Question

In a spectroscopy problem, d sin(theta)=n lamda.
Is d taken to be the number of slits per meter, slits per mm, or mm per slit/m per slit?

Answer 1

I believe it is the distance between the slits.

Answer 2

`d is the distance between slits (note that d = 1 / N if N, called the grating constant, is the number of lines per unit length) and n is the "order number", a positive integer (n = 1, 2, 3, ...) representing the repetition of the spectrum. `
http://www.physics.smu.edu/~scalise/emmanual/diffraction/lab.html