# Uncertainty in Double-Slit Diffraction

1. Feb 3, 2007

### mrjeffy321

I am asked to show that it would be impossible to determine exactly which slit a single photon of light passed through in a double slit diffraction grating without destroying the resulting interference pattern since in order to do so, we would need to know both the momentum and position of the photon to such a degree not allowed by the Heisenberg Uncertainty principle (ΔxΔp would need to be much less than h-bar / 2).

I am not sure how I would go about showing this…I am some-what stuck as to where to start.

I know the momentum of the photon is: p = h / λ.
To get a interference pattern, the size of the slits need to be roughly on the same order as the wavelength of the light. If we know the slits are on the same order as the wavelength of the light and in order for a photon to pass through either one slit or the other we would need to know the photon’s position on this same scale. But what about momentum? We know the photon needs to be traveling in the direction of the screen (not backwards), but this is not a very constraining piece of knowledge.

Once I get a sense of the sizes of Δx and Δp, I need to show that this is << h-bar / 2. And then from the uncertainty principle we know this is impossible, so that means that we cannot know which slit the photon passes through without destroying the interference pattern.