Reading Quiz When a light ray hits a surface, the plane which contains the incoming, reflected, and transmitted beams, is called the “plane of _________”: junction incidence normality action refraction

Reading Quiz To represent the two electric field polarizations that are parallel and perpendicular to the place of incidence, we use the symbols: n and w p and q r and u s and p t and v

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

Plane of incidence (this page or y-z) interface plane (x-y) Break linear polarization into two components: s: “sticking out” p: in plane of incidence k vectors:

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

Points farther down the interface are ahead in phase. Huygen’s construction and Snell’s law: Each point of space is imagined as a point source of forward semicircular waves. The sum of the circular wavefronts gives a wavefront of the real wave. n=2 n=1 Points farther down the interface are ahead in phase. They emit waves with different wavelength.  wave turns http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=16

Photon picture of Snell’s law Photon energy Photon momentum From our findings for k and w 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

Continuing our calculation of r coefficients The B field that must accompany Etp is_______. Parallel to Etp antiparallel to Etp Into the page Out of the page Along k

The B field that must accompany Etp has magnitude _____ nEtp/c ncEtp cEtp/n Etp/(cn) Etp/c Solving the 4 equations for our 4 unknown components of E gives us the Fresnel coefficients

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

Wave amplitude, energy and N-photons A laser puts out power P (watts): How many photons per second leave it? The beam is focused to an area A. What is the average amplitude of the E-field? What is the photon density photons/m3 in this case? References

Photon picture 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