Define coherence in the context of light interference.

Two in-phase coherent waves have path difference \(3\lambda\). Classify the interference.

Two in-phase coherent waves have path difference \(2.5\lambda\). Classify the interference.

A path difference of \(0.30\lambda\) corresponds to what phase difference?

Two coherent waves have source phase difference \(\phi_0=\pi/3\) and path difference \(\lambda/6\). Find the total phase difference.

Two coherent waves have initial phase difference \(\pi\). Find the smallest positive path difference that produces constructive interference.

A two-source experiment has path difference \(0.40\,\mu\mathrm{m}\) and wavelength \(600\,\mathrm{nm}\). The sources are in phase. Find the phase difference and classify the result qualitatively.

Two equal-amplitude coherent fields have phase difference \(2\pi/3\). Find the resultant amplitude in terms of one-wave amplitude \(E_0\).

Two waves have amplitudes \(3A\) and \(2A\). What are the maximum and minimum possible resultant amplitudes?

Explain why a stable interference pattern requires more than two waves having the same wavelength.

Derive the in-phase destructive condition \(\Delta r=(m+1/2)\lambda\) from the phase condition.

Two coherent sources have source phase difference \(\phi_0\). Derive the path-difference condition for constructive interference.

Two waves from the same source travel paths differing by \(1.2\,\mathrm{mm}\). The source has coherence length \(0.8\,\mathrm{mm}\). Predict what happens to fringe contrast.

A minimum in an interference pattern is not dark. Give a quantitative explanation using amplitudes \(A_1\) and \(A_2\).

Two beams have phase difference that drifts uniformly through many cycles during the detector integration time. Show why the observed intensity becomes the incoherent sum.

A source has finite bandwidth \(\Delta f\). Use a wave-packet argument to estimate the coherence length scale.

A laser has bandwidth \(1.0\,\mathrm{MHz}\). Estimate its coherence length. State why this is only an estimate.

Two equal-amplitude waves have a random phase difference that is equally likely to be \(0\) or \(\pi\) during exposure. What intensity is observed relative to one-beam intensity \(I_0\)?

A two-source pattern suddenly shifts sideways but keeps the same fringe spacing. Which model parameter changed: wavelength, source separation, or source phase? Justify.

Prove that interference cannot be modeled by adding intensities first, using two equal beams as a counterexample.