Announcements Have huygen’s wavelets set up on remote desktop Demos: use students phone glass with polarizers to look at R of light from screen Large prism showing TIR Movies of transmission

https://www. nature. com/articles/nature25176. WT https://www.nature.com/articles/nature25176?WT.feed_name=subjects_physics

Reading Quiz During total internal reflection when light strikes a glass-air interface (from the glass side), the electric field in the air just outside the glass is called the: Fluorescent wave Optometric wave Reduction wave Evanescent wave Vanishing wave

Reading Quiz Brewster’s angle occurs when qi and qt Are equal Are in a 2:1 ratio Sum to 45 Sum to 90

Fresnel Coefficients

R, T for complex index When k is complex in metals and absorbing dielectrics, A k still determines decay of wave Meaning of complex r and t?

Brewster’s angle

Brewster’s angle Occurs only for ___ polarization A

Brewster’s angle Occurs when reflected and transmitted rays are _____, but only for ___ polarization p-polarization: s-polarization: A Dipole radiation interpretation of why R0

Sunlight is essentially unpolarized. Why are the best sunglasses polarized? P1. What direction do you want to orient the transmitting axis of the polarizer in your sunglasses to let through only the polarization that reflects the least from the water? Horizontal Vertical

Apparent vs true depth

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 https://www.youtube.com/watch?v=ULcD-cQ8bGE

Another view of Snell’s law Periodicity along the interface must match! Because l is different, the angles must be different. (Phase shift is OK)

And another view of Snell’s law And another view of Snell’s law. Rays are perpendicular to wave front, which distorts because of change in v

Waves at an Interface, (Quicktime format 02:46) P- and S-Polarized Reflection and Transmission (Quicktime format 01:21) https://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html

Glass to air interface (internal reflection) Fresnel’s coefficients: Total internal reflection A Notice internal Brewster’s angle is the ______________ of the external one.

Phase of reflected E-fields come from sign of r P2. Check Phy123 rule: “180 degree reflection phase change occurs______” a) going from high to low index at all angles b) going from low to high index at all angles c) rule changes at Brewster’s angle for one polarization d) rule changes at Brewster’s angle for both polarizations Rp Rs rs rp

100% reflectors without metal And they reflect back to the light source!

Can you do anything from the outside to destroy the TIR?

Total internal reflection Derivation from Snell’s law: Above this angle, A

Simple way to think about complex functions (probably doesn’t help much in using them) A In TIR the wave decays not from ik, but from ik Photon picture of TIR

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