 Solution

Take the two interfering complex amplitudes to have equal intensities $I_0/2$ and relative phase $kx$. The interference cross term then givesThus the mean intensity is $I_0$, the maximum is $2I_0$, and the minima areThe optical path difference period is $\lambda$ and the mirror-displacement period is $\lambda /2$. The assumed equal intensities refer to the two fields at the chosen output, with matching polarization of waves and full optical coherence. They set the normalization; they should not additionally be interpreted as all incident light entering that output port. A physical lossless Michelson interferometer has a complementary second output.