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

Definitions

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

Laser cavities have this 1-D g(n) 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 Routput How could we get just one cavity mode to lase?

Laser cavities have this 1-D g(n) 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 Routput

E/M 3D wave modes in a vacuum Derive 3-D density of modes 1/8 shell, 2 polarizations: Independent of box size used for derivation

Classical thermo theory and the ultraviolet catastrophe Equipartition theorem (classical) gives infinite u Every “degree of freedom” in u (E2 and B2) is filled with energy of kT/2! Build and from these pieces

Quantum resolution Planck: 1. A mode at n accepts energy only in precise quanta (photons) of ____ 2. The avg n 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 106 K. Why don’t we die of x-rays? Emissivity e(n) comes from complex index n(n),k(n) and roughness. Where absorption is high, emission is high. blackbody I made

Compare three frequency regions near different photon energies: hn= 0 Compare three frequency regions near different photon energies: hn= 0.5 eV (IR), hn = 2 eV (red light) and hn = 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 g (modes per Hz per m3)? (Find relative factors) same 0.5 eV 2 eV 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 n (photons per mode)? (Find the n’s…take Euler’s e ≈ 3) same 0.5 eV 2 eV 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 r (energy per Hz per m3)? same 0.5 eV 2 eV 4 eV

When is a body not a “blackbody”? 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 less than more than the same as