Two identical diffraction gratings

[skrat]

Homework Statement

We shine a laser light on two identical diffraction gratings as shown in picture.

Calculate $x$, if in Fraunhofer diffraction image the seventh peak is missing.

Homework Equations

The Attempt at a Solution

No idea actually. I know how to do this with one diffraction grating.

For one grating all one has to do is compute a product of Fourier transformations of aperture function and sum of delta functions.
For one grating, the result is $u_p=C\frac{\sin(k_xa)}{k_xa}\frac{\sin(k_xNa)}{\sin(k_xa)}$.

But I have no idea what to do with two diffraction gratings? Is it simply a product of both where one is shifted for $x$ ?

 

[Simon Bridge]

What would you take as:
- the separation of the gratings?
- the thickness of the gratings?
... try redrawing the diagram in a more realistic representation.

There is a clue in the description involving the Fraunhoffer diffraction image... why would there be a peak missing?