Photons Moving Through a Single Slit (Uncertainty)

[trevor51590]

Homework Statement

The diagram is attached. Photons are being beamed with momentum $\rho_{0}$ and mass $m$ at a slit of width A

Estimate the uncertainty $\Delta p_{y}$ emerging from A
Sketch spot size at B as a function of slit width using the uncertainty principle
Determine minimum spot size expected at B as a function of L and the deBroigle wavelegth $\lambda_{0}$

Homework Equations

$\Delta p_{y}\Delta_{y}=\frac{\hbar}{2}$
$\lambda=\frac{h}{p}$

The Attempt at a Solution

My attempt for part one is shown in image two. I achieved an answer of $\frac{h}{\Delta y}$. $\Delta y$ is represented by $a$ in image one
Part two wants spot size as a function of width of slit - I found it as a function instead of L but I believe the sketch is relatively accurate. I'm not sure how to give it in the form it wants
Part three just throws me for a loop and I really don't have any idea

Thank you as always!

 

[mfb]

For part 2, don't neglect the width of the slit - if the slit is very large, this is relevant. As a practical example, you do not expect a beam spot of some micrometers if the slit has a width of one meter (like a window). In addition, I think you should express theta in terms of the width of the slit and the wavelength.

If you fix that part, part 3 will make sense.