Fringes from Different Interfering Wavelengths

[cecenn]

Homework Statement

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!

Homework Equations

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

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.

 

[dauto]

Use the constructive interference formula to find d and then use the destructive interference formula to find the new wavelength. There are two separate experiments here.

 

[kpisme]

equation you are using is of DIFFRACTION. I think you should use the one of interference , ie,
ß=λD/d ; ß=fringe width , λ=wavelength,D-distance to screen,d-distance b/w slits.