Chapter 36, Problem 30AP

In the What If? section of Example 36.2, it was claimed that overlapping fringes in a two-slit interference pattern for two different wavelengths obey the following relationship even for large values of the angle θ:

$\frac{m^{\prime }}{m}=\frac{\lambda }{{\lambda }^{\prime }}$

(a) Prove this assertion. (b) Using the data in Example 36.2, find the nonzero value of y on the screen at which the fringes from the two wavelengths first coincide.