Diffraction grating, number of slits, and intensity

[serverxeon]

Homework Statement

Got a question in a school examination, but here's the part I want to ask.

How does the number of slits per unit length, affect the intensity of the diffraction pattern?

What I do know is that the finer the slit separation, the wider the angle opens up.
But intensity is against per unit area...

Any formula I should be looking at?

I have only got d*sinθ=nλ

Level: Cambridge GCE Advanced Level

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I thought that since, on average 50% of the light hits the material, 50% of the light passes through the slit,
the intensity should be unchanged regardless of how fine the grating is ruled.

 

[jbsteele]

Homework Equations d*sinθ=nλThe Attempt at a SolutionIt is known that the intensity of the diffraction pattern is inversely proportional to the square of the slit separation. That is, the greater the slit separation, the lower the intensity of the diffraction pattern. This can be shown mathematically as follows:Intensity ∝ 1/(d^2)Where d is the slit separation.Therefore, as the number of slits per unit length increases, the intensity of the diffraction pattern decreases.