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, , ) 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 P1X: Optics, Waves and Lasers Lectures Lecture 4: Interference and diffraction of light (II) Young’s two slit experiment (Y&F ) 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 P1X: Optics, Waves and Lasers Lectures 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 P1X: Optics, Waves and Lasers Lectures 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 P1X: Optics, Waves and Lasers Lectures Lecture 1: Introduction to wave theory (I)  Mechanical Waves (see ): 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 ):

6 P1X: Optics, Waves and Lasers Lectures 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 P1X: Optics, Waves and Lasers Lectures 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 P1X: Optics, Waves and Lasers Lectures 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 P1X: Optics, Waves and Lasers Lectures 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 P1X: Optics, Waves and Lasers Lectures Example: 15-2 from Y&F (page 556) A transverse wave on a clothesline has frequency 2.0 Hz and amplitude 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 = m; (b) (c) Phase diference:  rad or /2