Chapter 25.4, Problem 3aTH

There is a systematic way of determining the locations of all of the minima in a single−slit diffraction pattern that uses the pairing method developed in sections I and II of the tutorial.

To determine the location of the second minimum, divide the slit in half, then apply the method you have developed in tutorial to each half of the slit. To
determine the location of the third minimum, divide the slit into thirds, then apply the same method to each third of the slit.

In this problem, you will generalize this procedure to find the angle to the $m^{th}$ minimum.

a. If the light that passes through one of the m equal parts yields a minimum at an angle θ for points far from the slit, would the light that passes through each of the other $m-1$parts yield a minimum at that same angle? Explain.