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Electromagnetic Radiation Physics 202 Professor Lee Carkner Lecture 20

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

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

EM Spectrum

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

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

Sensitivity of Your Eye

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

Inverse Square Law

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

Comet Hale- Bopp

Comet Tails

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

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)

Light Sail

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

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

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:

Traveling EM Wave

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

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

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

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

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