An elliptically polarized beam of light has a degree of polarization equal to 0.4. 55° The major axis is tilted at 55° to the x axis, as shown and the ratio of the minor axes to the major axis of the ellipse is 1-2. What is the Stokes vector for this polarization state, assuming the vector is normalized (i.e. E= 1)?

If the direction E in space 1 is given as shown below and the magnitude E, = 5 volt. Find E, in space 2 and the measure of angle a, If ɛ1, = 3,1; ɛ2r = 5; and 0 = 45°. a

It’s a sunny Saturday afternoon and you are walking around the lake by your house, enjoying the last few days of summer. The sidewalk surrounding the perimeter of the circular lake is crowded with walkers and runners. You then notice a runner approaching you wearing a T-shirt with writing on it. You read the first two lines, but are unable to read the third line before he passes. You wonder, ”Hmmm, if he continues around the lake, I bet I’ll see him again but I should anticipate the time when we’ll pass again.” You look at your watch and it is 5:07pm. You estimate your walking speed at 3 m/s and the runner’s speed to be about 14 m/s. You also estimate that the diameter of the lake is about 2 miles. At what time should you expect to read the last line of the t-shirt?

To study Brownian motion, Bob, a student at the University of Ottawa, used his camera to capture the positions (i.e. displacements) of 50 microscopic dust particles floating on the surface of the water of his aquarium. By setting his camera to record 10 frames per second and noting down each particle's 2D displacement for each recorded frame, he managed to obtain the following mean-displacement vs time graph: 1600 1400 1200 2 1000 V 800 600 400 200 20 40 60 80 100 120 140 Time (s) a. Use the above mean-displacement graph to roughly approximate the diffusion coefficient D of the dust particles with units of um? /s. b. From the diffusion coefficient estimate in a), calculate the root mean- square displacement expected between each consecutive frame? c. Are the diffusion coefficient D and mean-square displacement calculated reasonable for a microscopic particle, or did Bob make a mistake in his calculations? Mean-square disp. (cm²)