Title: ETH_Sem3 / Physik_III / Woche4

Q: What determines the colour of light?
A: Its frequency / wavelength.

Q: What is dispersion?
A: The property that the refractive index depends on the frequency.

Q: What are two possibilities to distinguish between different frequencies of light?
A: - Dispersion
- Interference

Q: What are positive and negative arguments for using a prism as a spectrometer?
A: - compact
- lets you look at the whole spectrum at once
- angle between frequencies is small
  - low spectral resolution

Q: How does a grating spectrometer work?
A: It uses interference of light coming from some sort of periodic pattern.

Q: What is the smallest frequency difference that can be resolved with a grating spectrometer?
A: \[\Delta\omega > 2\pi\frac{c}{2Nd}\]where \(N\) is the number of reflective stripes and \(d\) the distance between them.

Q: Why is a large \(N\) and a small \(d\) better for a grating spectrometer than the opposite?
A: The intensity of the peaks scales with \(N^2\), so for the same size of grating, this collects the most light.

Q: What is this and why is there a reference source?
A: Grating spectrometer, the reference source is here to determine the absolute wavelength.

Q: How does a Michelson interferometer look like?
A: What is this?

Q: What is the measured intensity for the Michelson-interferometer?
In which two ways can we use this?
A: \[I=\frac{I_0}{2}\big(1+\cos(2\omega x /c)\big)\]If the wavelength is known, we can measure changes in \(x\).
If we can change \(x\), then we can use it as a spectrometer and measure the wavelength.

Q: How is the spectral density \(S(\omega)\) defined?
A: The intensity between frequencies \(\omega\) and \(\omega+d\omega\) is given by \[I_0S(\omega)d\omega\]You can think of it as a probability density distribution for the frequency of the light.

Q: What is the spectral resolution of a Michelson interferometer according to the Rayleigh criteria?
A: \[\frac{\Delta\omega}{\omega_0} = \frac{\lambda}{2x_{max}}\]

Q: How does a Fabry-Perot etalon look like and what does it allow us to do?
A: What is this?
Answer for backside:
It allows us to increase the path difference without having to make a really long arm by letting the light bounce back and forth between two mirrors.

Q: What is statistical physics about generally?
A: Taking the microscopic details of a system, which are often impossible to keep track of completely, and connecting them to macroscopic properties.

Q: What is a microstate?
A: A particular configuration of the microscopic properties of the object.
For a gas, this would be the position and momentum of all the gas molecules.

Q: What is a macrostate?
A: A description of the macroscopic, bulk properties of the system.
For a gas, this would be a list of its pressure \(p\), volume \(V\), total particle number \(N\), temperature \(T\), etc.

A single macrostate can be consistent with many microstates.
However, a single microstate always specifies a single macrostate.
\(\longrightarrow\) A microstate contains all the information about the macrostate, but not vice-versa.

Q: What is the fundamental postulate of statistical physics and is it always true?
A: For a closed system with a fixed set of global constraints, every microstate that satisfies the constraints has an equal probability of being occupied.
This is not always true.

Q: What is a closed system in physics?
A: A system that does not exchange matter, but can exchange energy with the outside.

Q: When is a system in thermodynamic equilibrium?
A: When the fundamental postulate is true for that system.

Q: What is the second postulate of statistical physics and when is it true?
A: The macrostate occupied in thermodynamic equilibrium is the one with the largest number of microstates.
It is true for very large systems.

Q: What is the ergodic hypothesis?
A: Over a sufficiently long time, the system will sample each microstate that satisfies the constraints with equal probability.

Q: What is the concept of reversibility and how does it relate to the second postulate?
A: Each change of microstate is reversible. However, it becomes increasingly unlikely that you'll be able to reverse the process of equilibration.
The whole point of the second postulate is that the system always evolves towards equilibrium over time.

Q: What is \(\Omega(x_1,x_2,\ldots)\)?
A: The total number of microstates corresponding to the macrostate specified by \(x_1,x_2,\ldots\)

Q: Suppose you have two independent systems with macrostates specifed by \(x_1,x_2,\ldots\) and \(y_1,y_2,\ldots\).
For the total system, \[\Omega(x_1,x_2,\ldots,y_1,y_2,\ldots) = [...]\]
A: \Omega_1(x_1,x_2,\ldots)\cdot\Omega_2(y_1,y_2,\ldots)

Q: Def: \[\sigma = [...]\](In statistical physics)
A: \ln\Omega

Q: How can we define the temperature of a gas?
A: \[\frac1T = k_B\bigg(\frac{\partial\sigma}{\partial U}\bigg)_{N,V}\]Where \(k_B\) is the Boltzmann constant, \(U\) the inner energy of the gas and \(N\) the number of molecules.

Q: Another important quantity is the entropy \(S\):
\[S = [...]\]
A: k_B\ln\Omega