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Projekt z Obrazového inženýrství
Téma:
Vlastnosti
Jméno: Filip Mravec
světla a měření rychlosti světla
Datum:
Předmluva
Tato práce je koncipována do dvou myšlenkových okruhů. V prvním jsou velmi
zběžně zmíněny vlastnosti elektromagnetického záření a jejich fyzikální popis. Aplikace
jednotlivých vlastností byly ponechány pro konkrétní případy využití vlastností světla.
V druhé části jde o pohled do historie, přehled a postupy používaných metod stanovení
ryclosti světla.
Obsah
A. Vlastnosti světla
A1 Elektromagnetická vlna
A2 Difrakce
A3 Odraz
A4 Lom
A5 Inerference
A6 Koherence
A7 Polarizace
B Měření rychlosti světla
B1 Historie
B2 Michelsonův pokus
B3 Moderní metody
B4 Myšlenkové experimenty + zařízení
B5 Rychlost světla v různých prostředích
B6 Tabulka změřených hodnot
A1. Elektromagnetická vlna
Light Fundamentals
Characteristics of light as electromagnetic radiation:
1. it travels through a vacuum
2. its speed in a vacuum is 3 x 108 m/s
3. visible light ranges from 700 nm for red light to 400 nm for violet (blue) light where
1 nanometer = 1 x 10-9 m
electromagnetic spectrum written in order of decreasing wavelength and
increasing frequency
radio & TV , microwave, IR (infrared, or light with wavelength greater than 700 nm),
visible light (light with wavelengths between 400 and 700 nm), UV (ultraviolet, or
light with wavelength shorter than 400 nm), X-ray, gamma
o colors of visible light: red, orange, yellow, green, blue, indigo, and violet
Theories of light:
1. Newton's corpuscular theory: Newton predicted that light behaved like a particle,
called a corpuscle. Newton's theory supports reflection.
2. Wave theory (Maxwell): light is an electromagnetic wave. The wave theory supports
reflection, refraction, interference, and diffraction. Proof that light has a wave nature -only a wave can interfere and diffract.
Modern theory: dual nature of light. Light acts like a particle when it transfers or absorbs
energy; light acts like a wave when it moves through space. Einstein described the particle
nature of light. In his equation, E = hf, he describes the energy E of a particle and the
corresponding frequency f of the wave. Proof that light has a particle nature -- photoelectric
effect, Compton effect, pair production, and emission spectra.
Maxwell's Equations Maxwell showed that light is a traveling configuation of electric and
magnetic fields. He formulated differential equations that proved that electromagntic fields
spread in the form of polarized waves and at the speed of light. The speed of light is related to
purely electric and magnetic quantities.
Where µo and εo are the permeability of free space(µo = 4π x 10-7 T m/A) and
permittivity of free space (εo = 8.85 x 10-12 C2/N m2)
What is Light?
Light is a form of energy produced by the change in motion of a charged particle. Light does
not need a medium (solid, liquid or gas) in order to travel. Electrons moving back and forth
will cause light. When the electrons inside of an atom absorb energy they jump to a different
energy level. When these electrons fall back down to their original energy level they give off
a little packet of energy in the form of light. This packet of light energy is called a photon.
Light can either travel as a wave or as a particle. We will be studying how light behaves as a
transverse wave.
Some objects produce their own light will other objects reflect light. These sources of light
are called luminated objects. Sources of light include: the sun, a light bulb, a match and a
candle. Bioluminescent organisms are living things that can produce their own light. A
firefly is an example of a bioluminescent organism. Objects that reflect certain amounts of
light are called illuminated objects. Objects that reflect light include: a mirror, the moon and
a piece of paper.
What is so amazing about light is the speed at which it travels. Light travels 186,000miles per
second or 299,798 kilometers per second. That means light can travel a distance of 186,000
miles in one second! It takes eight minutes for light from the sun to reach earth. This is why
you hear lightening before you see thunder. Lightening and thunder happen at the same time,
yet light travels faster than sound so you see the lightening then a few seconds later you hear
the thunder.
Jednotlivé oblasti elektromagnetického spekta:
Gamma Rays
Gamma rays have the smallest wavelength and the most energy out of the entire
electromagnetic spectrum. These rays are very powerfull and can kill living tissue. Gamma
rays are used in therapy to kill cancer cells.
X-Rays
If you have ever broken a bone you have had an x-ray done to see what the break looks like.
Can you make out the image to the left? It is a left hand with a ring on the finger. An X-ray
camera works like any other camera except it gives off invisible energy rays called X-rays.
These X-rays travel through your skin. An X-ray camera won't work unless it finds something
hard to stop the rays. The X-rays bounce off of your bone and back to the camera. The x-ray
picks up the dense parts of the bone. The denser the bone, the more rays that were bounced
back, the lighter the bone appears on the "film." (The picture to the left is reversed.)
Ultraviolet Rays
These rays are responsible for giving us a tan or a sunburn when we sit outside. Long time
exposure to these rays can cause skin cancer.
This is the only portion of the visible spectrum that you are able to see. The colors of the
spectrum include: Red Orange Yellow Green Blue Indigo Violet.
Red having the least amount of energy and the longest wavelength and violet having the most
energy and the shortest wavelength. All the colors you see are from this little portion of the
electromagnetic spectrum.
Radio Waves
When you listen to the radio or watch T.V. you are using a part of the electromagnetic
spectrum with lowest energy and a long wavelength. When you turn the dial on your radio
you are adjusting to the same frequency as the radio station. Radio stations are either
amplitude modulation (AM) or frequency modulation (FM). Your favorite T.V. shows use a
combination of both, AM for the sound and FM for the picture.
Microwaves
These waves carry more energy than radio waves. These waves are responsible for heating
your food. They are also responsible for communications (satellites, cell phones etc…) and
radar.
Infrared Waves
This is an image of the infrared waves felt as heat from a human body. These waves are heat
waves. You can feel the warmth from the sun as infrared waves. Restaurants use infrared
waves to keep food warm after it has been cooked. These waves have a higher frequency and
shorter wavelength than microwaves. These waves are called infrared because they have a
frequency slightly longer than that of visible light.
Light terms:
transparent
transmits light readily
translucent
transmits light with distortion
opaque
doesn’t transmit light (it is absorbed or reflected)
spectrum
band of colors produced when light is broken into its constituent wavelengths
dispersion
scattering of light. A prism will separate whitle light into a rainbow of colors. When
incident upon a prism, the wavelengths of light are bent (or refracted) to varying
degrees. Violet light is bent them most and red light is bent the least. Rainbows are an
example of dispersion produced by drops of water.
•
•
•
•
•
color
the color of an opaque object is due to the color that it reflects.
A black object absorbs all color and a white object reflects all color.
The color of a transparent object is due to the combining of transmitted light colors.
Primary colors of transmitted light
red, green, and blue combine to form white light
Secondary colors
produced by combining two primary colors
yellow, cyan, and magenta
Complementary colors
produced by combining a primary color and a secondary color to form white light
An applet that allows you to mix colors and pigments. Color
The colors of a thin film result from the interference of light reflected from the front
and the back surfaces of the thin film. When the film thickness equals Ľ λ, that color
of light will be constructively interfered with as it reflects from the two surfaces of the
film. All others will be destructively interfered with.
Polarized light waves are either vertical or horizontal. They are produced by passing
light through a polarizer.
• Polarizer produces polarized light by allowing only vertical or horizontal light waves
through.
Analyzer polarizer whose orientation differs by 90 degrees; when a polarizer and analyzer are
used, no polarized light will be transmitted. The analyzer absorbs polarized light.
Light as wave
If we think of this figure as representing the electrical energy present in the light
waveform as it travels in the direction of the arrow, it looks as if the energy level is
becoming alternately positive and negative, with momentary crossovers of zero
electrical energy. In the basic model of light shown here, this is in fact the case; as
with all electromagnetic waves, light energy is constantly changing its form
between electrical energy and magnetic energy. The point of maximum magnetic
energy coincides with the moment of zero electrical energy. Beyond that instant,
energy shifts again from the magnetic field back into the electrical field, but with a
reversal from the previous polarity. This continues as long as that particular ray of
light exists.
There are other "modes" of propogation which involve more complex
interactions between the electric and magnetic fields, but in all cases the Law of
Conservation necessarily holds true: Energy is neither created nor destroyed as it is
transformed from one form to another; the total energy in the wave must somehow
remain constant throughout the full cycle.
NOTE: The sine wave shown here represents the strength and polarity of the
electrical field associated with the motion of this ray of light. The light itself,
assuming no outside influences, travels in the straight line indicated by the blue
arrow. The light energy does not "wiggle" back and forth as it moves along its path.
As an electromagnetic wave, light has some characteristics in common with all
forms of electromagnetic energy. These include wavelength, frequency, and speed
of propogation. These characteristics are actually related to each other, so that any
one can be calculated if the other two are known. Let's take a look at each of these
characteristics:
wavelength
Since light is a repeating waveform in motion, it is possible to measure
the physical distance between matching points of adjacent cycles of the
waveform. This is shown here:
The symbol used to represent this distance is the Greek letter "Lambda"
λ
The wavelength can actually be measured between any two
corresponding points on the waveform. It is convenient to use the most
positive point or the most negative point, both of which are shown above.
However, we could have just as easily specified two zero-crossing points, so
long as both crossed the zero line in the same direction.
Remember that the light itself does not wave back and forth along its
path of travel. What we are actually measuring here is the distance traveled
through space by this ray of light, while its electrical field goes from its
maximum positive value, through zero to its maximum negative value, and
then through zero again to once more reach its maximum positive value.
This distance is normally measured in meters (m) or some decimal
fraction of a meter, such as centimeters (cm). The correct units of
measurement are meters per cycle (m/cycle) or some appropriate derivation.
In the case of light, the wavelength is so short that a specific distance, called
the ångstrom (Å), has been defined.
One ångstrom = 10-10 m or 10-8 cm.
Visible light has a characteristic wavelength in the range of
approximately 3900 Å to 7700 Å. Electromagnetic energy outside this range
is no longer visible to the human eye.
Speed of Propogation
The speed at which light travels through any medium is determined by
the density of that medium. The presence of matter, even transparent matter,
will slow the light down. Even air will have some effect, and glass has a
more significant effect on the speed at which light will travel through it.
Ever more sophisticated experiments have determined the speed of light
quite accurately. According to current knowledge:
Speed of light in a vacuum = 2.997925 ± 0.000002 x 1010 cm/sec.
As made famous in Einstein's equation, the letter c is used as a general
symbol for the speed of light.
Frequency and Period
In any electromagnetic wave, it takes time for the energy in the wave to
change from electrical format to magnetic and then back again. The amount
of time required to do this twice, covering one complete cycle, or
wavelength of the signal is known as the period of the wave. Thus, the
period of any wave, measured as some amount of time per cycle, is in fact
the time interval that corresponds to the physical wavelength of the signal.
The frequency of the wave is the inverse or reciprocal of the period. That
is, the frequency is the number of cycles of the waveform that occur in one
second of time. For many years this was simply measured in units of cycles
per second. Recently, however, the specific name hertz (abbreviated Hz) has
now been designated as the appropriate unit to indicate cycles per second.
In general equations, the letter f is used to indicate frequency in hertz.
c = fЋ
Obecné vlastnosti elektromagnetické vlny
1)
2)
3)
4)
Elektrické pole E i magnetické pole B je vždy kolmé na směr šíření vlny
Elektrické pole je vždy kolmé k magnetickému.
Vektorový součin E X B udává směr šíření vlny
Je-li vlna harmonická, mají pole E i B stejnou frekvenci a jsou ve fázi.
Zápis polí jako sinusové funkce polohy x a času t
E = Emax.sin.(kx – ωt)
B = Bmax.sin.(kx – ωt)
Emax a Bmax jsou amplitudy polí; k úhlový vlnočet; ω úhlová frekvence vlny
A platí E/B = c
A.2 Difrakce:
Diffraction of light happens when light bends around a barrier. Light travels in straight lines
with little room to bend. That is why we have shadows, light does not bend as easily as sound.
The longer the wavelength of light the easier it will diffract. Radio waves are the longest so
they will bend the most. Gamma rays are the shortest, they will bend the least. Visible light
will diffract a little bit.
Diffraction is used experimentally to determine the wavelength of light:
n λ = d sin θ
Double Slit Diffraction
In 1801, Thomas Young experimentally determined the wavelengths of visible light,
obtaining experimental proof for the wave nature of light. In his experiment, light
from a single source falls on two closely spaced slits. If light behaved as a particle, we
would expect to see two spots on a screen. Instead, Young saw a series of bright lines
which he explained as a wave-interference phenomenon.
When the light falls on the two slits, it diffracts, spreading out. The diffracted waves
from each slit constructively and destructively interfere. If the waves from the two
slits travel the same distance, they are in phase, and produce a bright spot in the center
of the screen. Constructive interference also occurs when one wave travels an extra
distance that is a whole number multiple of a wavelength of the wave, producing
bright lines on the screen. Destructive interference occurs when one wave travels a
distance of one-half wavelength (or 3/2, 5/2, etc.) more than the other, producing dark
lines on the screen. One sees a bright central spot on the screen, with alternating dark
and bright lines (or fringes) on either side.
In his 1704 treatise on the theory of optical phenomena (Opticks), Sir Isaac Newton wrote that
"Light is never known to follow crooked passages nor to bend into the shadow". He explained
this observation by describing how particles of light always travel in straight lines, and how
objects positioned within the path of light particles would cast a shadow because the particles
could not spread out behind the object.
On a large scale, this hypothesis is supported by the seemingly sharp edges of shadows cast
by rays from the sun. However, on a much smaller scale, when light waves pass near a barrier,
they tend to bend around that barrier and spread at oblique angles. This phenomenon is known
as diffraction of the light, and occurs when a light wave passes very close to the edge of an
object or through a tiny opening such as a slit or aperture.
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Difrakci lze vysvětlit vlnovou teorií sětla vytvořenou Christianem Huygensem. Byla však
v rozporu s Newtonovským pojímáním světla, jako proudu částic. Prosadit vlnovou podstatu
difrakce se podařilo až Augustinu Fresnelovi. Optické difrakční jevy dělíme na Fresnelovu
difrakci (intenzita jako funkce polohy v nějaké rovině pozorování umístěné v konečné
vzdálenosti za difrakčním stínítkem) a Fraunhoferova difrakce(intenzita jako funkce polohy
v nějaké rovině pozorování umístěné v nekonečné vzdálenosti za difrakčním stínítkem).
A.3 Odraz:
Reflection is the bouncing back of a wave. As we see in the diagram to the left. Light waves
hit a smooth surface and bounce off with the same angle in which they hit the surface. This is
the Law of Reflection: the angle of incidence is equal to the angel of reflection. Since both
angles are equal the image appears to be the same. This will happen when we reflect light off
of a flat smooth surface.
What happens when the surface is not smooth? When light bounces off of a rough surface
difuse reflection is seen. Objects appear blurred, like the reflection of the setting sun on the
water. We do not get a clear picture of the sun as we would if the light was being reflected off
of a mirror.
Surfaces can also be curved. A satilite dish is a perfect example of a concave surface. The
dish is curved inward as to direct all of the light waves in toward the center receiver and then
through a cable into your house.
***
So that we can agree fully on what we are talking about, we need to define a few
terms:
Incident Light
Light approaching a surface is known as incident light. TWhen light reflects off
a surface, it follows some rather basic rules which have been gradually determined
by observation. Consider the animation to the left. A ray of light approaches a
reflecting horizontal surface at an angle of 45°, bounces from the surface, and
leaves at an angle of 45°.
his is the incoming light before it has reached the surface.
Reflected Light
After light has struck a surface and bounced off, it is known as reflected light. This is
the light that is now departing from the surface.
Angle of Incidence
The angle at which a ray of light approaches a surface, reflective or not, is
called the angle of incidence. It is measured from an imaginary line perpendicular
to the plane of the surface in question to the incoming ray of light.
Angle of Reflection
Once the light has reflected from a reflective surface, the angle at which
the light departs from the surface is called the angle of reflection. This angle
is also measured from a perpendicular to the reflecting surface to the
departing ray of light.
When light reflects from a surface, the angle of reflection is always equal to the
angle of incidence.
When multiple rays of light approach a reflecting surface, each individual ray behaves
independently of all the others. If all three angles of incidence are the same and the surface of
reflection is perfectly flat as shown, all three angles of reflection will also be the same.
A.4 Lom: (refraction)
Refraction is the name given to the observed phenomenon that light changes direction, or
"bends," as it passes the boundary between one medium and another. This is shown to the
right, in a general sense.
Here, we see a beam of light traveling through air, until it meets a pool of water. It arrives
at some angle to the surface as shown. As it passes through the boundary, going from air into
water, it actually slows down. Since even a single ray of light has a finite thickness, the part
that enters the water first slows down first, causing the light ray to change direction to a
steeper angle in the water.
If we change the angle at which the light enters the water, we find that the angle of the
light in the water also changes, such that we see no change at all if the light source is directly
overhead so that the entering ray of light is perpendicular to (in mathematical terms normal
to) the surface. As we change the entering angle more and more away from the perpendicular,
we see that the ray of light in the water has bent more and more away from the direction taken
by that ray of light in the air.
The basic Law of Refraction was first formulated by Willebrord Snell in 1621.
Consider the diagram to the left. We see here two parallel rays of light in red. They are
passing through a boundary between air and water at a measurable angle of incidence,Θr. The
rays of light in the water remain parallel, and are now leaving the boundary at a measurable
angle of refraction, Θr.
When light changes speed and direction as it moves from one medium to the next, light is said
to refract. You can try this cute experiment to see how light refracts. Below is a picture of
marbles placed over a checkered background. Notice how the squares are a different size
when you look through the glass of the marble.
If you wear glasses you are refracting light. The glasses have lenses to bend light on to your
retina. There are two types of lenses as shown in the diagrams below. Concave is like a cave
and goes inward while convex curves outward.
Refraction index of any material depends upon the wavelength of
the light. This fact can be used to resolve the light beam into the
spectral components it consists of. One of the tools used for
spectrum analysis of light is the glass prism.
Let us consider and beam of the light propagating symmetrically to
prism (see the figure). If α is the refractive angle of the prism, then
we can find from the condition n = sin ξ0 / sin ξ = sin ζ / sin ζ0 that
n = sin (α/2 + ϕ/2) / sin ( α/2 )
(1)
In practice the refraction index n depends upon the light wavelength λ , so the angle
ϕ at which the prism refracts the light will depend upon the light wavelength too:
D = dϕ / dλ = (dϕ / dn)(dn / dλ )
Vlnová délka a index lomu
(2)
Vlnová délka světla v prostředí závisí na jeho indexu lomu. λn = λ / n Fázový rozdíl se tedy
může měnit, jestliže vlny procházejí různými látkami s různým indexem lomu.
A. 5 Intererence:
Light interfernce is easy to see. When you look at the demonstration of diffraction above you
will see interfence patterns. Light wave interference happens when the light wave come in
contact with one another. Constructive interference produces a more intense band of light
while destructive interference produces a less intense band of light or no light at all.
Interference is caused by waves overlapping with each other, causing a cancellation of the
wave at that point, or an amplification of the wave at that point.
Pozn.:
Mýdlová bublina nebo olejová skvrna vytvářejí jasné barvy konstruktivní a destruktivní
interferencí světla, na rozdíl od lomu světla na kapkách vody tvořících duhu.
A. 6 Koherence:
Nutnou podmínkou, aby se interferenční obrazec objevil na stínítku je,aby se ázový rozdíl vln
dopadající do libovolného bodu s časem neměnil. Takové světlo se nazývá koherentní
(dokolnale). Příkladem dokonale koherentního sětelného zdroje je laser.
A.7 Polarizace:
Polarized Light
Maxwell's theory of light predicts that light can be polarized since it is a transverse wave. The
direction of polarization is taken as the direction of the electric field vector. Polarized light is
said to be plane-polarized, or the oscillations are in a plane. In unpolarized light, the electric
field vectors vibrate at all angles.
A polarizer produces plane-polarized light by transmitting only the component of light
parallel to the axis. An analyzer determines if the light is polarized and what is the plane of
polarization.
Light can also be partially polarized by reflection. If light traveling in air is reflected from a
medium with index of refraction of n, the incident beam is completely polarized if the
incident beam's angle is given by tanθ = n.
An applet that allows you to create polarized light.
B) Rychlost světla:
B.1 HISTORIE
About 1675, Ole Roemer, a Dutch astronomer, computed tables to show the times of future
eclipses of Jupiter's satellites, such as may be found today in the "Astronomical Almanac." He
observed the phenomena from time to time and was astonished to find variations and that at
the end of six months some of the observed times were over 16 mins behind the predicted
times. Continuing to observe and time, he found that there was a certain regularity in the
discrepancies. When the Earth was at its closest to Jupiter, the eclipses occurred on time, but
when the two planets were at their farthest distance apart, the eclipses were late. He deduced
that the discrepancy must be due to the difference in the distance that light had to travel.
Calculation showed that light must take one second to travel 186,000 miles.
Now then, is it possible to measure the velocity of light without resort to astronomical means?
The answer is yes. Nowadays there are many approaches but, between 1878 and 1882, Albert
A. Michelson, an American naval officer constructed an apparatus to do just that.
*******
Galileo's attempt
Galileo used lanterns between two hilltops. Saw essentially no travel time. If the distance
were, say 2 miles, then the sound distance would be about 10 seconds. He had no reason to
believe that the velocity of light was significantly faster than that of sound.
Astronomical measurements
In 1676 Rømer made careful measurements of the times at which satellites of Jupiter were
eclipsed by the planet. The times observed did not agree with those calculated on the
assumptions of a constant period of rotation and of instantaneous transmission of light.
Starting at a time when the Earth was at its nearest to Jupiter, the apparent period increased
and the eclipses became increasingly later than the calculated times as the Earth receded from
Jupiter. Similarly, the period shortened when the Earth was moving toward Jupiter. The
observed times were consistent with a finite velocity of light such that the time for it to
transverse the Earth's orbit is about 1,000 seconds. Taken with modern values of the size of
the Earth's orbit, the derived value of the velocity is 298,000 kilometres per second. It is
remarkable that this first measurement was even of the correct order; the most important
conclusion was that the velocity of light is finite. An English astronomer, James Bradley
(died 1762), obtained a similar value by the so-called aberration method, based on the
apparent motion of stars as the Earth travels in its orbit about the Sun.
Early terrestrial experiments
In terrestrial experiments by method (1), the beam of light is periodically marked either by
interrupting it at regular intervals or by modulating it (alternately increasing and decreasing its
intensity). The marked beam is transmitted to a distant mirror and the return beam passes
through the apparatus that interrupts or modulates the outgoing beam and then to a detector. If
the time required for transmission to the distant mirror and return is 1/2, 3/2, 5/2, . . . times the
period of the interrupter (or modulator), then the amount that reaches the detector is small. It
is usual to adjust either the path length or the period of the interrupter or modulator until the
light registered by the detector is a minimum. In the earlier experiments, a mechanical
chopper was used as interrupter, and the eye was the detector. Later experimenters used
electronic modulators and photoelectric detectors.
The apparatus used by Fizeau in 1849 is shown in Figure 6, in which M1 is a partially
reflecting mirror and M2 is a fully silvered mirror. As the speed of the wheel (which has 720
teeth) was increased from zero, it was found that the light was first eclipsed by a tooth when
the speed was about 12.6 revolutions per second--i.e., when the time to make the round trip
was 560 microseconds (0.00056 second), the length of the double path being 17.3 kilometres
(about 10 miles). The chief error in the measurement lay in the difficulty of determining the
exact speeds at which the light received by the eye at E was at a minimum. Essentially
the same method was used by others between 1874 and 1903. The accuracy gradually
improved, and it was shown that the velocity is between 299,000 and 301,000 kilometres per
second. In 1834 Sir Charles Wheatstone of England suggested a method incorporating a
rotating mirror for interrupting the light that was later developed by Arago (1838) and
Foucault (1850). It was considerably improved by Michelson, who made measurements from
1879 to 1935.
B.2 Michelsonův pokus
He arranged for a beam of light to be brought to a focus and passed through a slit (A) on to a
revolving mirror (B1). From here it was reflected by stationary mirrors (C and D) to a
concave mirror (E). From this point the beam was directed across country where, 22 miles
distant, was another concave mirror (F) that reflected (G) the beam back to the first concave
mirror (H). Here, by means of other mirrors (I and J), the beam was directed to a mirror (K5)
on a revolving drum and then by another stationary mirror to a small telescope. Adjustments
were made so that the observer saw the original slit as a bright line on a graduated scale
marked in the eyepiece of the telescope. The revolving mirrors were driven at high speed by
suitable gearing from an electric motor, and as they rotated they reflected the light as an
intermittent beam along its 44 mile path, "out and home." It is easy to understand that when
the original beam from the mirror at (B) is returned to (K), if the mirrors are revolving, it will
not find the individual mirrors in the same position as they were when the beam commenced
its journey. As the revolving mirrors have moved, the beam will be sent slightly to one side of
the telescope slit, so that nothing will be seen. By speeding up the rotating mirrors, however, a
point will be reached when the beam will impinge on mirror B1, travel the 44 miles, and find
that in the meantime the mirror has made 1/8 of a revolution allowing mirror 4 exactly to take
the place of mirror 5. When the mirror velocity has been so adjusted that this happens, the
light will be seen in the telescope.The measurement of the elapsed time for the displacement
of mirror 4 to position 5 enables the further calculation of the distance that light travels in one
second and gives our, now well understood, figure of (about) 300,000 kms per second.
(299,792.5 ??)
další zdroj pro Michelsonův experiment
Figure 7 shows the arrangement used in 1927. The mirror M3 is a little above the plane of the
diagram, and M3' is a little below. Light from the source S passes to one face of the octagonal
mirror M1 and then to M2, M3, and M4. From M4 it goes to the mirror M5 at a distance of
about 35 kilometres (about 22 miles). It returns via M6, M4, M3', and M' to the octagon. An
image of S is seen in an eyepiece at E. The octagonal mirror rotated at 528 revolutions per
second. It turned through approximately one-eighth of a revolution during the transit of the
light. If the rotation were exactly one-eighth of a revolution, the image would be undisplaced
from the position it had when the mirrors were stationary. In some of Michelson's
experiments, the speed of rotation was slowly changed until this condition was obtained. In
others, the speed and distance were fixed, and a small displacement of the image was
measured.
B.3 Moderní principy
The electro-optical shutter
This device, based on the Kerr effect, makes it possible to modulate a beam of light at
frequencies more than 10,000 times the highest frequency of interruption used by Michelson
and obtain values in reasonably good agreement with each other and with Michelson's later
work. This method was greatly improved by E. Bergstrand in Sweden, who reduced the
random errors by a factor of more than 30 and obtained a value for the velocity of light of
299,793.1 kilometres per second.
Radio-frequency measurements
The velocity of electromagnetic waves of radio frequency in vacuum has been measured by
several methods. An English physicist, Louis Essen, measured (1950) the resonance
frequency of a cavity resonator (an electromagnetic device) whose dimensions were
also determined with high accuracy. Keith Davy Froome, a physicist in England, measured
(1952 and 1958) the wavelength in air, corresponding to a known frequency, using a
microwave interferometer. The results of these and other measurements are in agreement with
those of Bergstrand to within a few parts per million. The velocity of radio waves in vacuum
is thus equal, within this accuracy, to the velocity of light. The velocity of gamma rays is also
the same, within the much lower accuracy of this last measurement. Table 1 summarizes the
measurements of the velocity constant (c) and shows that there is now satisfactory agreement
between results obtained over a wide range of conditions. Since the publication of the special
theory of relativity (1905), the constant c has been recognized as one of the fundamental
constants of modern physics. For this reason, attempts will undoubtedly be made to measure
it with even greater precision. The use of lasers may help, but a major improvement will
require the establishment of better standards of length and time than those now available.
Modifikovaný školní experiment
The aim of this experiment is to measure the speed of light in an experiment available to do at
school. The principle is quite simple. Let a ray of light strike a rotating mirror that reflects the
light three meters away to a second mirror, so that the light is reflected back at the rotating
mirror and back to the laser. The rotating mirror has during the time it took for the light to
travel the six meters to the second mirror and back rotated some degrees and the light spot has
moved from the origin. And if you know how fast the mirror is rotating, you can calculate
how fast the light is traveling.
The apparatus is set up like the figure below shows. When we did the experiment and
measured, x was measured to approximately 3.0 mm - 3.5 mm. So we know that the velocity
of light is the distance it travels divided by the time it takes ( c = d / t ), and the distance is 30
meters since the light should travel to the second mirror and back. The how do we know how
long time it takes? Well, if we use a tuning fork we can set the mirror to do 512 rotations per
second. And since we know the distance between the rotating mirror and the laser, and the
angular velocity of the rotating mirror, we can calculate how long time it takes.
So
q = x / 10 = 3
E-4T = 1 / 512 " 0.001953
t = q / 2p * T = ( 0.3E-4 m / 2p ) * ( 1 / 512 ) = 9.32E-8
Then,
c = d / t = 30 / 9.32E-8 " 321719678 m/s " 322 000 km/s
When we are measuring these small distances with a ruler, and using such high
velocities as the speed of light, it is very hard to be precise and the result may vary quite
much. According to the book the velocity of light is 299,792,458 m/s, so it wasn't that bad
measured, but on the other hand, the difference is approximately 22,000km/s which is a very
high velocity.
B.4 Myšlenkové experimenty + zařízení
Velocity of Light
11224.93 Velocity of Light Apparatus
•
Accurate and dependable results
•
Rapid and simple student set-up
•
Measures velocity in air or liquids
•
No mechanical moving parts
The beam from a 50 MHz modulated LED is directed to a receiving diode through an optical
path that is reversed by a pair of mirrors which can be moved to change the path length. The
modulated received signal is phase shifted relative to the original signal as a function of the
length of the light path. The phase relation is represented as a Lissajous figure on a twochannel oscilloscope. Both the emitted and the received signals are frequency shifted with a
1:1000 reduction, so that simple oscilloscopes and frequency counters having 1 MHz
bandpass can be used. Receiving and emitting diodes are installed and aligned in the chassis.
The apparatus has a measuring path of 1.5 m. With the assistance of a phase shifter, a defined
phase relation (e.g. a Lissajous straight line) can be adjusted for a position of the mirror
directly in front of the emitter receiver unit.
******
This is a thought experiment to show how two different observers might measure the speed
of light along a single path if they could get a cylinder to rotate at 107 revolutions per second.
In figure 1 observer A has a hollow cylinder 3 meters long and not moving relative to the light
source. Both ends are closed. In the top is a small hole near the circumference. In the bottom
is a similar hole offset from the top hole by 36o or 1/10 the distance around the bottom. Light
enters the top and travels the length of the cylinder. If the cylinder were rotating at 1.0 x 107
revolutions per second then the hole in the bottom and the light will arrive at the at the same
point at the same time and the light will exit the cylinder. The light exits the bottom hole and
traces a circle of light on a flat screen below the cylinder. The time for the light to travel 3
meters is 10-8 second. The number of revolutions in that amount of time is 1.0 x 107 x10-8 =
0.1 revolution or 36o. If the cylinder were rotating at any other velocity the bottom hole and
the light would not coincide and the light would not exit the cylinder.
**********
In engineering terms the velocity of light in free space c is given by the expression c =
1/(µ0ε0)1/2, where in mks units µ0 = 4π x 10-7 H/m and ε0 = 8.854 x 10-12 F/m, are,
respectively, the magnetic permeability and dielectric permittivity of the vacuum. Therefore,
the argument that c is fixed is, at base, an argument that µ0 and ε0 are fixed and not subject to
manipulation by technological means.
B.5 Rychlost světla v různých materiálech
Velocity in material mediums
All measurements of the velocity of light involve interruption or modulation of a beam of
light so as to form groups of waves and the velocity measured is the group velocity. The
difference in magnitude between the wave velocity and the group velocity of light in air
is only about one part in 50,000, but in most glasses and in some liquids it is much larger.
Michelson obtained 1.758 for the ratio of the velocity in air to the velocity in carbon
disulfide. The inverse ratio of their indices of refraction is 1.64 and the value calculated
from this for the ratio of group velocities is 1.745 for wavelength 580 nanometres, close to
Michelson's observations. Bergstrand found that the ratio of the velocity in vacuo to the
velocity in a certain glass was 1.550 +/- 0.003. The refractive index of the glass was 1.519,
but the ratio of c to the group velocity was 1.547. The experimental results thus agree with
thosecalculated on the assumption that the measured velocity is the group velocity.
A.6 Tabulka některých dosud změřených hodnot
Experimenter
Roemer-Chaffin
Date
c, km/sec
1675
320 000
1675
300 000
1675
292 000
Roemer-Mammel
1675
317 700
Roemer-Setterfield
1675
307 500
Cassini
1693
352 000
Roemer-Goldstein
(1)
Roemer-Goldstein
(2)
Value current
20207,54
8500
2
No.
obs.
Method
50
1
1500 207,542
50
1
50
1
50
1
50
1
50
1
error, ±
7792,458
17907,54
2700
2
5400 7707,542
52207,54
18000
2
5400
Bradley (first
1727
accepted) (KO)
Auwers (Kew)
1727
Newcomb
1727
Delambre
1738
(definitive)
Bradley (17261740
1754)
Auwers (Wanstead) 1727-47
Fizeau (Journal
1849,5
value)
Fizeau. (textbook
1849,5
value)
Fizeau (often
1855
omitted)
Fizeau (bad
1855
citation?)
Maxwell
1868
284 000
W.Thomson/King
1869
280 900
Nyren-Wagner
1861-1879
1870
299 980
Cornu (Rejected)
1872
298 500
1000
Nyren (PO)
1873
299 810
200
McKichan
1874
289 700
6800
1874,8
1874,8
1874,8
1876,5
300 400
299 990
299 900
299 921
300
200
200
13
Cornu
Cornu-Helmert
Cornu-Dorsey
Harvard (1844-
303 430
750 3637,542
800
2
301 416
299 289
1070 1623,542
1750 -503,458
800
800
2
2
303 320
65 3527,542
1000
1
300 650
750 857,542
2300
2
300 313
920 520,542
15507,54
10000
2
13507,54
10000
2
700
2
14
3
14
3
5000 5857,542
25
3
25
3
12
7
33
7
950
2
658
3
50
2
33
7
208
208
208
500
3
3
3
1
315 300
313 300
305 650
298 000
1792,458
20000 15792,45
8
8300 18892,45
8
5000
60 187,542
1292,458
17,542
10092,45
8
607,542
197,542
107,542
128,542
1909)
Sampson (18441909)
Michelson
(rejected)
Stoletov
Newcomb
(doubtful av.)
Newcomb-Dorsey
Exner
Newcomb (full
approval)
Michelson
Michelson-Dorsey
Nyren (definitive)
J.J.Thomson
Comstock
Blondlot
Pellat
Doolittle (FO)
Internat Lat.
Service
Perrotin-Prim
Perrotin
Pease/Pearson
Sollenberger (W0)
Romanskaya (PO)
Rabe, indirect
Anderson
Anderson-Birge
Hüttel
Hüttel-Birge
Anderson
Essen/GordonSmith
Essen/GordonSmith
Jones
Smith, Franklin,
Whiting
Jones-Cornford
Scholdstrom
Plyler/Blaine/Conn
or
Wadley
Wadley
1876,5
300 011
13 218,542
500
1
1878
300 140
480 347,542
10
4
1881
299 000
2000 -792,458
33
7
1881,8
299 810
50 17,542
189
4
1881,8
299 780
?
4
1882
287 000
33
7
1882,7
299 860
66
4
1882,8
1882,8
1883
299 853
299 850
299 850
563
563
2000
4
4
2
1883
296 400
33
7
1890,5
1891
1891
1901,5
300 560
302 200
300 920
299 760
60 60,542
250 57,542
90 57,542
20000
3392,458
170 767,542
8500 2407,542
600 1127,542
130 -32,458
50
12
33
50
2
6
7
2
1901,5
299 660
60 -132,458
50
2
1902,4
1902,4
1932,5
1933
1935
1935,5
1936,8
1936,8
1937
1937
1940
299 901
299 860
299 774
300 420
299 790
299 920
299 771
299 771
299 768
299 771
299 776
84
80
10
60
100
60
10
10
10
10
10
108,542
67,542
-18,458
627,542
-2,458
127,542
-21,458
-21,458
-24,458
-21,458
-16,458
1232
1233
2885
50
14783
50
651
651
135
?
2895
3
3
5
2
2
2
8
8
8
8
8
1947
299 798
3
5,542
3
9
1947
299 792
3 -0,458
4
9
1947
299 687
25 -105,458
50
10
1947
299 695
50 -97,458
50
10
1949
1955
299 701
299 792,4
25 -91,458
0,4 -0,058
50
50
10
11
1955
299 792,0
6 -0,458
58
13
1956
1956
299 792,9
299 792,7
2
2
40
24
14
14
80 -12,458
23000 12792,45
8
30 67,542
0,442
0,242
Edge
Edge
Wadley
Froome
Kolibayev (av.
date)
Karolus
Simkin et al.
Grosse
Bay/Luther/White
NRC/NBS
NRC/NBS
Evenson et al.
Blaney et al.
Woods/Shotton/Ro
wley
Baird/Smith/Whitf
ord
NBS (U. S.)
1956
1956
1957
1958
299 792,4
299 792,2
299 792,6
299 792,5
0,11 -0,058
0,13 -0,258
1,2 0,142
0,1 0,042
50
50
14
21
11
11
14
12
1960
299 792,6
0,06
0,142
23
11
1966
1967
1967
1972
1972
1973
1973
1974
299 792,44
299 792,56
299 792,5
299 792,462
299 792,460
299 792,458
########
########
0,2 -0,018
0,11 0,102
0,05 0,042
0,018 0,004
0,006 0,002
0,002 0,000
0,0011 -0,001
0,0008 0,001
278
70
50
50
50
50
50
50
15
16
11
17
17
17
17
17
1978
########
0,0002
0,001
64
17
1979
########
0,0019
0,000
50
17
1983
########
50
17
Mean
STDEV
VAR
Unknown
Moons of Jupiter
Aberration
Toothed wheel
Rotating mirror
Polygonal mirror
Waves on wires
ESU/EMU
Kerr cell
Cavity resonator
Radar
Geodimeter
Radio
interferometer
Spectral lines
Tellurometer
Modulated light
Microwave
Laser
Quartz Modulator
0,0003 0,001
1390,668
300 288,662
496,20
3
3684,916
5181,28
5181,28
8
1357861
26845703,4
2
558
The Atomic Clock was first used as the standard in
1967.
The velocity of light was defined to be a constant in 1983.
The value chosen for c was 299,792.458 km/sec.
WO Washington Observatory
SO Strasburg Observatory
GO Greenich Observatory
Ho Honolulu Observatory
PO Pulkova Observatory
BO Berlin Observatory
FO Flower Observatory
SFO San Francisco Observatory
KO Kazin Observatory
Type of Data
P Primary Data
S Secondary Source
R Reworking of data
for P
P* Primary value preferred by authors
R* Reworking of data preferred by authors
Pulkova Data has been corrected
Lg Error
Uncertainty in error bars too great to show trend
Outlier
Data lies well outside nearby data points
Reject
Value rejected by experimenter or by subsequent analysis
C) Zdroje
http://www.infoline.ru/g23/5495/Physics/pris_txt.htm
http://www.mic-d.com/java/airydiskformation/index.html
http://homepages.ihug.com.au/~flavios
http://www.nidsci.org/articles/seti.html
http://www.daedalon.com/velight.html
http://homepages.ihug.co.nz/~ddowning/dec2001
http://www.essaybank.co.uk/free_coursework/27.html
http://www.cyberclassrooms.net/~pschweiger/light.html
http://www.sciencejoywagon.com/physicszone/lesson/09waves
http://www.angelfire.com/scifi/dschlott
http://www.play-hookey.com/optics/what_is_light.html