# Using diffraction slit as a lens

1. Nov 16, 2013

### gildomar

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

"A TV tube manufacturer is attempting to improve the picture resolution, while keeping
costs down, by designing an electron gun that produces an electron beam which will make
the smallest possible spot on the face of the tube, using only an electron emitting cathode
followed by a system of two well-spaced apertures. (a) Show that there is an optimum
diameter for the second aperture. (b) Using reasonable TV , tube parameters, estimate the
minimum possible spot size."

2. Relevant equations

ΔpΔx≥$\frac{\hbar}{2}$

a sin θ = mλ ?

3. The attempt at a solution

I was thinking that I need to use single slit diffraction on this, since while the single slit equation is for the minimum on the screen, if it goes an equal distance past that, it will create a maxima. I'm a little fuzzy on how Heisenberg's equation fits, since this was from the chapter on the uncertainty principle.

p.s. I was unsure if this question should go here, or in the introductory questions section. I thought that quantum mechanics should be directed here though.