How Do You Set the Angle of a Diffraction Grating for Retroreflection?

AI Thread Summary
To set the angle of a diffraction grating for retroreflection of a specific wavelength, it is essential to maximize intensity along the retroreflected path. The equation provided relates to the intensity of the diffracted light based on the number of slits and their dimensions. Understanding the parameters β and α in the context of the grating's geometry is crucial for determining the correct angle. The goal is to find the angle θ that satisfies the conditions for constructive interference at the desired wavelength. Clarifying the question may help others provide more targeted assistance.
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I'm choosing an angle for a diffraction grating such that a particular wavelength λ is retroreflected (reflected back along incident path). The book that I'm looking through treats the blazed diffraction grating as a set of N slits. This results in the equation

I(θ)=\frac{I(0)}{N^{2}}(sinc(β)^{2})(\frac{sin(Nα)}{sin(α)})^{2}

where β=(kb/2)sin(θ) and α=(ka/2)sin(θ) with b=length of slit and a=distance between center of two adjacent slits

k is the wavenumber(I think).

What I'm looking for is a kick in the right direction. I'm not sure how this equation helps me. I think there is something fundamental that I'm not understanding. Obviously I want the intensity to be maximized along retroreflected path. Any help would be great. Thank you.
 
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Does anyone know how to determine the angle at which to place a diffraction grating such that a particular wavelength of light is reflected back along the path of incidence? Do I need to rephrase the question? Any help is much appreciated.
 
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