# Diffraction Grating Angles

1. Jan 2, 2012

### phantom113

1. The problem statement, all variables and given/known data

I'm choosing an angle for a diffraction grating such that a laser of particular wavelength λ is retroreflected (reflected back along incident path).

2. Relevant equations
If you have a better way than using the equation below, feel free to explain. 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)=$\frac{I(0)}{N2}(sinc(β)^{2})(\frac{sin(Nα)}{sin(α)})^{2}$

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).

3. The attempt at a solution
What I'm looking for is a kick in the right direction. I'm not sure how this equation helps me. I don't know how to use k and and I don't really know a or b (although I could calculate them). I'm not sure how N^2 comes into play since I don't know the total number of slits on the grating. Also I don't know why the total number of slits should play much of a role when the laser is incident on only a tiny portion of the grating. 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.

Last edited: Jan 2, 2012
2. Jan 2, 2012

### phantom113

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.