1. P1X: OPTICS, Waves and Lasers Dr Paul Soler, Room 453 Lecture 1: Introduction to wave theory (I) Characteristics of wave motion (Y&F,11 th 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) http://ppewww.ph.gla.ac.uk/~psoler/p1x.html

2. 2 P1X: Optics, Waves and Lasers Lectures. 2005-06 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

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

4. 4 P1X: Optics, Waves and Lasers Lectures. 2005-06 Introduction to Wave Theory 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. Objectives:

5. 5 P1X: Optics, Waves and Lasers Lectures. 2005-06 Lecture 1: Introduction to wave theory (I)  Mechanical Waves (see http://library.thinkquest.org/27948/waves.html ): 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). Characteristics of wave motion (Y&F 15.1-2):

6. 6 P1X: Optics, Waves and Lasers Lectures. 2005-06 o 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. o 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)

7. 7 P1X: Optics, Waves and Lasers Lectures. 2005-06 o Sinusoidal waves: a continuous succession of transverse sinusoidal disturbances.  Wavelength  )  length of the periodic shape (m). oPoint 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 in the time T. Therefore the wave speed: We shall assume that v does not change with 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

8. 8 P1X: Optics, Waves and Lasers Lectures. 2005-06 o 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) Mathematical description of waves (Y&F 15.3): y T3T/4 T/2 T/4t - A A x=0 Vertical displacement with time.Profile of wave at t=0. y 3 /4 /2 /4 x - A A t=0 v o Wave diagrams (wave left to right):

9. 9 P1X: Optics, Waves and Lasers Lectures. 2005-06 o Define wave number k: (radians/m) o Wave function (wave travelling from right to left): Time displacement is t+x/v. Hence, wave function is: o Phase of wave is: (in radians) o 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:

10. 10 P1X: Optics, Waves and Lasers Lectures. 2005-06 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) (c) Phase diference:  rad or /2