Understanding Sideways Momentum in Heisenberg's Thought Experiment

[FeDeX_LaTeX]

Hello;

I was reading a book that described Werner Heisenberg's thought experiment. It said that, when a particle scatters electromagnetic radiation with wavelength $$\lambda$$, for the scattered photons to enter the lens of the microscope, they must have a 'sideways momentum' between $$-\frac{h}{\lambda}\sin\alpha$$ and $$+\frac{h}{\lambda}\sin\alpha$$. My question is, what is meant by 'sideways momentum' and how is it any different to ordinary momentum? Can anyone give an analogy to something that I might be more familiar with?

Also, is there a geometrical reason why, for the uncertainty of a particle;

$$\delta x = \frac{\lambda}{\sin\alpha}$$

Thanks.

 

[tiny-tim]

Hello FeDeX_LaTeX!

It just means the component of the total momentum in the sideways direction.