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## Main Question or Discussion Point

I'm trying to calculate the uncertainty in momentum/direction resulting purely from the certainty in position caused by a small slit, as a function of the slit width. Can anyone tell me if I'm doing this right?

Starting with the HUP:

dX * dP >= h/4pi

dX = the slit width w

P = h/lambda * sin(theta)

where theta is the angle that the photon might be travelling after the slit relative to the center of the slit

so

dP = 2 * h/lambda * sin(theta)

A factor of 2 because the uncertainty can extend in either direction from the center of the slit

so

w * 2 * h/lambda * sin(theta) >= h / 4pi

sin(theta) >= lambda / (8pi * w)

Is that right?

My only concern with the calculation is that "w" could be so small that sin(theta) could be greater than 1, which is of course impossible, so that's why I think I made an error somewhere.

Thanks for any ideas!

Starting with the HUP:

dX * dP >= h/4pi

dX = the slit width w

P = h/lambda * sin(theta)

where theta is the angle that the photon might be travelling after the slit relative to the center of the slit

so

dP = 2 * h/lambda * sin(theta)

A factor of 2 because the uncertainty can extend in either direction from the center of the slit

so

w * 2 * h/lambda * sin(theta) >= h / 4pi

sin(theta) >= lambda / (8pi * w)

Is that right?

My only concern with the calculation is that "w" could be so small that sin(theta) could be greater than 1, which is of course impossible, so that's why I think I made an error somewhere.

Thanks for any ideas!