Major Concepts of Physics PHY102 – Lecture #3

1. Major Concepts of Physics PHY102 - 2006Lecture #3 January 24th Waves and Interference 1 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

2. Homework - E-mail address: Go to: http://www.physics.syr.edu/~lmovilea/spring2006longschedule.pdf Identify your section, so your TA The Tas’ e-mail accounts are the following: Ganesh Srinivasan: gsriniva@physics.syr.edu Earnest Akofor: eakofor@syr.edu Levon O Vogelsnag: lovogels@syr.edu 2 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

3. Announcement: Workshops Workshops They begin this week! Subject of either the Wednesday or the Friday workshop: Workshop #1: Waves and Interference Labs meet in Room 110. The Workshop schedule will be posted on line at: Timetable/Miscellaneous PHY 102 3 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

4. Update…Time is Flying Tues., January 17th: Lecture #1 Introduction to Course. Thurs., January 19th: Lecture #2 Waves and the Concepts Describing Them Tues., January 24th: Lecture #3 Interferences of Waves: Young’s Experiment Thurs., January 26th: Lecture #4 Traveling Waves; Longitudinal vs. Transverse Waves Tues., January 31st: Lecture #5 Diffraction: a close look Thurs., February 2nd, Lecture #6 Electromagnetic Waves Tues., February 7th; Lecture #7 Review Meeting, Part I Thurs., February 9th: Exam 1 4 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

5. Outline – Lecture Objectives 1)Review of the basic concepts of waves. 2)       The nature of interference. 3)       The Thomas Young Experiment of 1801. 5 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

6. Review fundamental wave concepts 1. The frequencyf: This is the number of full cycles per time, performed by the wave. Note: The location (along the wave direction) is fixed. 2. The wavelengthλ: This is the distance for a full cycle. It is taken along the wave direction. Note: Time is fixed. 3. The wave-speedv. We allow both location and time to vary, now. The wave-speed v is the speed of the crests. Recall: A crest occurs when the wave-value is maximum. 6 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

7. The Wave Relation The Wave Relation This relation connects these three quantities: v, f and . It states: v = fλ. So, if we know any two of these quantities, we can compute the third quantity. 7 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

8. Interference: a way to detect waves Detection of Waves Interference is a way to detect waves Interference Suppose that more than one wave occupies the same space at the same time. Then, the wave values add. This is the superposition principle. 8 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

9. First Example We have two waves. Suppose that the crest of the first wave overlaps the crest of the second wave. Then, the effect is that the net wave has increased amplitude at this point and time. This is constructive interference. d sin  = m, m= 0, 1, 2, 3, … d=the distance between slits 9 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

10. Second Example Suppose the crest of the first wave overlaps the valley of the second wave. Then, the net wave has its amplitude reduced. This isdestructive interference.  d sin  = (m+1/2), m= 0, 1, 2, 3, … 10 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

11. Demonstration of Interference Theinterference model. Two sinusoidal waves superpose on each other. When the waves are in-phase, we have constructive interference. When the waves are 180 degrees out-of-phase, we have destructive interference. 11 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

12. Wavelength The issue was settled in 1801 by the experiment of Thomas Young.Light passes through two holes.Demonstration: The Young ExperimentObserve: Some places light adds, at other places it cancels.This would not happen if light is a particle. If so, the intensity would always add. 12 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

13. The wave-speed Controversy: Is light a particle or a wave? Newton: Particle Descartes: Wave 13 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

14. The Thomas Young double-slit experiment Thomas Young first demonstrated interference in light waves from two sources in 1801. Light is incident on a screen with a narrow slit, So. The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S1 and S2. The narrow slits, S1 and S2 act as sources of waves. The waves emerging from the slits originate from the same wave front and therefore are always in phase. 14 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

15. Resulting Interference Pattern The light from the two slits form a visible pattern on a screen The pattern consists of a series of bright and dark parallel bands called fringes Constructive interference occurs where a bright fringe occurs Destructive interference results in a dark fringe 15 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

16. Interference Patterns • Constructive interference occurs at the center point • The two waves travel the same distance • Therefore, they arrive in phase 16 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

17. Interference Patterns, 2 • The upper wave has to travel further than the lower wave • The upper wave travels one wavelength further • Therefore, the waves arrive in phase • A bright fringe occurs 17 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

18. Interference Patterns, 3 • The upper wave travels one-half of a wavelength farther than the lower wave • The trough of the bottom wave overlaps the crest of the upper wave (180 phase shift) • This is destructive interference • A dark fringe occurs 18 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

19. Interference Equations • The path difference, δ, is found from the triangle • δ = r2 – r1 = d sin θ 19 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

20. Interference Equations, 2 • This assumes the paths are parallel • Not exactly, but a very good approximation (L>>d) 20 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

21. Interference Equations, 3 • For a bright fringe, produced by constructive interference, the path difference must be either zero or some integral multiple of of the wavelength • δ = d sin θbright = m λ • m = 0, ±1, ±2, … • m is called the order number • When m = 0, it is the zeroth order maximum • When m = ±1, it is called the first order maximum 21 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

22. Interference Equations, 4 • When destructive interference occurs, a dark fringe is observed • This needs a path difference of an odd half wavelength • δ = d sin θdark = (m + ½) λ • m = 0, ±1, ±2, … 22 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

23. Interference Equations, 5 • The positions of the fringes can be measured vertically from the zeroth order maximum • y = L tan θL sin θ • Assumptions • L>>d • d>>λ • tan θsin θ θ is small and therefore the approximation tan θsin θ can be used 23 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

24. Interference Equations, Final • For bright fringes (use sinθbright=m λ/d) • For dark fringes (use sinθdark=λ (m + ½)/d) 24 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

25. Summary • Young’s Double Slit Experiment provides a method for measuring wavelength of the light (Ex. 24-3 from pp. 670-671. • This experiment gave the wave model of light a great deal of credibility • It is inconceivable that particles of light could cancel each other 25 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University

26. Homework/Textbook Textbook, Chapter 24, 24-3, pp. 668-669 No Homework for the next week, Take a look at Examples 24-1 through 24-3 From textbook, pp. 670-671 26 Major Concepts of Physics PHY102 – Lecture #3 2005Syracuse University