PHYS 408 HOMEWORK 6 SOLUTIONS

B2 kb 2 exp i kd cos x 4 d 2d d dkx ei 2 k2 kx d

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ￿ ￿￿ 1 2π k kx2 exp i kd + − π /4 |α| d 2d (67) (68) (69) The wave fronts are parabolic, i.e. d ∝ x2 . Compare this problem to the f (x, y ) = δ (x)δ (y ) discussed in class. Note that (at least in my opinion) accurate intuition for a delta-function slit is more difficult to attain than that for a slit of finite (but arbitrary) width, in large part because the delta function model leads expressions that are not as easy to handle analytically or numerically. 11 11.4 two delta-function slits, relative phase difference f (x, y ) = δ (x − b) + iδ (x + b) (70) ￿ ￿ ˜ f (kx , ky ) = e−ikx b + ie+ikx b δ (ky ) g (x, y ) = = = = ≈ = = ￿ ￿ ￿ dkx dkx ￿ ￿ dky ei √ dky ei √ √ 2 2 k2 −kx −ky d i(kx x+ky y ) e 2 2 k2 −kx −ky d i(kx x+ky y ) e ￿ ￿ e−ikx b + ie+ikx b δ (ky ) ￿ e−ikx b + ie+ikx b δ (ky ) ￿ e−ikx b + ie+ikx b ￿ ￿ √ √2 2 2 i k2 −kx d ikx (x−b) iπ /2 dkx e e +e dkx ei k −kx d eikx (x+b) ￿ ￿ ￿ 1 2π k...
View Full Document

Ask a homework question - tutors are online