Lecture 09 Wednesday, January 27, 1999

1. Lecture 09 Wednesday, January 27, 1999 Chapter 24: Interference Coherent Sources Young’s Experiment Physics 112

2. Exam # 1 Wednesday, February 3, 1999 in class Ch. 22, 23, 24 (Sect. 1-6) Hint: Be able to do the homework (both the problems to turn in AND the recommended ones) you’ll do fine on the exam! You may bring one 3”X5” index card (hand-written on both sides), a pencil or pen, and a scientific calculator with you.

3. Homework #3 Will not be due until MONDAY, February 1. The Physics 112 Help Session Mondays 5:30 - 7:00 pm Tuesdays 6:00 - 7:00 pm NSC Room 118

4. d(right) d(left) The sound wave from the left speaker arrives in time t = d(left) / vsound The sound wave from the rightspeaker arrives in time t = d(right) / vsound

5. From the left... From the right... vsound = 343 m/s vsound = 343 m/s If d(right) > d(left), then the sound waves from the left speaker arrive before those from the right speaker. For a typical audible frequency (3430 Hz), l = 10 cm

6. From the left... From the right... For this case, the right speaker is exactly 10 cm further away than the left speaker... How do I know that? Notice that the blue wave is exactly one wavelength away when the red wave arrives.

7. From the right... So, when the blue wave first arrives, the second crest of the red wave will just be arriving as well. This is a case of constructive interference. The sound will be louder at this spot on the field. From the left... The crests and troughs arrive from the two speakers simultaneously and in phase!

8. From the right... a crest arrives From the left... a trough arrives What will happen if I now move to a point on the field that is 5 cm closer to the left speaker than the right speaker?

9. + For this case, the crests arrive from the left speaker at the same time as the troughs arrive from the right speaker. And the troughs arrive from the left speaker at the same time as the crests from the right speaker. In this case, the waves interfere destructively and the sound we hear is softer.

10. Wait a minute... You're not going to tell me that the same thing happens with light?!?!

11. Afterall I’ve frequently walked around in a room with two light bulbs, and I’m gonna tell you, I never ever notice places in the room that are lighter and darker (unless there are shadows in the room).

12. Well, you’re right... You’ll never detect constructive or destructive interference of light waves in a room with two light bulbs. Technically, one reason why has to do with the relationship between the phase of the two light bulbs. For the sound waves from the two speakers, an amplifier is generally attached to both speakers. The amplifier keeps the phase difference between the two speakers constant. Sources with constant phase differences are known as Coherent Sources

13. For the case of the two light bulbs, however, no single device controls the emission of photons from the filament in the two bulbs. In fact, random fluctuations and unevenness in the heating of the filaments pretty much guarantee that no matter how hard we might try, the light coming from the two bulbs will NEVER have a constant phase difference! The phase of the light from these two sources will be changing constantly! Sources like the light bulbs are called Noncoherent Sources

14. Put up a wall with two slits in it between you and the light source Non-coherent sources cannot produce a recognizable interference pattern. If we’re clever, however, we just might be able to think of a way to produce coherent signals from a light source... Any Guesses?

15. Make a Prediction! Let’s Try! In this configuration, it looks like to me like there are two light sources on the wall, one at the location of each slit. Furthermore, the light from the two sources originates from the same light bulb! So the “two sources” must be coherent, right? So, you go home, punch a couple of holes in a black curtain, hang an incandescent bulb on the other side, and what do you see?

16. A black curtain with two dots of white light shining through. I still don't see the interference pattern! Which is to say, as I wander around the room on the far side of the curtain (provided I stay at the same distance from the slits), I don’t find parts of the room brighter and other parts of the room darker. In general, the room is darker the further away from the slits I am (which is what I expected anyway)! What's Going On?

17. d(right) d(left) + There really is no place on the field where we hear nothing… unless… We might also note that for our sound example, we really never find places in the field at which we hear no sound, as suggested by our addition of the waves.

18. Our example assumed that the speakers were emitting a SINGLE frequency. In reality, a human voice or piece of music contains many frequencies that are transmitted simultaneously. Because each of these frequencies has an associated wavelength, all of which will be slightly different from one another, the addition of these waves cannot produce 0 for all frequencies at the same time in the same place! A similar thing is happening with the light from the incandescent bulb...

19. White light from the bulb actually contains light of a variety of wavelengths (just recall what happens when white light passes through a prism). To best observe the interference, therefore, we really need both sources of light to coherently emit the same, single wavelength. A light source that emits a single wavelength of light is known as a monochromatic source. One good example of a nearly monochromatic light source is a laser (Like my laser pointer).

20. Light arrives at the slits of the second screen in phase. monochromatic light source Viewing Screen The screen is used to produce a coherent, in phase light source for the slits in the second screen. Young's Experiment (circa 1800) To demonstrate the interference properties of light waves.

21. Now we’ve created an experiment for light that is completely analogous to the sound in the field around our outdoor stage monochromatic light source bright crests troughs dark

22. The bright lines dim as we move away from the center. Alternating bright and dark regions called fringes! So what do we actually see projected on the screen???

23. central maximum The crests arrive at the same time. The bright fringes appear where the light waves from the two sources arrive in phase. They represent constructive interference. screen double slit

24. trough Zeroth dark fringe crest The dark fringes appear where the light waves from the two sources arrive 180o out of phase. They representdestructive interference. The waves arrive exactly 1/2 a wavelength out of phase. screen double slit

25. The crests arrive at the same time. If we keep moving down the screen, we’ll find the first-order maximum. At this point, the waves are exactly 1 wavelength out of phase, which is equivalent to being in phase! The waves arrive exactly 1 wavelength out of phase. screen double slit

26. Zeroth order maximum 2nd 1st 1st 2nd 1 0 0 1 dark fringes So the image on the screen will look like the following: