A diffraction grating 23.3 mm wide has 8210 rulings. Light of wavelength 700 nm is incident perpendicularly on the grating. What are the (a) largest, (b) second largest, and (c) third largest values of θ at which maxima appear on a distant viewing screen?

11. A diffraction grating 23.3 mm wide has 8210 rulings. Light of wavelength 700 nm is incident perpendicularly on the grating. What are the (a) largest, (b) second largest, and (c) third largest values of θ at which maxima appear on a distant viewing screen?
a. _____degrees
b. _____degrees
c. _____degrees
12. A grating has 420 lines/mm. How many orders of the visible wavelength 524 nm can it produce in addition to the m = 0 order? (_____units)
13. The mean lifetime of certain subatomic particles is measured to be 1.7511 μs when they are stationary. However, the mean lifetime of fast-moving particles of the same kind observed in a burst of cosmic rays is measured to be 18.596 μs. What is the speed parameter β of these cosmic-ray particles relative to Earth? (_____units)
14. You wish to make a round trip from Earth in a spaceship, traveling at constant speed in a straight line for exactly 3 months (as you measure the time interval) and then returning at the same constant speed. You wish further, on your return, to find Earth as it will be exactly 1000 years in the future.
a. (a) To eight significant figures, at what speed parameter must you travel? (____units)
b. (b) Does it matter whether you travel in a straight line on your journey? (Yes/ No)
15. An unstable high-energy particle enters a detector and leaves a track 1.37 mm long before it decays. Its speed relative to the detector was 0.931c. What is its proper lifetime in seconds? That is, how long would the particle have lasted before decay had it been at rest with respect to the detector? (____units)
16. An electron of β = 0.999 995 moves along the axis of an evacuated tube that has a length of 2.32 m as measured by a laboratory observer S at rest relative to the tube. An observer S’ at rest relative to the electron, however, would see this tube moving with speed v (=βc). What length would observer S’ measure for the tube? (____units)
17. A meter stick in frame S’ makes an angle of 42° with the x’ axis. If that frame moves parallel to the x axis of frame S with speed 0.97c relative to frame S, what is the length of the stick as measured from S? (____units)
18. Observer S reports that an event occurred on the x axis of his reference frame at x = 2.51 x 108 m at time t = 1.89 s. Observer S’ and her frame are moving in the positive direction of the x axis at a speed of 0.475c. Further, x = x’ = 0 at t = t’ = 0. What are the (a) spatial and (b) temporal coordinate of the event according to S’? If S’ were, instead, moving in the negative direction of the x axis, what would be the (c) spatial and (d) temporal coordinate of the event according to S’?
a. _____units
b. _____units
c. _____units
d. _____units
19. The origins of two frames coincide at t = t’ = 0 and the relative speed is 0.998c. Two micrometeorites collide at coordinates x = 114 km and t = 282 μs according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S’?
a. _____units
b. _____mus
20. An experimenter arranges to trigger two flashbulbs simultaneously, producing a big flash located at the origin of his reference frame and a small flash at x = 32.8 km. An observer, moving at a speed of 0.372c in the positive direction of x, also views the flashes. What is the time interval in seconds between them according to her? (____units)