## PHY 103: Waves, Oscillations and Optics

3 credits | Prerequisites: MAT 104, PHY 102

### Course rationale

This is one of the courses offered by the university which is mandatory for the students who wish to major in Physics. The course forms a one-year standard course in Waves, Oscillations, and Optics. Prerequisites for this course are PHY 101, PHY 102, and MAT 104. It is highly recommended that the students must have a fair amount of background in Linear Algebra. Especially, knowledge of Calculus of Several Variables will be required sometimes.

### Course content

Oscillations: Periodic and Oscillatory Motion with examples; Elastic restoring force; Simple harmonic motion (SHM); mass-spring System; Energy conservation Mass-Spring System; Differential equation of SHM & its solutions with explanation; Examples of SHM; Damped SHM; Forced Oscillation; Resonance; Combinations of simple harmonic oscillation: Lissajous Figures. Mechanical Waves and Vibrating Bodies: Waves in elastic media: Transverse and Longitudinal Waves; Periodic Waves; Mathematical description of a wave; Phase velocity and group velocity; Principle of Superposition; Boundary condition for a string; Standing waves; Huygens principle; Vibration of a string fixed at both ends. Acoustic Phenomena: Sound Waves; Intensity level and loudness; Quality and pitch; Beats; the Doppler effects; Application of acoustic Phenomena. Nature and propagation of Light: Nature; Reflection and Refraction; Total internal reflection; Reflection at a plane surface; Reflection at a spherical surface; Focal point and focal length; Lenses: Thin lens; Diverging and Converging lenses. Interference: Coherent sources; Conditions for Interference; Mathematical derivation of Interference; Young’s Experiment; Fringe width; Fresnel bi-prism; Newton’s Ring; Michelson interferometer. Diffraction: Fresnel and Fraunhofer Diffractions; Fraunhofer Diffraction at a single slit and double slit; diffraction grating; Transmission and reflection gratings. Polarization: Definition of Polarization; Plane; Circular and Elliptic Polarizations; Malus Law; Polarization by the polarizer and by reflection. Full-wave, half-wave & quarterly wave plates; Nicol & Wollaston prisms. Dispersion and Scattering: Normal and anomalous dispersion; Cauchy and Sellmeir equation; Rayleigh scattering; polarization log scattering, the blueness of the sky and the sunset and sunrise. Fourier Optics: Fourier transformation in two dimensions, inverse Fourier transformation, examples, Dirac delta function, optical applications, convocation and convolution theorem, Fourier methods in diffraction theory, lens as a Fourier transformation.

### Course objectives

1. Familiarize and memorize the fundamental concepts of oscillation, wave, and light, the basic laws that underlie the interaction of waves.
2. Recognize, memorize and re-express problems of the mechanical and electromagnetic wave using the proper mathematical form, like matrix, vector, and basic calculus.
3. Identify and explain the different modes of oscillation.
4. Recognize and solve numerical problems related to wave interaction using the proper mathematical form, like vector and basic calculus.
5. Familiarizer with the dual nature of light and identify the wave-particle duality in nature.
6. Familiarizer with the various phenomenon of the light such as interference, diffraction, polarization, etc.
7. Understand Rayleigh scattering.
8. Recognize Fourier transformation and apply it in the lens.

### References

1. The Physics of Waves: Howard Georgi, Harvard University
2. Vibrations and Waves: A. P. French: CRC Press: 6th edition.
3. Fundamental of Optics: F. A. Jenkins and H. E. White, McGraw-Hill, 4th edition
4. Introduction to Fourier optics: Joseph W. Goodman
5. Fourier Optics: An Introduction: Edward G. Steward