P1X: OPTICS, Waves and Lasers Dr Paul Soler, Room 453

1. P1X: OPTICS, Waves and LasersDr Paul Soler, Room 453 http://ppewww.ph.gla.ac.uk/~psoler/p1x.html • Lecture 1: Introduction to wave theory (I) • Characteristics of wave motion (Y&F,11th ed.,15.1-2) • Mathematical description of waves (Y&F, 15.3) • Lecture 2: Introduction to wave theory (II) • Mathematical description of waves (cont.,Y&F, 15.3) • Simple harmonic motion (Y&F, 13.1-2, 13.4-5) • Lecture 3: Introduction to wave theory (III) • Principle of superposition (Y&F,15.6) • Constructive and destructive interference and coherence (Y&F,35.1) • Interference and diffraction of light (I) • Physical optics: wave behaviour of light (Y&F,35.1-2) • Huygen’s principle (Y&F,33.7)

2. Lecture 4: Interference and diffraction of light (II) • Young’s two slit experiment (Y&F 35.2-3) • Lloyd’s mirror • Lecture 5: Interference and diffraction of light (III) • Thin films (Y&F,35.4) • Newton’s rings (Y&F,35.4) • Tutorial • Lecture 6: Lasers and their applications (I) • Coherent and incoherent light sources (Y&F, 35.1) • Spontaneous and stimulated emission and population inversion (Y&F,38.6) • Lecture 7: Lasers and their applications (II) • Requirements for lasing action (Y&F,38.6) • 3 and 4 level lasers (Y&F,38.6) • Applications (Y&F,38.6) • Revision/Tutorial P1X: Optics, Waves and Lasers Lectures. 2005-06

3. General aims • To serve as an introduction to the various aspects of optics, and to • provide a good basic understanding of geometric optics and physical • optics. • To introduce the fundamental ideas of wave theory, developed both in physical optics and in the behaviour of waves in gases and on strings. • To gain an appreciation of the various aspects of physics involved in lasers, including optics, waves and atomic physics, and to learn about some of the many applications of lasers. • To be able to solve simple problems relating to current applications • involving waves and optics. P1X: Optics, Waves and Lasers Lectures. 2005-06

4. Introduction to Wave Theory Objectives: i)to understand the characteristics of wave motion, in particular sinusoidal waves and simple harmonic motion, and to understand the mathematical description of such waves; ii) to appreciate the importance of simple harmonic motion in a wide diversity of physical situations; iii) to understand the principle of linear superposition for waves and what is meant by constructive and destructive interference, and coherence; iv) to solve simple problems on travelling waves. P1X: Optics, Waves and Lasers Lectures. 2005-06

5. Lecture 1: Introduction to wave theory (I) Characteristics of wave motion (Y&F 15.1-2): • Mechanical Waves (see http://library.thinkquest.org/27948/waves.html): • A mechanical wave is a disturbance that travels through some material or substance called the medium of the wave. • The particles in the medium undergo displacements that depend on the type of wave. • Transverse wave: the displacements perpendicular (transverse) to the direction of travel of wave; ie. wave on a string. • Longitudinal wave: displacements are in the same direction as the direction of travel of wave; ie. wave in a gas (sound). P1X: Optics, Waves and Lasers Lectures. 2005-06

6. Common features of waves: • There is a well defined equilibrium condition (ie. string stretched in straight line or gas in tube has constant density) • The medium as a whole does not move: the disturbance travels with a well defined speed v, the wave speed. • Energy has to be applied to the system to generate disturbance. • The disturbance transports energy from one position to another. • Periodic waves: If the disturbing force varies in time in a regular manner, periodic waves are generated. They have a well defined: a) Frequency f: number of times per second that a pattern repeats itself. (Units: 1 Hertz = 1 cycle/s = 1 s-1) b) Angular frequency: (rad/s) c) Period: time between repeating patterns (s) P1X: Optics, Waves and Lasers Lectures. 2005-06

7. Sinusoidal waves: a continuous succession of transverse sinusoidal disturbances. • Wavelength (l): length of the periodic shape (m). • Point moves up and down with period T and cross is displaced by t-x/v. That means that cross has the same pattern as at an earlier time t-x/v. • The marker moves along the axis a distance l in the time T. Therefore the wave speed: We shall assume that v does not change with l and f. Not true for light travelling through a medium since speed depends on frequency (dispersion of light). Example: What is the wavelength of a sound wave if the frequency is f= 262 Hz (middle C on a piano)? Speed of sound = 344 m/s P1X: Optics, Waves and Lasers Lectures. 2005-06

8. v y y x=0 t=0 A l/2 l/4 3l/4 l x - A A T/2 T/4 3T/4 T t - A Mathematical description of waves (Y&F 15.3): • Transverse Waves: • Vertical displacement of wave varies with time. • At a given time, wave has a well defined profile and the displacement is different for different particles. • Amplitude A is maximum displacement in y direction (m) • Wave diagrams (wave left to right): Vertical displacement with time. Profile of wave at t=0. P1X: Optics, Waves and Lasers Lectures. 2005-06

9. Wave function (wave travelling from left to right): • General function of wave depends on x and t: • y = y(x,t) • At a time t, the particle is displaced from x=0 case by t-x/v: • Define wave number k: (radians/m) • Wave function (wave travelling from right to left): • Time displacement is t+x/v. • Hence, wave function is: • Phase of wave is: (in radians) P1X: Optics, Waves and Lasers Lectures. 2005-06

10. Example: 15-2 from Y&F (page 556) A transverse wave on a clothesline has frequency 2.0 Hz and amplitude 0.075 m. The wave speed is v=12.0 m/s. At t=0 s, the end has zero displacement and moves in the positive y direction. (a) Find amplitude, angular frequency, period, wavelength and wave number. (b) Write wave function. (c)Write equation of displacement as function of time at end of string and at a point 3.0 m from end. (a) A = 0.075 m; (b) Phase diference: p rad or l/2 (c) P1X: Optics, Waves and Lasers Lectures. 2005-06