A What you learned in 123 “Normal incidence” We have complete picture in 471: All angles Polarization (refers to E direction, not to polarized atoms) Complex index (next time)

Break linear polarization into two components Plane of incidence vs interface plane

Equations we must write: Unknowns we want to solve for: Any one of these gives us: Frequency cons. Reflection law Snell’s law Amazing!

n=2 n=1 Huygen’s principle and Snell’s law: Each point of space or matter can be imagined as a point source of forward semicircular waves. The sum of the circular wavefronts gives a wavefront of the real wave. Points farther down the interface are ahead in phase. They emit waves with different wavelength.  wave turns

Photon picture of Snell’s law Photon energy Photon momentum From our findings for k and  across the interface, which is not conserved?  Photon energy  Photon momentum perpendicular to interface  Photon momentum parallel to interface  All are conserved  None are conserved

The B field that must accompany E t p is_______. a)Parallel to E t p b)antiparallel to E t p c)Into the page d)Out of the page e)Along k

The B field that must accompany E t p has magnitude _____ a)nE t p /c b)ncE t p c)cE t p /n d)E t p /(cn) e)E t p /c

Fresnel Coefficients

Suppose we have a laser beam entering a piece of glass under special conditions so R = 0. What is the same for both beams?  Beam intensity  Beam power  both  neither

R and T from r and t

References Wave amplitude, energy and N-photons The beam is focused to an area A. What is the average amplitude of the E-field? A laser puts out power P (watts): How many photons per second leave it? What is the photon density photons/m 3 in this case?

Suppose we have a laser beam entering a piece of glass at normal incidence. Assume it’s anti-reflection coated so we can ignore reflection. In the glass the photons move slower. The energy density u is ____ than in air.  larger  smaller  the same Photon picture