1. notes: problem with illustrating gauss’ law and polarization divergence is that this is valid for continuous functions, and we cant illustrate that well.

2. Reading Quiz
The dipole moment per volume has the symbol P H R D M

3. Reading Quiz
The wave equation has the form:

8. Maxwell’s equations in vacuum
To derive any wave equation, we have to differentiate equations and then substitute into each other.
What is the starting Maxwell’s Eqn (1-4) to get:

9. Wave equation in free space (vacuum)
“To Maxwell, mystery was revealed—
how light could move through space.
A change in E makes changing B,
but B makes E, and off they race!”

10. a 3-D wave equation for each component!

11. Wave equation P1. is a solution to It is also a solution to ____: 1)2)
eqn 1
eqn 2
both
neither

12. For light in a material, we add “source terms” on right.

13. Electrons bound in atoms form dipoles in a “dielectric” (insulator)
Dipole from two equal charges +q, -q.
Dipole of a polarized atom

14. Electrons bound in atoms form dipoles in a “dielectric” (insulator)
Need to define a useful volume for calculating how atoms influence light fields: it must be large compared to ___________, and small compared to ______________
All these atoms get replaced by
So in our theory will be continuous, smooth functions in space…no atomic-scale features

15. Polarization P of a material with many atoms or molecules:
P will oscillate when light goes through a material! So
Oscillating P is a current, and a direct source of B

16. Can P provide a charge density too, and be a direct source of E?
Yes, if
So we get charge densities (direct source of E) if the polarization is has divergence.
This happens only in one special case

17. Which is hardest to model in optics? (most likely to have) charge
Glass
For light (l>>d_atoms), amorphous materials are more uniform than crystals, because of directional differences in crystals. It’s only in crystals that we have charge densities from

18. So in the most common optical materials (glass, plastics, water, air…all amorphous):

19. Review
What does mean?
E field at a point spreads out due to charge nearby
E fields near a point spread out due to charge there
The E field’s change at a point is due to charge there
The E field’s change at a point is due to charge nearby

20. Review What does “displacement current” at some point represent?
charges building up at that point
charges passing that point
electric field changing at that point
magnetic field changing at that point

21. Nature of wave equation
f(x, t) = F(x - c t) + G(x + c t)
What does this mean mathematically?
P2. Sketch f(t) at points x1 and x2. Get the signs of first and second derivative right
did it
tried