Solve the following problems:

Problem A: On a very large distant screen, how many totally dark fringes (indicating complete cancellation) will there be, including both sides of the central bright spot? Solve this problem without calculating all the angles! (Hint: What is the largest that sin? can be? What does this tell you is the largest that m can be?)

Problem B: At what angle will the dark fringe that is most distant from the central bright fringe occur?

Show all work, use additional paper if necessary.