Why does moving one Michelson mirror by \(\Delta L\) change the optical path by \(2\Delta L\)?

Write the relation between mirror displacement, wavelength, and number of fringes shifted.

A mirror moves \(300\,\mathrm{nm}\) using \(600\,\mathrm{nm}\) light. How many fringes pass?

Using \(500\,\mathrm{nm}\) light, 24 fringes pass. Find the mirror displacement.

A mirror movement of \(8.0\,\mu\mathrm{m}\) causes 32 fringes to pass. Find the wavelength.

The arms differ in length by \(0.80\,\mu\mathrm{m}\). What is the round-trip path difference?

A mirror is translated at \(20\,\mathrm{nm\,s^{-1}}\) using \(500\,\mathrm{nm}\) light. At what rate do fringes pass?

A mirror displacement produces a phase change \(\Delta\phi=6\pi\). How many fringes pass, and what is \(\Delta L\) in terms of \(\lambda\)?

A gas cell of length \(L\) and refractive index \(n\) is placed in one arm. Derive the double-pass fringe shift relative to air.

A \(4.0\,\mathrm{cm}\) gas cell produces 30 fringes using \(600\,\mathrm{nm}\) light. Find \(n-1\).

A mirror mounted on a piezo moves \(0.25\,\mathrm{nm}\) per volt. Using \(632.8\,\mathrm{nm}\) light, how many volts are needed for one fringe shift?

A Michelson interferometer is used to measure wavelength. The mirror moves \(0.100\,\mathrm{mm}\), and 316 fringes pass. Find \(\lambda\).

A mirror displacement is reported as \(N\lambda\) instead of \(N\lambda/2\). Identify the conceptual error.

A Michelson arm contains a transparent plate of thickness \(t\) and index \(n\). Derive the equivalent mirror displacement that would produce the same fringe shift.

A sample plate of thickness \(1.0\,\mathrm{mm}\) is inserted in one arm and causes 1200 fringes using \(500\,\mathrm{nm}\) light. Find \(n-1\).

A mirror oscillates as \(L(t)=L_0+A\cos\Omega t\). Derive the time-dependent fringe count relative to \(L_0\).

A Michelson interferometer is adjusted from bright to the next dark output at the detector. What mirror displacement is required?

A thermal expansion changes one arm length by \(\Delta L=\alpha L\Delta T\). Derive the number of fringes shifted.

A Michelson measurement gives a fringe shift but the source coherence length is shorter than the arm path difference. Explain the failure mode.

Prove why Michelson displacement measurements naturally have a factor-of-two sensitivity advantage over a one-way path measurement.