Moire pattern and interference of plane EM waves

[Nikitin]

Homework Statement

Look at the Moire pattern in "Oppgave 5" (assignment 5) in the attached pdf file. The Moire pattern you see is supposed to represent the interference between two plane EM waves whose directional $\vec{k}$ vectors form an angle $\theta$ with each other.

Anyway, the main question is: "What is the angle $\theta$ between the patterns if the distance between the interference-strips is $\Lambda = 2mm$ and the wavelength of the light is $\lambda = 550nm$.

Homework Equations

The Attempt at a Solution

According to the solutions manual, the distance between the interference-strips is given by $\Delta \vec{k} = \vec{k_2} - \vec{k_1}$

I do not understand how this is possible. Can somebody explain? This is the only thing I struggle with understanding.

 

[haruspex]

According to the solutions manual, the distance between the interference-strips is given by $\Delta \vec{k} = \vec{k_2} - \vec{k_1}$

That doesn't seem right for two reasons. First that gives a vector, not a scalar. Did you mean d = ||$\Delta \vec{k}$||? Secondly, it surely depends on λ.
Draw a diagram with two sets of parallel lines representing the wave peaks at some instant. Identify the regions of constructive and destructive interference. With a little geometry, find the relationship between d, θ and λ.

 

[Nikitin]

I'm sorry, I was so tired yesterday I didn't explain it. What I meant was:

$\frac{2 \pi}{\Lambda} = |\Delta k|$

thanks for the reply, I'll try that :)

 

[Nikitin]

OK I got it now, thanks. Turns out I was just set astray by the solutions manual as this was really easy...