Major Concepts of Physics PHY102 – Lecture #  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 Room 211, Physics Bldg., Major Concepts of Physics PHY102

Major Concepts of Physics PHY102 – Lecture #  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

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

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

Major Concepts of Physics PHY102 – Lecture #  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

Major Concepts of Physics PHY102 – Lecture #  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.

Major Concepts of Physics PHY102 – Lecture #  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.

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

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

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

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

Major Concepts of Physics PHY102 – Lecture #  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

Major Concepts of Physics PHY102 – Lecture #  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

Major Concepts of Physics PHY102 – Lecture #  Syracuse University Interpretation of Interference Data

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 #  Syracuse University Interference Patterns, 2

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 #  Syracuse University

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 #  Syracuse University

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 #  Syracuse University Interference Equations, Final

Major Concepts of Physics PHY102 – Lecture #  Syracuse University 1. Reading: Chapter 25 th, Sections 25.1, 25.4 Example 25.1, Example 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