Solving Doublet Slit Problem: Find Wavelength of Laser 2

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To solve for the wavelength of the second laser, lambda_2, the equations for the positions of interference maxima and minima must be set equal, as both lasers will produce patterns at the same angle. Given that the first laser has a wavelength of d/8 and the slit separation d is 0.350 mm, the relationship between the maxima and minima can be established using the equations dsin(theta) = m(lambda1) and dsin(theta) = (m + 0.5)(lambda2). By substituting m values for the second maximum of the first laser (m=2) and the fourth minimum of the first laser (m=3.5), the equations can be manipulated to find lambda_2. The calculations involve solving for x in the equation 2/d*d/x = 3.5/d*d/8. The final result will yield the required wavelength for the second laser.
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Homework Statement


A laser with wavelength d/8 is shining light on a double slit with slit separation 0.350 mm. This results in an interference pattern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits.

What is the wavelength lambda_2 of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.350 mm?


Homework Equations


location of interference maxima: dsin(theta) = m(lambda1)
location of interference minima: dsin(theta) = (m+.5)(lambda2)


The Attempt at a Solution



i know that sin(theta) has to be the same for both of them, so i set these equations equal to sin(theta):
sin(theta) = (m*lambda1)/d
sin(theta) = ((m +.5 )*lambda2)/d

therefore:
(m*lambda1)/d = ((m +.5 )*lambda2)/d

d is given in the problem, so you know d for both sides. you also know that d/8 equals lambda one, so that can be solved. i have tried 2=m for lambda one because it is the second maxima and 3.5=m for lambda two (mastering physics told me to remember that the first minima is zero, not 1). i keep on getting the wrong answer though! please help!
 
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What is the wavelength lambda_2 of the second laser that would place its
second maximum at the same location as the fourth minimum of the first laser, if d = 0.350 mm?
So the equation should be
2/d*d/x = 3.5/d*d/8 .Solve for x, and then find the wavelength.
 
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