Solving Doublet Slit Problem: Find Wavelength of Laser 2

[noellcm]

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!

 

[rl.bhat]

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.