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Electromagnetic Radiation Physics 202 Professor Lee Carkner Lecture 20

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What is Light? A light wave has no medium A light particle is called a photon The speed of light in a vacuum is a constant, called c c = 3 X 10 8 m/s As for all waves, f = v = c

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The Electromagnetic Spectrum We often think of light as being visible light Visible light is just the portion from 400-700 nanometers (nm) Radio waves, microwaves, gamma rays etc. are all forms of electromagnetic radiation with different wavelengths We will use the terms “light”, “photons” and “electromagnetic (EM) radiation or waves” interchangeably

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EM Spectrum

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The EM Spectrum Radio > 1 meter Millimeter (microwave) 1 m - 1 mm Infrared 1 mm - 700 nm Visible 700-400 nm Ultraviolet 400 nm - 100 A X-ray 100 A - 0.01 A Gamma Ray < 0.01 A hard to produce and dangerous

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Atmospheric Transmission Gamma + X-ray Infrared O 2, N 2 Absorption H 2 O, CO 2 Absorption

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Sensitivity of Your Eye

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Intensity of Light If a light source has a power P s (in J/s), then the intensity at any point is: I = P s / 4 r 2 This can also be written: F = L / 4 d 2 Where F is the flux (J/s/m 2 ) and L is the luminosity (J/s) Light (like sound) falls off with an inverse square law

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Inverse Square Law

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Radiation Pressure If someone shines a flashlight on you, the light is trying to push you away EM pressure is due to the fact that light has momentum which can be transmitted to an object through absorption or reflection

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Comet Hale- Bopp

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Comet Tails

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Momentum Transfer p = U/c Where p is the momentum change and U is the energy change For reflection the momentum change is twice as much: p = 2 U/c

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Light Pressure From Newton’s second law The amount of energy delivered in time t is: 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)

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Light Sail

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Example: Light Sail A light sail is a very large, very thin, very reflective piece of fabric to which a spacecraft is attached Can also use a laser Do need very large sails

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The EM Wave Lets consider light as a wave What is oscillating? An EM wave consists of an electric field wave (E) and a magnetic field wave (B) traveling together An EM wave is transverse (like string waves) The field waves are sinusoidal and in phase

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Wave Equations We can generalize the waves as: E = E m sin (kx - t) B = B m sin (kx - t) Nothing is actually moving A moving E field induces a B field The two fields continuously create each other The speed of the wave is related to the fields:

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Traveling EM Wave

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

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Poynting Vector The amount of energy delivered per unit area per unit time is given as flux: flux = W/m 2 = J/s/m 2 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

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Intensity We generally are interested in the time averaged value of S, known as the intensity I = (1/c 0 ) E rms 2

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Next Time Read: 33.8-33.10 Homework: Ch 33, Q: 3, P: 21, 34, 45, 54

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