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)

1. In a double-slit arrangement the slits are separated by a distance equal to 110 times the wavelength of the light passing through the slits.
(a) What is the angular separation between the central maximum and an adjacent maximum?
(b) What is the distance between these maxima on a screen 52.4 cm from the slits?
2. A double-slit arrangement produces interference fringes that have an angular separation of 3.32 x 10-3 rad for light with a wavelength of λ = 418 nm. For what wavelength would the angular separation be 9.93% greater?
3. Monochromatic light of wavelength 555 nm illuminates two parallel narrow slits 6.07 μm apart. Calculate the angular deviation of the third-order (for m = 3) bright fringe? Units
4. We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.27) so that reflection of light at wavelength 689 nm is eliminated by interference. What minimum thickness can the coating have to do this? (in nm)
5. A 660-nm-thick soap film (n = 1.43) in air is illuminated with white light in a direction perpendicular to the film. For how many different wavelengths in the 300 to 700 nm range is there
a. (a) fully constructive interference (__units)
b. (b) Fully destructive interference in the reflected light? (__units)
6. The rhinestones in costume jewelry are glass with index of refraction 1.50. To make them more reflective, they are often coated with a layer of silicon monoxide of index of refraction 2.00. What is the minimum coating thickness needed to ensure that light of wavelength 471 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference? ____nm
7. Monochromatic light of wavelength 577 nm is incident on a narrow slit. On a screen 1.51 m away, the distance between the second diffraction minimum and the central maximum is 1.73 cm.
a. (a) Calculate the angle of diffraction θ of the second minimum. (____units)
b. (b) Find the width of the slit in nanometers.(____units)
8. Light of wavelength 547 nm is incident on a narrow slit. The angle between the first diffraction minimum on one side of the central maximum and the first minimum on the other side is 1.34°. What is the width of the slit? (____units)
9. (a) How far from grains of red sand must you be to position yourself just at the limit of resolving the grains if your pupil diameter is 1.7 mm, the grains are spherical with radius 54 μm, and the light from the grains has wavelength 660 nm? ( _____units) (b) If the grains were blue and the light from them had wavelength 430 nm, would the answer to (a) be larger (show 1) or smaller (show 0)?
10. The radar system of a navy cruiser transmits at a wavelength of 1.5 cm, from a circular antenna with a diameter of 1.9 m. At a range of 8.3 km, what is the smallest distance in meters that two speedboats can be from each other and still be resolved as two separate objects by the radar system? (_____units)