Electromagnetic waves E/M oscillations at any frequency can propagate in a vacuum. = 3.00 x108 m/s Plane waves are the simplest. E and B are perpendicular

Electromagnetic waves E/M oscillations at any frequency can propagate in a vacuum.

Electromagnetic waves E/M waves in materials travel slower, and can be absorbed. l shrinks when they go slower Index of refraction:

How are E/M waves started? ______________ of charges in atoms and antennas

How are E/M waves started? Far from the charges they become plane waves Direction of greatest intensity: _______ to the line of acceleration.

Polarization of E/M waves The direction of E is the polarization direction.

Polarization of E/M waves Light from the sun, lightbulbs is unpolarized (all E directions  to ray, or random polarization).

Polarizing filter Final polarization is along the filter’s transmission axis

Polarizing filter How much light gets through? Unpolarized light is randomly half in x direction , half y direction, by components. So half the intensity gets through

Malus’ law If light is well polarized, how much gets through a polarizing filter? Angle between light polarization and filter axis

P1. Light is horizontally polarized, and then hits a polarizer with its axis at 45 degrees vs x axis, then another at 60 degrees vs the x axis. Which is true? a. b. c. d.

Polarization by reflection One polarization (horizontal) reflects better off horizontal surfaces at medium angles. Use polarized sunglasses to absorb that

Reflection by polarization At Brewster’s angle: only one polarization reflects.

Polarization in devices, 3-D

Plane wave amplitudes and energy E and B magnitudes are linked: equal energy in E and B

Light pressure

Creation of image with very dim light

Quantum view of an E/M wave E/M waves actually exist in pieces called photons! The higher the frequency, the “bigger” the piece’s energy and momentum. They each have energy E = hf=hc/l, and momentum p =E/c= h/l Planck’s constant:

Which color of light has the largest energy photons? blue red same

Photons and wave energies Write these in terms of the number of photons N and the frequency f of the light:

Suppose we have two laser beams emitting the same power of light (energy/ time) hitting a screen. P1. Which beam has the most photons hitting the screen per time? A. infrared (hf = 2.0 eV) B. blue (hf = 3.0 eV) C. neither…same P2. Which beam has the most force (momentum per time) on the screen, assuming all the photons are absorbed?

National ignition facility 192 huge laser pulses focusing on a pellet 2 million joules of energy 300 billion atmospheres pressure