 Solution

For the double-slit experiment with oblique incidence, the optical path difference has an unknown incident contribution plus $a\sin \theta$ in the outgoing direction. It cancels between adjacent angular features. From a minimum to the next maximum, the path difference changes by $\lambda /2$:This incidence-independent adjacent-fringe wavelength uses the statement that intensity rises directly from the stated zero to the following peak. No absolute interference order or incidence angle is needed; nonadjacent extrema would require the number of intervening fringes.