Help with deriving this diffraction equation

[Emidy]

Homework Statement

Hi! I need help with showing how to derive this formula for the diffraction of a laser:
m λ = d (sin(θm) - sin(θi))

where:
d = groove spacing
m = order of diffraction
λ = wavelength of laser
θi = angle of incidence
θm = angle of diffraction

Homework Equations

I found this site that has diagram and sort of explains it, but not really. Also, their equation is a bit different:
http://www.madsci.org/posts/archives/2003-05/1053350704.Ph.r.html"

2. The attempt at a solution
Well... I've tried to understand the website's way of deriving it, but they just say "using trigonometry, you can find that..." blah blah blah, and that doesn't really help.

Any help at all would be appreciated. Thank you!

 

[ehild]

The figure shows two rays (1, 2) of the incident beam, and two ones (1', 2') diffracted by θ_m. CD is the last common wavefront in the incident beam, and AB is the first common wavefront in the diffracted beam. The ray 1 travels the length AD after the last common wavefront till it reaches the grating and 2' travels the length BC after leaving the grating before it reaches the first common wavefront with 1'. So the difference of path lengths is BC-AD. The formula in the article is wrong.

ehild