The loupe (50 pts) a loupe is basically a magnifying lens used to magnify objects so that they become easier to see, gemologists use it to examine gems, photographers use it to view slide film. here we'll look at a cheap single lens system: a) (10) the lens is a double convex with radii of curvature of 20.8mm. the material is glass with index 1.82. what is the focal length (mm) of this lens? (15) you place a diamond (index of refraction=2.417) beneath the loupe and examine it. the top face of the diamond is located at 16.0mm away from the lens. what is its magnification? e) (15) draw a principal ray diagram for b) and clearly label the following: the lens, the object, the image, the p-ray, the o-ray, the f-ray, the focal length, the object distance, the image distance, the object height, and image height. d) (10) you noticed a small imperfection inside the diamond with your naked eye. it appears to be 0.2mm beneath the top facet. what is its real position?

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.