What is optics? Mathematical and physical background of: E/M waves in materials and at boundaries Control and description of polarization Waves: interference, diffraction, laser beams, coherence photons and quantum optics rays, imaging

Divergence and curl P1. Can field lines that stay parallel (e.g. point only in the z direction) have divergence? a)yes b)no P2. Can field lines that stay parallel (e.g. point only in the z direction) have curl? a)yes b)no

Divergence and curl Divergence Curl Figures from Griffiths, 441/442 text Know physical interpretations in terms of fluid flow!

Light is an E/M wave, obeying… Maxwell’s equations Integral form Derivative form

Narration of Maxwell’s equation One source of E: The part of E with div. is due to charge right there The other source of E: The part of E that curls is due to B change B never has div. The sources of B are physical currents and change in E (displacement current). It circles those vectors, but has curl only right where there is J or

Participation record with clicker: a) I got it right (at most a sign or constant off) (10 pts) b) I tried (9 pts) Suppose you want to have the following E-field in this room P1. Find the charge density that must be present Could this charge density be consistent with a different E?

P3. Find Participation record with clicker: a) I got it right (at most a sign or constant off) (10 pts) b) I tried (9 pts) P4. Find a consistent with P5. Find the direction of B at the point (x,y,z) = (1,0,0) B circles the room a)CW viewed from above b)CCW viewed from above

What can we say about the nature of the current density J? Continuity equation The part of J with divergence comes from a changing charge density. The part of J with curl represents “divergence free currents”, and can be supplied by neutral wires.

Of the 5 terms, only the last has divergence, and comes from  t, so the first 4 terms have to be supplied by wires to get the E field we want.