Two diffraction gratings one on top of the other

[zimo]

Homework Statement

Two diffraction gratings are stuck together, both with vertically aligned slits. Grating A has S1 slits and B has S2 slits.
What is the new equivalent grating that is the product of two of the diffraction gratings above?

(s1>s2>>>1)

Homework Equations

a. N* = 1/d

The Attempt at a Solution

Assuming that there are ajacent slits in both - I tried to think of a way that it will make sense.
If s1>s2 , s1 should be a multiple of s2, but I couldn't figure out a way to come to the new grating equivalent.

 

[TSny]

Suppose d₁ and d₂ are the distances between consecutive slits for the gratings. What if the ratio of d₂/d₁ happens to reduce to 3/2? What would be the answer to the question? How about if the ratio reduces to 5/3?