# Constructive interference and maximums of interference

I am getting really confused about the experiment of Michelson and Morley. As I understand it, we should be able to observe a destructive interference because light beams go through different optical paths. Destructive interferences form minimums of interference whereas constructive interferences form maximums. Then I translate here what my book says: "After the rotation of $90^\circ$ degrees of the interferometer, we should see a number of fringes equal to the times the width of the phase shift, which is $$\delta\ =\ 4\pi \frac{L_0}{λ} \frac{v^2}{c^2}$$ (which is the sum in absolute value of the longitudinal and transversal phase shift, as I understand it) contains $2\pi$, since according to the following equation, Intensity $$I\ =\ I_0\ cos^2 \frac{\delta}{2}$$ and $$\delta\ =\ \frac{2\pi}{λ} \Delta R,$$ where $2 \pi$ is the phase shift between 2 consecutive maximums of interference"

So what I don't understand is the last line. If a destructive interference is expected, shouldn't we be looking for minimums(that is what destructives interference forms)? Why here are we assuming that the expected result is a constructive interference? Please don't delete this post since I really need help on this.