Find Lambda_2 for Double Slit Interference Pattern

[yo_man]

Homework Statement

A laser with wavelength d/8 is shining light on a double slit with slit separation d. 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?
Express your answer in terms of d

Homework Equations

I have (dsin(theta)) = 2(lambda_1)
and dsin(theta)= (9/2)(lambda_2)

The Attempt at a Solution

I set the two equations equal to each other, and solve for lambda_2 and get (2/9)dsin(theta), but then it said the answer does not depend on theta.. so I just guessed and put (2/9)d and it said I was off by a multiplicative factor. basically, I'm confused and do not know how to go about solving this problem. please help!

 

[rl.bhat]

I have (dsin(theta)) = 2(lambda_1)
and dsin(theta)= (9/2)(lambda_2) Check this.
Second maximum of second laser and fourth minimum of the first laser

 

[yo_man]

is it

(2(lambda_2)L)/d = ((4+.5)(d/8)L)/d

 

[rl.bhat]

Yes.