1. The problem statement, all variables and given/known data The problem along with its solution is attached as ProblemSolution.jpg. 2. Relevant equations Δx = λ/sinθ (Eq. 1) Δp_x = (h/λ)(sinε) (Eq. 2) 3. The attempt at a solution In Wikipedia, I found this article: http://en.wikipedia.org/wiki/Heisenberg's_microscope which uses (Eq. 2) from the “Relevant equations” section above but, comparing it to my attached jpg file, ε = 2θ so I feel that the equation should become Δp_x = (h/λ)(sin(2θ)) but my jpg file states that it is Δp_x ≈ 2(h/λ)(sin(θ)) instead. Why is this the case? I even confirmed with Wolfram Alpha that sin(2θ) ≠ 2sin(θ). sin(2θ) = 2sinθcosθ but I don't see any cosθ anywhere. Also, in the solution in the jpg file, there is the Δp_x ≈ 2h(v/c)sinθ equation; is it this equation that “[shows] that if we minimize Δx by reducing λ, this will result in a loss of information about the x-component of the elctron momentum?” If so, then what's the purpose of the Δx Δp_x product? Is the value of Δx Δp_x ≈ 4πħ = 2h supposed to be an approximation to the Heisenber Uncertainty Principle equation: Δx Δp_x ≥ ħ/2? Lastly, the last part of the solution says “We can attempt to overcome this difficulty by [ . . .].” What's the difficulty we are attempting to overcome? Is it the difficulty of measuring both the position and momentum of an electron simultaneously? Could someone please explain, confirm and/or deny these things to me even if it seems obvious to you? If more information is needed or you want me to rephrase something, just ask. Any input would be GREATLY appreciated! Thanks in advance!