Coherent light with wavelength 597 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe. For what wavelength of light in micrometers will the first-order dark fringe be observed at this same point on the screen? To solve this, I must use the formula for destructive interference: d*sin(theta) = (m + 1/2)*lambda, where m= 0 or -1 since it is the first dark fringe, but I am stuck on using small-angle approximations where sin(theta) = tan(theta) to find d. Could someone please explain this method to me clearly? After finding d, what formula must I use for the 2nd beam's interference pattern to find the 2nd wavelength? Thanks.