1. Major Concepts of Physics PHY102 – Lecture #3 1 2015  Syracuse University Lecture #3 How do the waves mix each other up? Interference January 21 st, 2015 Prof. Liviu Movileanu wwww.physics.syr.edu/MajorConceptsPhysics2015.html lmovilea@syr.edu Room 211, Physics Bldg., 443-8078 Major Concepts of Physics PHY102

2. Major Concepts of Physics PHY102 – Lecture #3 2 2015  Syracuse University 1. Review the quantitative description of waves  Review quantitative parameters describing waves  Review periodical expressions describing waves  Simple Harmonic Motion (SHM) 2. What is the interference?  Constructive and Destructive Interference (Hypothesis)  Young’s double-slit experiment (Experimental evidence)  Interference patterns (Interpretation) 3. Lecture demonstration (double-slit interference) 4. Repeat Sam’s demonstration…another beaker 5. Announcements Lecture objectives

3. Major Concepts of Physics PHY102 – Lecture #3 3 2015  Syracuse University Quantitative understanding of waves

4. Major Concepts of Physics PHY102 – Lecture #3 4 2015  Syracuse University Periodicity of waves: time and space

5. Major Concepts of Physics PHY102 – Lecture #3 5 2015  Syracuse University Simple Harmonic Motion (SHM) Idea: Any object that is initially displaced slightly from a stable equilibrium point will oscillate about its equilibrium position. It will, in general, experience a restoring force that depends linearly on the displacement x from equilibrium: Hooke's Law: F s = - kx x is the displacement, or the distance of the mass from the equilibrium point and k is a constant that depends on the system under consideration. The equilibrium point is considered at x=0 The units of k are: [k] = Total energy=Kinetic energy + potential energy

6. Major Concepts of Physics PHY102 – Lecture #3 6 2015  Syracuse University Simple Harmonic Motion Simple Harmonic Motion Definitions: Amplitude (A): The maximum distance that an object moves from its equilibrium position. A simple harmonic oscillator moves back and forth between the two positions of maximum displacement, at x = A and x = - A. Period (T): The time that it takes for an oscillator to execute one complete cycle of its motion. If it starts at t = 0 at x = A, then it gets back to x = A after one full period at t = T.

7. Major Concepts of Physics PHY102 – Lecture #3 7 2015  Syracuse University Simple Harmonic Motion Simple Harmonic Motion Definitions: Frequency ( f ): The number of cycles (or oscillations) the object completes per unit time. f = 1/T The unit of frequency is usually taken to be 1 Hz = 1 cycle per second. Simple Harmonic Oscillator: Any object that oscillates about a stable equilibrium position and experiences a restoring force approximately described by Hooke's law. Examples of simple harmonic oscillators include: a mass attached to a spring, a molecule inside a solid.

8. Major Concepts of Physics PHY102 – Lecture #32015  Syracuse University Interference can be observed only with coherent light 8

9. Major Concepts of Physics PHY102 – Lecture #3 9 2015  Syracuse University Constructive Interference: Amplitudes are added up When the waves are in-phase, we have constructive interference.

10. Major Concepts of Physics PHY102 – Lecture #3 10 2015  Syracuse University Destructive Interference When the waves are 180 degrees out-of-phase, we have destructive interference.

11. Major Concepts of Physics PHY102 – Lecture #3 11 2015  Syracuse University Interference: How does it work? Maximum Minimum

12. Major Concepts of Physics PHY102 – Lecture #3 12 2015  Syracuse University The issue was settled in 1801 by the experiment of Thomas Young. Light passes through two holes. Demonstration: The Young Experiment Observe: 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. Wavelength

13. Major Concepts of Physics PHY102 – Lecture #3 13 2015  Syracuse University The Thomas Young double-slit experiment 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

14. Major Concepts of Physics PHY102 – Lecture #3 14 2015  Syracuse University Interpretation of Interference Data

15. 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 Major Concepts of Physics PHY102 – Lecture #3 15 2015  Syracuse University Interference Patterns, 2

16. 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 Major Concepts of Physics PHY102 – Lecture #3 16 2015  Syracuse University

17. 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 Major Concepts of Physics PHY102 – Lecture #3 17 2015  Syracuse University

18. For bright fringes (use sinθ  bright =m λ  /d) For dark fringes (use sinθ  dark =λ (m + ½)/d) Major Concepts of Physics PHY102 – Lecture #3 18 2015  Syracuse University Interference Equations, Final

19. Major Concepts of Physics PHY102 – Lecture #2 19 2015  Syracuse University 1. Reading: Chapter 25 th, Sections 25.1, 25.4 Example 25.1, Example 25.4 2. First Workshop this week! 3 Homework #1 for the next week (on paper): Please pick up the print outs 4. Do you want to be challenged? More MCAT preps? Problems 25.1, 25.4Announcements