# Fringes from Different Interfering Wavelengths

1. The problem statement, all variables and given/known data

The questions is…
Coherent light with wavelength 597nm 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 will the first-order dark fringe (the first dark fringe next to a central maximum) be observed at this same point on the screen?

But I am doing something wrong because I keep getting an incorrect answer.
Any help would be appreciated! Thank you!

2. Relevant equations

dsinθ=mλ –constructive interference
dsinθ=(m+1/2)λ –destructive interference
λ/d=x/L

3. The attempt at a solution

I think that I should use the equation for constructive interference: dsinθ=mλ
And I am pretty sure you can use the approximation that sinθ≈tanθ
But doing this, and looking at the triangle, I am getting confused as to where to put the values. I think that "m" would be 1, but I am not sure if that is correct.

I also tried using the third equation: (597E-3)*(3E6)/(4.84E3)=370, but this answer is not correct either.

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