
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 it’s 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 Newton’s inverse
square law for gravitation. 1/16
1/9
1/4
1
P 1m 2m 3m 4m
angle = arc length = 1 unit
Solid Angles
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 radius
part of the circumference. By definition this = 1 unit
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.
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.
P 1m 2m 3m 4m
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).
Credits
Numerous Images as well as information were obtained from the following sources:
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Credits (cont.)
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