For two equal coherent beams each of intensity \(I_0\), write the intensity as a function of phase difference \(\delta\).

For two equal coherent beams each of intensity \(I_0\), find \(I\) at \(\delta=0\) and \(\delta=\pi\).

Write the general two-beam interference intensity formula for intensities \(I_1\) and \(I_2\).

Two equal beams each have \(I_0=5.0\,\mathrm{W\,m^{-2}}\). Find the maximum and minimum intensities.

Two coherent beams have intensities \(16\) and \(9\,\mathrm{W\,m^{-2}}\). Find \(I_{\max}\) and \(I_{\min}\).

For \(I_1=16\), \(I_2=9\,\mathrm{W\,m^{-2}}\), find the intensity when \(\delta=\pi/2\).

A pattern has \(I_{\max}=49\) and \(I_{\min}=1\,\mathrm{W\,m^{-2}}\). Find the visibility.

A double-slit point has path difference \(\lambda/3\). For equal beams each of intensity \(I_0\), find the resultant intensity.

Derive \(I=4I_0\cos^2(\delta/2)\) for two equal coherent beams.

Derive the unequal-beam maximum and minimum intensities from the general formula.

A measured interference pattern has visibility \(V=0.80\). If \(I_{\max}=90\,\mathrm{W\,m^{-2}}\), find \(I_{\min}\).

Two beams have intensity ratio \(9:1\). Find the visibility of their interference fringes.

A phase difference fluctuates uniformly over \(0\) to \(2\pi\) during exposure. Use the intensity formula to find the observed average.

A pattern has nonzero minimum intensity. Give two distinct physical reasons and connect each to a model parameter.

A two-beam pattern has \(I_{\max}=36\) and \(I_{\min}=4\,\mathrm{W\,m^{-2}}\). Recover the individual beam intensities assuming perfect coherence.

For equal beams, find the phase width around a maximum for which intensity is at least half the maximum.

A detector saturates at \(30\,\mathrm{W\,m^{-2}}\). Two equal coherent beams each have \(I_0=10\,\mathrm{W\,m^{-2}}\). Which phase range causes saturation?

Show that two coherent beams can produce local intensity greater than the sum of their separate intensities without violating energy conservation.

For unequal beams, derive visibility directly in terms of \(I_1\) and \(I_2\).

Prove that maximum fringe visibility requires equal beam intensities.