Fraunhofer intensity pattern

1. Mar 25, 2007

Qyzren

1. The problem statement, all variables and given/known data
Derive the equation describing the Fraunhofer intensity pattern from a single
slit of width b centered at the origin. Then show that the same intensity pattern is obtained for a slit that is not centred at the origin (i.e assume the slit edges are at x = a - b/2 and x = a + b/2). Is this physically reasonable? Discuss briefly.

3. The attempt at a solution
Suppose the coordinates of P are (X, Y, Z), and the coordinates of a point Q on the aperture are (x, y,z) where z = 0.
http://img133.imageshack.us/my.php?image=picbe2.jpg
If the distance QP is d then.
http://img84.imageshack.us/my.php?image=pic2qv3.jpg
Now chuck that in
http://img224.imageshack.us/my.php?image=pic3fl2.jpg
to obtain
http://img81.imageshack.us/my.php?image=pic4lr2.jpg

now, how would i attempt the second part of the question?
would my d² = (X - (x+a))² + (Y-y)² + (Z-z)²
and L² = (x-a)² + Y² + Z² ??

meaning d² = L²[1 + (2ax + x² + y²)/L² - (2xX+2yY)/L²]
so d ~= L[1 - (2xX + 2yY)/L²] like earlier?

or am i doing it completely wrong?

Thank you all for your input.
Thanks