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Hi I'm reading through a Quantum Mechanics textbook called Quantum Mechanics by Book by Alastair I. M. Rae and in the opening chapter it talks about the Heisenberg uncertainty principle and talks about how a measurement of position of a particle causes an uncertainty from the momentum due to the recoil from the interaction with the illuminating photon.

In the mathematical analysis is sates that in standard optical theory the uncertainty in the resolving uncertainty for the position of an object is.

Δx≈λ/sin(α)

I've tried googling various combinations of the words lens, microscope, resolution, and resolving power and I have not found where this equation/approximation comes from. Can anyone please be of a help?

In the mathematical analysis is sates that in standard optical theory the uncertainty in the resolving uncertainty for the position of an object is.

Δx≈λ/sin(α)

I've tried googling various combinations of the words lens, microscope, resolution, and resolving power and I have not found where this equation/approximation comes from. Can anyone please be of a help?

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