Interferometry

Mach-Zehnder Interferometer, He-Ne Laser

Answer the following in writing:

1. In the case of a perfect Mach-Zehnder interferometer, we could observe an intact spot of light for complete constructive interference and complete darkness for distructive interference. In the experiment you will mostly observe patterns of fringes (dark-light stripes), with their complementary images seen at the second screen. Why? How will you be able to achieve a circular diffraction pattern? Read more about interferometry if you find it helpful.
2. What is the advantage of a Mach-Zehnder over the Michelson interferometer? What kind of observations it enables?
3. The He-Ne laser source in the experiment has a principle wavelength of λ₀=632.816±0.001 nm. Calculatle its coherence length using the following equation: $$L_c={c\over {\Delta \nu}}={{\lambda_0}^2 \over {\Delta \lambda}} $$ where L_c is the coherence length, c is the speed of light and Δν is the bandwidth. How is this parameter related to the experimental limitations of the interferometer?
4. How will a change in the angle of any of the mirrors in the interferometer affect the diffraction pattern? What will a change in one of the length of one of the arms cause?
5. Use the equation for the refractive index of the sample, and show how the sample thickness, t, can be extracted from it (when n is known): $$ n={({Nλ\over t}+\cos⁡θ-1)^2+\sin^2⁡θ \over 2(-{Nλ \over t} -\cos⁡θ + 1)} $$

Michelson Interferometer, Thermal Source

Answer the following in writing:

1. Why in the case of a white light source we use a Michelson interferometer and not the Mach-Zehnder configuration? Use the term of "coherence length" and support your explanation with relevant calculations for a Tungsten lamp (T=3,000K).
2. In order to measure the inteference in the frequency domain, a perfectly aligned interferometer is required, and we must avoid fringes. Why is that?
3. The observed spectrum will have the following shape:

   

   Given the energy conservation law must subsist, why are there wavelengths with minimal intensities?
4. In your measurement you have observed four peaks: λ=557, 600, 650, 709 nm. Calculate the temporal delay, Δt, between the two interferometer arms.
5. After addition of a 180 μm thick slide to one of the arms from the previous question, the new observed peaks are: λ=570, 573, 576, 579.1, 582.2 nm. Calculate the slide's refractive index. Why is Δλ constant in this case?