Physics For Teachers (PS.122 - §102, 2019 Fall => CRN 3671)
Class Meets in : Science 179 ... Tue & thRs 6:30pm - 8:20pm
My office: Science 159 (below ramp to 3rd Ave) e-mail : foltzc @ marshall.edu phone : (304) 696-2519
Topic 9 (Light & Images)
including reflection geometry and photons
Electric Field disturbance couples with Magnetic Field disturbance to make Light
As one electron oscillates into a new situation, it emits (gives off) one piece of light ... called a photon
the photon's Electric Field points along the electron's acceleration; its Magnetic Field points perpendicular to the electron's velocity
the photon is like an "atom" of light ... a few thousand wavelengths long.
ending "-on" means "one" (akin to "unit" ; c.f. proton, neutron, electron) ... "photo" means light
same amount of Energy in the Electric Field as is in the Magnetic Field
think of the one Field as the PE in the wave, and the other Field as the KE part.
. . . Both Fields are perpendicuar to the direction that the photon travels (away from the source charge)
so photons (and the light waves they comprise) are transverse waves.
=> the polarization of the light is (by convention) the direction of its Electric Field .
a photon is absorbed when it causes another electron (far from the source) to move the same way as the original (source) electron moved
the photon's Energy and momentum and spin are also absorbed as the photon's Electric Field does Work on the receiving electron.
. . . light transfers Energy from the source to the receiver (like any other wave does) - the Energy must be absorbed for the light to be detected (seen or felt) !
unlike other transverse waves , light also carries linear momentum in the direction of its motion ... along the ray (in the direction of PE flow).
. . . (unlike other waves, a photon of light also carries spin (angular momentum) , usually clockwise or counter-clockwise around its motion ... right-handed or left-handed)
=> draw the momentum as the light ray , along the direction the light travels
. . . draw the Electric Field polarization as the wave-fronts ... | to the ray .
there are so many photons coming from most objects that the discrete nature of light is seldom noticeable
they are tiny ... about 2000 wavelengths long ... 2000 × ½ micrometer = 1 millimeter long
. . . similar to water trickling from a faucet is seldom treated as 10^24 discrete molecules emerging each second
as a model , you can treat light as rays that emerge , in every direction , from every part of an object's surface
. . . rather than the 10^20 discrete photons that are emitted by a light bulb each second
Visible Light is a small portion of the Electro-Magnetic Wave Spectrum
all EM waves have the same speed ... thru a vacuum ... c = 300 million m/s !
. . . people learned how to make radio waves 130 years ago (first called "wireless telegraphy")
broadcast frequencies 500 kilocycles/sec - 1600 kHz (AM) ...to... 88 Mega-Hz - 109 MHz (FM)
(each radio station tells any listener the frequency that they broadcast)
. . . since c = λ f slow oscillations have very long waves:
λ = 300 million m/s / 1470 kHz = 204 meters for WHRD (run by Marshall 1988-91)
. . . vertical antennas (¼ λ tall) make vertical E-fields ... receivable by vertical car antennas
of course, FM radio waves are shorter (~3m), and TV (~600 MHz) even shorter (~ ½ m)
. . . about 40 years ago consumer electronics got good enough to control "microwaves"
. . . called that because they are much smaller than earlier radio waves
0.6 Giga-Hz - 40 GHz has wavelengths ½ meter to 7½ milli-meter
cell-phones range from .8 GHz to 1.9 GHz (375mm - 158mm) . . . home microwave ovens emit 2.45 GHz, 122 mm
. . . natural Infra-Red light comes from (polar) molecules spinning
and hot surfaces, like heat lamps and people
f ≈ .04 TeraHz - 400 THz , λ ≈ 7.5 mm - .75 micrometer
light is visible to humans from Red (.75 μm) thru Orange, Yellow, Green, Blue, to Violet (0.38 μm , 850 THz)
so we are able to see only 1 octave (factor of 2 in frequency)
. . . at frequencies this high, an individual photon carries enough energy to cause chemical reactions
even a red photon is able to push an electron thru 1.66 Volt (some IR can cause chem rx also)
a violet photon has about twice as much energy ... their Energy proportional to frequency (c/λ)
. . .
Color Mixing via 3 - Color Model
. . . Typical human has 3 distinct color receptors in their eye (retina) ... (some have only 2 kinds ; very few have 4 kinds)
each is most sensitive to a different Energy photon ; call them R , G , B .
. . . Human brains perceive color by interpreting the signal strength ratio from the different receptors
we can make any signal strength ratio occur by adjusting the intensity of 3 lights : Red , Green , Blue
. . . computer monitors (and TV displays) mimic colors by adding light :
=> R + G ≈ yellow ; R + B ≈ magenta (violet) ; G + B ≈ Cyan (aqua) ; R + G + B ≈ White
Pigment mixing 3 - Color Model
. . . when light reflects from a surface, some wavelengths can be absorbed
a Red surface reflects Red light, and probably some Orange light
- the other colors (Y, G, B, V) get absorbed ... subtracted from the white
. . . when light tries to pass thru a filter, some wavelengths can be absorbed
a Blue filter will transmit G B V ... that's why the filtered light looks Blue
a more expensive (interference) filter might transmit a narrower range of colors
momentum is conserved as a vector, so light travels in a straight line . . . until it interacts with its environment
Reflection . . . the light bounces off (does not enter) the new material
. . . occurs where the electric polarizability changes ... especially at a metal surface
that is why we make mirrors by putting "silver" on glass (aluminum or chromium are more common these days).
metals, being good electrical conductors, reflect all light frequencies fairly well ... (does gold reflect all colors as effectively?)
. . . and reflect all polarizations equally well.
. . . but molecules in glass polarize more than air molecules do , so a plain glass surface also reflects
about 4% of light's Energy reflects if light hits the glass "along the Normal" ... that is : squarely , at right angles to the surface
more reflects if light comes in at other angles , approaching 100% for light that just grazes the surface
. . . especially the light whose Electric Field is oriented along the glass (or water) surface
=> most "glare" has been polarized parallel to the reflecting surface ... polaroid sunglasses (designed to absorb glare from water puddles) does not reduce glare from building windows.
A light ray reflects from the surface at the same angle as it approached the surface
we always measure these angles from the Normal ... not from the surface
the light retains its momentum along the surface ... like a tennis ball bounces off the court.
. . . objects in front of flat ("plane") mirrors send rays that reflect from the mirror surface
looking at the reflected rays, they appear to come from the other side of the mirror.
=> the image appears to be the same size as the object , at the same distance from the mirror , but behind the mirror
the inversion is along the Normal ... an object facing the mirror has an image that faces the mirror
If there's an object and a mirror (#2) , in front of a mirror (#1)
. . . there's a mirror image of the object behind mirror #1
and a mirror image of mirror #2 behind mirror #1
. . . and a mirror image of the object behind mirror #2
and a mirror image of mirror #1 behind mirror #2
. . . and a mirror image of each image behind the other mirror.
curved mirrors cause images that can be smaller or larger , and closer or farther ... or interesting distortions !
Refraction . . . the light bends as it enters (is transmitted into) the new material
. . . occurs where the electric polarizability changes ... at glass surface , or more gradual optical density change
cold air is more dense than hot air , so more molecules in each liter, so it polarizes more
. . . light travels slower in cold air than it does in hot air . . . slower in hot air than in empty space.
same frequency of Electric Field vibrations ... implies shorter wavelengths in denser material ... (recall v = λ f )
if one side of the wave front becomes slower than the other side of the wavefront , the ray deflects slightly
. . . (the ray must always be perpendicular to the wave front ; one side is taking smaller steps ! ← Huygens)
=> light rays deflect toward the slower material , where it encounters a local difference .
speed of light in vacuum (empty space) is 3E8 m/s
. . . speed in water is 3/4 this fast (2¼E8 m/s) , so wavelengths are only 3/4 as long .
speed in glass is about 2/3 as fast as in vacuum (2E8 m/s) .
. . . the "slowness" caused by the material is called the material's index of refraction
water's refractive index is 4/3 = 1.33 . . . glass has index of refraction about 3/2 = 1.5
=> higher refractive index means smaller wavelength , more deflection of the transmitted ray
Most transparent materials do not respond as effectively to higher frequency light
. . . because they do not polarize as much , the refractive index is less for blue light than for red light
red light deflects more ... especiall at a sharp boundary (glass surface).
=> light can be spread (sorted) sideways by its frequency ... if 2 glass surfaces are not parallel (a prism)
wavelength is sorted also , in the reciprocal order : ROY G BV ( long-to-short λ = low-to-high f )
Diffraction . . . the light wavefront spreads sideways after going thru a narrow opening
. . . because visible light wavelengths are so short ( ~ ½ micro-meter) ,
only very small openings cause noticeable diffraction for visible light.
diffraction is often combined with interference effects
. . . diffraction grating spreads the light because of the close spacing of its openings (small size of each)
but each color is separated from the others by only that wavelength having constructive interference there.
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