New Jersey TRIVIA QUESTION! Which Actor/ Actress for the following characters from GAME OF THRONES is from New Jersey? (a) Tyrion Lannister (b) Cersai Lannister (c) Arys Stark (d) Jon Snow (e) Samwell Tarly

New Jersey TRIVIA QUESTION! Which Actor/ Actress for the following characters from GAME OF THRONES is from New Jersey? Tyrion Lannister – Peter Dinklage was born in Morristown, NJ

Maxwell’s Equations applied across a boundary A short summary of results for PLANE waves: In general, in addition to the incident wave, there will be reflected and transmitted waves. All k vectors lie in a single plane … the ‘Plane of Incidence’. Frequencies of all waves are the same Law of reflection Law of Refraction (Snell’s Law) The fraction of transmitted or reflected power depends on the ORIENTATION of the electric field relative to the plane of incidence. This is termed POLARIZATION of the light wave. Fresnel Equations

Let’s define the coordinate system Arbitrary Incident Electric Field can be broken into two Components: one PARALLEL to plane of incidence (p-polarization) and one perpendicular to the plane of incidence (s-polarization) z

Wave Vectors and E fields y z

Boundary Conditions for Faraday’s Law NOTE: Applies to TOTAL E field Area is SMALL so E does not change over area. As and , area of rectangle goes to zero so that one is evaluating E and B fields right next to the boundaries.

Boundary Conditions for Faraday’s Law NOTE: Applies to TOTAL E field =0

Boundary Conditions for Ampere’s Law NOTE: Applies to TOTAL B field Area is SMALL so B does not change over area. As and , area of rectangle goes to zero so that one is evaluating E and B fields just over the boundaries.

Boundary Conditions for Ampere’s Law NOTE: Applies to TOTAL B field =0

Apply BC that E parallel continuous NOTE: Applies to TOTAL E field y Apply Boundary condition to z=0. Parallel direction is x and y direction Perpendicular direction is z direction z z=0

Apply BC that B parallel continuous NOTE: Applies to TOTAL B field y Apply Boundary condition to z=0. Parallel direction is x and y direction Perpendicular direction is z direction z z=0

Four Equations and 4 Unknowns Solve in terms of reflection coefficients….

Fresnel Equations In these equations, of course Snell’s Law holds.

Fresnel Equations Remember, these equations are for reflection coefficients in ELECTRIC field NOT power. So, the reflection coefficients CAN be negative. Also, for certain angles (eg. near 60 degrees in Figure 3.3), the reflectivity CAN be zero. If the reflectivity is zero, where does the optical power go?

Fresnel Equations – r<0? What does it mean if r < 0? Direction of E is OPPOSITE to what we assumed in Figure 3.1

Power T and R coefficients Area

‘Typical’ R and T curves

Practice Problem Problem 18: A beam of unpolarized, incoherent red (600nm wavelength) light incident in air on a glass (n=1.5) interface at 50 degrees is partially reflected and partially transmitted. (a) Calculate the REFLECTION coefficient of POWER of the interface for light polarized PARALLEL to the plane of incidence.   (b) Calculate the transmission coefficient of POWER of the interface for light polarized PARALLEL to the plane of incidence. (c) Calculate the REFLECTION coefficient of POWER of the interface for light polarized PERPENDICULAR to the plane of incidence. (d) Assuming that the total power of the unpolarized incident light is 10mW, how much total power (in mW) is REFLECTED from the glass interface?

Brewster’s Angle Transmission goes to unity for P polarization Reflectivity goes to zero for P polarization

Brewster Plate Some S polarization will be transmitted, so need a ‘stack’ of Brewster plates to ‘Purify’ P polarized light.

Brewster’s angle Put this angle relation into Snell’s law

Total Internal Reflection

Exceed Critical Angle – Evanescant Wave http://optics.byu.edu/Animation/wavintfc.mov Start animation at 2:00 to see just total internal reflected wave.

Frustrated Total Internal Reflectance

Reflectivity of a metal NOTE: Reflectivity is NOT 100%. Why? Brewster-like angle At normal incidence, incident and transmitted angles are equal to zero, so NOTE: Significant phase shift of reflected wave from metal. Unless the complex refractive index of the metal is MUCH LARGER than that of air (eg. 1), the magnitude of reflection will be measurably below 1. nReal=0.13 and nImag=4.0 (problem P2.5)

Practice Problem Problem 1: A person standing on a dock shines a beam of light into a pond at an angle of 60 degrees. The refractive index of water is 1.33. Assuming that the surface of the water is perfectly smooth, at what angle does the REFLECTED light leave the water’s surface? At what angle does the refracted light emerge into the water? If the person moves the light beam such that the angle of incidence of the light into the water becomes much larger, will the light become totally internally reflected? EXPLAIN YOUR ANSWER. What would be the result if the person were UNDERWATER shining a light a the surface of the water at a 60 angle? Would the light be totally internally reflected?

Practice Problem