MS2040_01 Introduction to crystal structures and diffraction theories
Homework #5
Due: 11/20 after class
You are encouraged to organize a study group to solve the problem set.
1. Suppose we have two slits at a distance A apart and each has the width
B. One can describe the system as
1

f ( x )  1
0

 A/ 2  B/ 2  x   A/ 2  B/ 2
A/ 2  B/ 2  x  A/ 2  B/ 2 ; (look at following picture!)
otherwise (for other x )
Please find the Fourier transform of f(x).
2. Please prove that the Fourier transform of d 3 f ( x ) dx 3 is (2iu)3F(u),
where F(u) is the Fourier transform of f(x).