Question

GIVEN: Light of wavelength 585 nm falls on a slit 6.66×10−2 mm wide.

Part 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?
*Answer: ?????

Part B: At what angle will the dark fringe that is most distant from the central bright fringe occur?
*Answer: I'm asuming that this will be the equation to use: d*sinA=(N+.5)*L , but I need help finding N in part A to complete this.

Answer 1

A) How many integer values of N satisfy the "dark line" equation
d*sinA = N*L
with |sin A| < 1 ?

N = (d/L) sin A = 113.8 sin A

N can range from -113 to 113 while |sin A| remains below 1. That allows for 226 lines. That includes negative integer values of N.

A central bright fringe occurs at N = 0.

For N=113 (the farthest possible dark fringe from center),
sin A = (113) (L/d) = 0.99257
A = 83 degrees