General aim:

The general aim of this course is twofold:

to develop and put on a firm footing the mathematical techniques needed to discuss both qualitatively and quantitatively the optical physics presented in the course;

to study in detail the properties of electromagnetic waves, in particular in the visible region of the spectrum.

Objectives

Section 1 : Introduction and Superposition of Waves

On completion of this section you should be able to

• describe wave propagation in terms of Huygens secondary wavelets
• write down the equation of a wave in real and complex form
• state the relationship between optical path difference and phase difference
• obtain an expression for the resultant amplitude due to addition of two waves of arbitrary amplitude and phase using complex notation and Argand diagrams
• explain the concept of coherence and its influence on superposition of waves
• state and use various mathematical relationships: series expansions for sin(x), cos(x),and tan(x) for small x; sum of geometrical series

Section 2 : Interference

On completion of this section you should be able to

• describe examples of the "division of wavefront" and "division of amplitude" methods of producing interference
• derive the fringe intensity equation for Young's double slit arrangement
• explain the factors influencing fringe visibility
• explain how Lloyd's mirror experiment shows evidence for a phase change on reflection
• describe the Michelson interferometer and explain how circular and straight line fringes are produced
• derive an equation for positions of circular fringes and give the fringe intensity formula for the Michelson
• describe and explain various uses for the Michelson interferometer
• explain how interference in thin films can be used to make non-reflecting glass
• explain qualitatively how a Fabry-Perot interferometer produces fringes, and describe what the fringe intensity pattern looks like compared to the Michelson

Section 3 : Diffraction

On completion of this section you should be able to

• state the conditions under which Fraunhofer and Fresnel diffraction are observed
• derive the intensity distribution in the Fraunhofer diffraction pattern for a single slit
• state Rayleigh's criterion and apply it to resolving power of telescopes
• derive the intensity distributions for a double slit and N slits - the diffraction grating
• derive the chromatic resolving power of a diffraction grating