Diffraction grating, angular with of the intensity peaks to the first maximum

[Leb]

Homework Statement

A diffraction grating is ruled with 500 lines/mm and
is 1 mm in width. Calculate the angular width of
the intensity peaks to the first minimum in the
Fraunhofer diffraction pattern of this grating, when
illuminated with light of λ = 600 nm.

Homework Equations

n- order, d separation of slits
nλ = dsinθ

Single slit function ψ(θ)=Aa sinc (kθa/2) (not sure if relevant)
A-amplitude,
a -width of the slit
k = 2π/λ
b = 1mm the width of the

The Attempt at a Solution

TBH, I am not really sure what do they mean by angular width ( I assume θ). But I was not sure how to attempt this problem. I was thinking of convolving f(x) = ...+ δ(x+ 2d)+δ(x+d)+δ(x)+δ(x-d)+δ(x-2d)+... [the infinite array of slits of negligible width] with g(x) = (from -b/2 to b/2)∫dx [the width of the grating] and then looking for zeros of intensity, from which I can tell the θ. Does this sound correct ?

 

[jbsteele]

If yes, how can I do this? Maybe it is easier to just solve the equation nλ = dsinθ ? Any help would be greatly appreciated. Thanks!