1. Final Exam Lectures EM 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 a ngle 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)