2. 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

4. Definitions

5. 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

6. 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?

7. 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

8. 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

9. 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

10. 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 _____

11. 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

12. 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

13. 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

14. 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

15. 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