Chapter 45: Problem 39

Question: A broad source of light ( $\lambda~=~680~{\rm nm}$) illuminates normally two glass plates of length $L~=~120~{\rm mm}$ that touch at one end and are separated by a wire of diameter $d~=~0.048~{\rm mm}$ at the other end, see figure 25, chapter 45. How many bright firnges appear over the $L~=~120~{\rm mm}$ distance?

Solution: The air gap n = 1 between the plates is the thin film we are dealing with here. Light reflected from the top surface of the bottom plate of glass suffers a $\pi$ phase change while that reflected from the lower surface of the upper plate of glass does not. Maxima occur for $2 d~=~(p+{1\over 2})\lambda$, inserting $d~=~0.048~{\rm mm}$ and $\lambda~=~680~{\rm nm}$ gives p = 140.6, and hence there are 140 bright fringes along the length of the plate.