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Light Physics 202 Professor Vogel (Professor Carkner’s & CJV notes, ed) Lecture 10

Light  Electromagnetic wave  oscillating electric and magnetic fields –  no material medium that is moving!  energy transfer at speed v (c=3X10 8 m/s in vacuum)  wavelength = distance between repeats  frequency = # repeats per second f =v v=c in vacuum c=3X10 8 m/s f

EM Spectrum

The EM Spectrum  Radio > 1 meter penetrates solid objects easily  Millimeter (microwave) 1 m - 1 mm used for communication  Infrared 1 mm - 700 nm we feel as heat  Visible 700-400 nm eyes evolved to see  Ultraviolet 400 nm - 100 A higher energy, causes sunburn  X-ray 100 A - 0.01 A penetrates soft things but not hard  Gamma Ray < 0.01 A hard to produce and dangerous

The EM Wave  Lets consider light as a wave  What kind of wave is it?  What is oscillating?  An EM wave consists of an electric field wave (E) and a magnetic field wave (B) traveling together  The 2 fields are perpendicular to each other and to the direction of travel  An EM wave is transverse (like string waves)  The field waves are sinusoidal and in phase

Wave Equations  We can generalize the waves as: E = E m sin (kx -  t) B = B m sin (kx -  t)  Nothing is actually moving  There is no string  A changing E field induces a B field  A changing B field induces an E field  The two fields continuously create each other  The speed of the wave is related to the fields: c = E/B

Traveling EM Wave

Key Constants  Two important constants in E and M are the permittivity constant  0 and the permeability constant  0  Permittivity is the electric force constant:  0 = 8.85 X 10 -12 F/m  In farads per meter  Measure of how electric fields propagate through space  Permeability is the magnetic force constant:  0 = 1.26 X 10 -6 H/m  In henrys per meter  Measure of how magnetic fields propagate through space  The wave speed depends on these constants: c = 1/(  0  0 ) ½

Poynting Vector  EM waves transport energy  The amount of energy delivered per unit area per unit time is given as flux: flux = W/m 2 = J/s/m 2  Flux for an EM wave can be given by the Poynting vector: S = (1/  0 ) EB  However, E and B are related by E/B = c so we can rewrite S as: S = (1/c  0 ) E 2

Intensity  The value of S depends on where the EM wave is in its cycle  We generally are interested in the time averaged value of S, known as the intensity I = (1/c  0 ) E rms 2  Where E rms is the root-mean-square value of the electric field

Radiation Pressure  EM waves exert a pressure on objects  If someone shines a flashlight on you, the light is trying to push you away  like ball bouncing off object pushes object back  The force is very small in most cases  EM pressure is due to the fact that light has momentum which can be transmitted to an object through absorption or reflection

Momentum Transfer  The change in momentum due to light is given by:  p =  U/c  Where  p is the momentum change and  U is the energy change  The above equation is for absorption  For reflection the momentum change is twice as much:  p = 2  U/c

Light Pressure  From Newton’s second law F =  p/  t  The amount of energy delivered in time  t is:  U = I A  t  where I is the intensity and A is the area  Since pressure (p r ) is force per unit area the pressure becomes: p r = I/c (total absorption) p r = 2I /c (total reflection)

Comet Hale- Bopp

Comet Tails

Light Sail

Color Vision  Rods and cones  one type of cone responds to long ’s: “R”  one type of cone responds to mid wavelengths: “G”  one type of cone responds to short ’s: “B”  How our eyes view pure waves:  red : R-type responds  green : G-type responds  blue : B-type responds  yellow : R- and G-types respond  Cyan : G- and B-types respond

Color Addition  How our eyes view mixtures :  blue + red: R- and B-types respond  magenta  green + blue : G- and B-types respond  indistinguishable from cyan  red + green : R- and G-types respond  indistinguishable from yellow  Demo of color addition -- HELP (Like no pure color)

Color Addition  How our eyes view mixtures :  red + green : R- and G-types respond  indistinguishable from yellow  red + green + blue : R-, G-, and B-types respond  white  yellow + blue : R-, G-, and B-types respond  white

Color Subtraction  How our eyes view pigments (absorb light)  white - blue: R- and G-types respond  pigment that absorbs blue looks yellow  white - red : G- and B-types respond  pigment that absorbs red looks cyan  white - (blue + red): G-type responds  pigment that absorbs blue and red looks green

Color Subtraction  How our eyes view pigments:  white - (blue + red):  pigment that absorbs blue and red looks green  Pigment: yellow + cyan:  pigments that absorb blue and red look green  A demo of subtractiondemo  usflag-neg.gif

Complementary color = white - color primary color  red  green  blue Complementary color  cyan  magenta  yellow

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