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Final Exam Lectures EM Waves and Optics

Explore the properties of electromagnetic waves and optics, including Maxwell's equations, energy transport, radiation pressure, and concepts of reflection and refraction.

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Final Exam Lectures EM Waves and Optics

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  1. Final Exam LecturesEM Waves and Optics

  2. Electromagnetic Spectrum

  3. Traveling EM Wave • Maxwell’s equations predict the existence of em waves propagating through space at the speed of light • The waves consist of oscillating E and B fields that are perpendicular to each other and the direction of wave propagation

  4. EM Waves cont • EM waves generated with transformers and LC circuits • EM waves is composed of changing E and B fields and will therefore travel in a vacuum • Maxwell’s equations can be used to develop a wave equation from which the form of the waves can be deduced

  5. Properties of EM Waves • The solutions of Maxwell’s equations are wavelike, with both B and E satisfying a wave equation. • EM waves travel through a vacuum at the speed of light. • The components of the E and B fields of plane em waves are perpendicular to each other and to the direction of propagation (transverse waves) • The magnitudes of E and B in empty space are related by the expression • EM waves obey the principle of superposition

  6. Energy Transport • Poynting vector—the rate of energy transport per unit area in an em wave • Its units are • The direction of the Poynting vector is the direction of wave propagation • Intensity—the time averaged value of S over one or more cycles

  7. Radiation Pressure • Radiation pressure is the linear momentum transported by an em wave • If the surface absorbs all the incident energy • An example of this type of surface is a black body • If the surface is perfectly reflecting for a normally incident wave • An example of this type of surface is a mirror

  8. Optics Definitions • Geometrical optics—the study of the properties of light waves under the approximation that it travels as a straight line (plane wave) • Reflection—when light hits a surface and bounces back • Refraction—travel of light through a surface (or interface) that separates 2 media. Light is bent at the surface, but inside the medium it travels in a straight line

  9. Index of refraction n—associated with a medium of travel. It also depends on the wavelength of light for all media except vacuum. • Angle of incidence I—the angle the light makes to the normal to the surface when it hits the surface • Angle of reflection r —the angle the light makes to the normal to the surface when it bounces back • Angle of transmission t —the angle the light makes to the normal to the surface inside the surface

  10. Polarization • Polarization – em waves which vibrate randomly in all directions are made to vibrate in one direction • An E field component parallel to the polarizing direction is passed (transmitted) by a polarizing sheet; a component perpendicular to it is absorbed

  11. Reflection • Law of reflection – the angle of incidence equals the angle of reflection • Total internal reflection – when all light incident on a surface is reflected

  12. Refraction • Refraction – the travel of light through an interface (bending of light by an interface) • Law of refraction (Snell's Law)

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