Walker, Halliday & Resnick — Interference: Problem 32

32 Two rectangular glass plates ($n = 1.60$) are in contact along one edge and are separated along the opposite edge (Fig. 35-25). Light with a wavelength of $700\text{ nm}$ is incident perpendicularly onto the top plate. The air between the plates acts as a thin film. Nine dark fringes and eight bright fringes are observed from above the top plate. If the distance between the two plates along the separated edges is increased by $700\text{ nm}$, how many dark fringes will there then be across the top plate?