Blackbody radiation How does a solid contain thermal energy? Can a vacuum be “hot”, have a temperature? Why does solid glow when it’s hot? Yes its fields (photons) can be in equilibrium with objects at T Hot vacuum oven with a cold object inside

Definitions

E/M wave modes in a vacuum or laser 1-D waves (used for lasers!) Derive modes per hertz per length If we double L, number of modes/Hz doubles, but modes/Hz/L is constant large L small L Derive mode spacing  fundamental frequency

Laser cavities have this 1-D g( ) 1. Gain medium 2. Laser pumping energy 3. High reflector (R  1 4. Output coupler (R <1) 5. Laser beam Depends on L of atoms in gas, crystal Most laser emits many lines (modes). 1/decay time: Sharper for higher R output How could we get just one cavity mode to lase?

E/M 3D wave modes in a vacuum Derive 3-D density of modes Independent of box size used for derivation

Build and from these pieces Classical thermo theory and the ultraviolet catastrophe Equipartition theorem (classical) gives infinite u Every “degree of freedom” in u (E 2 and B 2 ) is filled with energy of kT/2!

Quantum resolution Planck: 1. A mode accepts energy only in precise quanta of ____ 2. The avg no of quanta in a mode goes down fast if _____ 3. Equipartition (classical) works only for modes where _____

When is a body not a “blackbody”? Sun’s corona is 10 6 K. Why don’t we die of x-rays? Emissivity e( ) comes from complex index n( ),  ( ) and roughness. Where absorption is high, emission is high. blackbody I made

In a vacuum, which frequency region has the most g (modes per Hz per m 3 )? (Find relative factors) a)same b)0.5 eV c)2 eV d)4 eV Compare three frequency regions near different photon energies: h = 0.5 eV (IR), h = 2 eV (red light) and h = 4 eV (soft UV). They are in equilibrium with the surface of the sun at kT≈ 1 eV

In a vacuum, which frequency region has the most n (photons per mode)? (Find the n’s…take Euler’s e ≈ 3) a)same b)0.5 eV c)2 eV d)4 eV Compare the three frequency regions in equilibrium with the surface of the sun at kT≈ 1 eV

In a vacuum, which frequency region has the most spectral density  (energy per Hz per m 3 )? a)same b)0.5 eV c)2 eV d)4 eV Compare the three frequency regions in equilibrium with the surface of the sun at kT≈ 1 eV

When is a body not a “blackbody”? If you throw a piece of transparent glass into a glowing furnace, and it stays transparent glass. As it comes to equilibrium with the furnace, you will see the glass glow ___ the furnace walls a)less than b)more than c)the same as