Phys. 122: Thursday, 08 Sept. HW 2 returned: please pick up yours in front. Written HW 3: due by 2:00 pm. Written HW 4: Ch. 25, probs. 12, 18, 21, 26, 34, and 40. Due in one week. Mast. Phys.: Assign. 2 due Tuesday evening. Reading: Finish ch. 25 by Tuesday. Begin ch. 26 after that. Exam 1: will be over material we've covered in chapters 23, 20, 21, and 22, sometime after your HW 3 has been graded and returned. (So this will be no earlier than 2 weeks from today, but no later than 3 weeks from today.) A study guide will be available soon from our website. HW hints needed? Two-source interference For large L, the distances to the two sources are different by d sin . It will be useful later to notice that tan = y/L. Two-source interference Negative m values are also allowed! For small angles, we can use the approximation sin tan . If measured in radians, both of these are also approximately itself (for small angles)! In that case, we can replace sin by y/L. Analyzing Double-Slit Interference The mth bright fringe emerging from the double slit is at an angle: where m is in radians, and we have used the small-angle approximation. The y-position on the screen of the mth bright fringe on a screen a distance L away is: Slide 22-34 A laboratory experiment produces a double-slit interference pattern on a screen. The point on the screen marked with a dot is how much farther from the left slit than from the right slit? A B C D E QuickCheck 22.3 Slide 22-35 Clickers: Coherent light of a single color is passed through a two-slit apparatus, producing spots on the far wall. If the slits are moved closer together, what happens to the spots in the pattern? a) They get closer together. b) They move farther apart. c) They remain in the same place, but change color. d) They go away completely. e) They get clustered and become one large spot. Clickers: Coherent light of a single color is travelling in vacuum through a diffraction grating (multiple-slit apparatus), producing interference on a screen. If the whole setup is immersed in water, what happens to the spots in the pattern? a) They get closer together. b) They move farther apart. c) They remain in the same place, but change color. d) They go away completely. e) They get soggy and spread out like wet ink. Clickers: Suppose that instead of 2 slits with separation d, we have many slits all equally spaced (at separation d each). Where are the brightest spots in the many-slit pattern (compared to the 2-slit one, using the same color of light)? a) They will have moved apart b) They will have moved inward c) They will stay in the same location d) They will all be replaced by dark spots e) They will be directly opposite to the slits, since many slits act like a comb for the light, straightening it out. Figure 32.8 Notice that the brightest spots are in the same place as for 2 slits! New dark spots between appear, though, making the lines more narrow. Clickers: in a five slit system, how many minima lie between the zeroth and first order maxima (in the interference pattern)? a) Zero b) One c) Two d) Four e) Five Reflection Gratings In practice, most diffraction gratings are manufactured as reflection gratings. The interference pattern is exactly the same as the interference pattern of light transmitted through N parallel slits. Slide 22-62 Reflected waves can also act like many slits! This occurs (for example) from glancing reflections off a CD or DVD, or a crystal (here). Clickers: Okay... suppose that instead of many slits, we now only have one slit (for coherent light to go through, in an otherwise opaque screen). Can there possibly be any interference now? a) Of course not, you silly professor. b) Yes, if the slit is very, very wide. c) Yes, if the slit is very narrow. d) Yes, if white light is used instead of one color. e) Yes, if black light is used. Light coming from one part of a single slit can interfere with light from other parts of the slit! Single-slit DARK spot formula is similar to the many-slit BRIGHT spot formula, with the slit width a replacing the slit spacing d. (Important Difference: m=0 is NOT allowed for a single-slit dark spot.) Pattern from two slits which are not too far apart compared to the width of each slit: BOTH the two-slit and one-slit patterns appear! Clickers: Approximately how wide is each slit a, compared to the slit separation d, for the pattern produced below? a) Can't tell without more information. b) They are about the same (d a). c) d 100 a d) d 10 a e) a 10 d In SI units, k is usually written as The two charges must be different! Otherwise, all charges would fly apart. SI charge unit = Coulomb or Coul or just C. [k = 9 x 10 N m/C] Electric Forces: another type of force in Nature Clickers: one Coulomb is... a) A large, dangerous amount of charge b) A typical charge on your socks when they come out of the dryer c) the amount of charges needed to produce one Newton of force at one meter from each other d) the typical amount of charge on a hard drive in a computer e) the typical amount of charge on an atomic nucleus elementary particle