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Intensity distribution of a grating

mprovod
in Homework Help

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A grating with N slits of spacing d is iluminated normally with monochromatic light of wavelength λ, and the p-th order principal maximum is observed at an angle Өp. The intensity at angle Ө is given by:

 

I(α) = sin²(Nα/2)/sin²(α/2) where α=(2Π/λ)d*sin(Ө)

 

Show from this equation that adjacent minima fall at angles Өp+αӨp and α-Өp, where αӨp = λ/(Ndcos(Өp))

 

 

 

Could someone please help me? I tried to differentiate the Intensity equation w.r.t. α to find what the values of the minima and maxima are, but then realised, that the separation of minima from maxima must depend on the angle Ө. I don't know how to approach this further.

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