1. The problem statement, all variables and given/known data In-phase light from a laser with an effective power of 2x105J and a wavelength of 1064nm is sent down perpendicular 4km arms of the LIGO detector. (i) Determine the number of photons travelling in the interferometer arms. (ii) Assuming the detector is sensitive enough to detect single photons at the initial position, estimate the precision with which a change in the length of one of the arms can be detected. 2. Relevant equations c=ƒλ E=hƒ ρ=E/c ΔpΔx ≥ ħ/2 3. The attempt at a solution (i) Photon frequency = c/λ = (3x108)/(1064x10-9) = 2.82x1014Hz Photon Energy = hƒ = (6.626x10-34)(2.82x1014) = 1.87x10-19J Time for light to travel the length of the arms twice (i.e. return to initial position)= 2 x (4000/c) = 2.66x10-5s Laser releases 2x105J per second, which is 1.07x1024 photons per second 1.07x1024 photons per second x 2.66x10-5s = 2.85 x 1019 photons (ii) I was very unsure how to do this part. My initial thought was the uncertainty principle so I tried that but I don't think it is correct. Sensitive to single photons, ΔE = hf = 1.87x10-19J Δρ = ΔE/c = 6.23x10-28Ns ΔpΔx ≥ ħ/2 Δx = ħ/2Δp = 8.46 x 10-8m I don't think my answers are correct, especially (ii). Am I using the wrong methods? Or correct methods but have made a mistake?