# 2-d Diffraction

1. Oct 19, 2008

### Haftred

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

I am trying to solve the following homework problem:

1) A laser beam of light with wavelength λ=600nm shines perpendicular to a slide that has a
rectangular pattern of small holes that can be viewed as point sources. The spacing
between the holes is a=40μm and b=30μm along the x and y directions, respectively. The
light passing through the slide is projected on a screen 2 meters behind the slide.
Determine the positions of the spots on the screen using the small angle approximation.
Describe how the answer to problem 1 changes if the holes are squares of side 10μm.

2. Relevant equations

Sigma[e^i(Delta(k)*T]*S(g)

S(g) = integral[(e^(G dot r)*A(r))dr]

3. The attempt at a solution

For the first part, I solved for G, which is the basis for the reciprocal lattice. Since a1 = 40 um and a2 = 30 um, I used the formula which states that a(i) dot b(j) = 2Pi (kronecker delta i,j), so b1 = 2Pi / 40 and b2 = 2Pi / 30. I am confused how I use these reciprocal lattice vectors. Also, do I solve for S(g) in the first part as well as the second part?

Thanks