Chapter 25.6, Problem 2bTH

A plate of glass $\left(n=1.5\right)$ is placed over a flat plate of plastic $\left(n=1.2\right)$ . A thin film of water $\left(n=1.33\right)$ is trapped between the plates as illustrated in the diagram at right.

Light of frequency $f=4.8\times {10}^{14}Hz$ is incident from above at essentially normal incidence. The locations of the dark and bright fringes, as viewed from above, are indicated in the top view diagram at right.

In this problem, ignore reflections from the top surface of the glass plate and the bottom surface of the plastic.

b. Determine the thickness of the gap between the plates at the end where the plates are not in contact. (Express your answer in mm.) Show all work.