1. A laser of unknown wavelength is aimed at a double slit in an opaque screen, with slits 0.8 mm apart. The resulting wave pattern is projected onto a screen 2.0 m beyond it. You make the following measurements relative to the central maximum: Bright Fringes: 1.1 mm, 2.2 mm, 3.4 mm, 4.5 mm Dark Fringes: 0.6 mm, 1.7 mm, 2.8 mm, 3.9 mm Given this information, find the following: a) The wavelength of your laser. b) The position of the 5th order bright fringe to the nearest one-tenth of a millimeter. c) The position of the fifth order dark fringe to the nearest one-tenth of a millimeter. Note that your position measurements are accurate to only the nearest 0.1 mm. This means your wavelength calculation from each position measurement will vary slightly from the others. How should you handle this

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.