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

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P1X OPTICS, Waves and Lasers Dr Paul Soler,
Room 453
http//ppewww.ph.gla.ac.uk/psoler/p1x.html

• Lecture 1 Introduction to wave theory (I)
• Characteristics of wave motion (YF,11th
  ed.,15.1-2)
• Mathematical description of waves (YF, 15.3)
• Lecture 2 Introduction to wave theory (II)
• Mathematical description of waves (cont.,YF,
  15.3)
• Simple harmonic motion (YF, 13.1-2, 13.4-5)
• Lecture 3 Introduction to wave theory (III)
• Principle of superposition (YF,15.6)
• Constructive and destructive interference and
  coherence (YF,35.1)
• Interference and diffraction of light (I)
• Physical optics wave behaviour of light
  (YF,35.1-2)
• Huygens principle (YF,33.7)

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• Lecture 4 Interference and diffraction of light
  (II)
• Youngs two slit experiment (YF 35.2-3)
• Lloyds mirror
• Lecture 5 Interference and diffraction of light
  (III)
• Thin films (YF,35.4)
• Newtons rings (YF,35.4)
• Tutorial
• Lecture 6 Lasers and their applications (I)
• Coherent and incoherent light sources (YF,
  35.1)
• Spontaneous and stimulated emission and
  population inversion (YF,38.6)
• Lecture 7 Lasers and their applications (II)
• Requirements for lasing action (YF,38.6)
• 3 and 4 level lasers (YF,38.6)
• Applications (YF,38.6)
• Revision/Tutorial

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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.

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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.
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Lecture 1 Introduction to wave theory (I)
Characteristics of wave motion (YF 15.1-2)

• Mechanical Waves (see http//library.thinkquest.o
  rg/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).

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• 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)

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• 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
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Mathematical description of waves (YF 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 t0.
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• 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 x0
  case by t-x/v

• Define wave number k
  (radians/m)

• Wave function (wave travelling from right to
  left)
• Time displacement is tx/v.
• Hence, wave function is
• Phase of wave is (in radians)

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Example 15-2 from YF (page 556) A transverse
wave on a clothesline has frequency 2.0 Hz and
amplitude 0.075 m. The wave speed is v12.0 m/s.
At t0 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)