Textbook: 10.1 Homework: Read pg 494 – 498 Do: pg 498 # 1 – 5 Polarization Textbook: 10.1 Homework: Read pg 494 – 498 Do: pg 498 # 1 – 5

EM Waves Electromagnetic waves are transverse because they can be polarized Light polarized in direction of E field

Unpolarized Light Unpolarized light (or any EM waves) have both x & y components of the electric field vectors.

Polarized Light (EM waves) Polarization is the removal of one component of the electric field.

Malus’ Law: The Intensity of Transmitted Light (through ONE filter) I0 is the intensity of the incident light and I1 is the intensity of the ray exiting the polarizing filter.

Malus’ Law: The Intensity of Transmitted Light (through TWO filters) I2 is the intensity of the ray of light emerging from the analyzer (the second Polaroid), The polarizer produces polarized light. Rotating it doesn’t affect the intensity of light. The emerging light’s intensity is always ½ I0. The analyzer determines the plane of polarization. Rotating the analyzer causes the intensity of the emerging light to vary.

Applications of Polarization Glare: Light bouncing off a flat surface is partially polarized Scattering: Light moving through a fluid (ex. Air) can be partially polarized Calcite Crystals: Are doubly refractive (refractive index depends on polarization) Photoelasticity: Some materials (lucite) polarize depending on stress on the material

Special Relativity Textbook: 11.1, 11.2, 11.3 Homework: pg. 568 # 5, 6; pg. 579 # 1, 2, 6, 8, 9

Special Relativity Einstein’s Postulates: The relativity principal: All of the laws of physics are valid in all inertial reference frames. The Constancy of the Speed of Light: Light travels through empty space with a speed of c = 3.00 x 108 m/s, relative to all inertial reference frames. Ex. Discuss simultaneity of events

Simultaneity Two events that are simultaneous in one frame of reference are not necessarily simultaneous in another frame of reference The order in which events occur depends on your frame of reference

Time Dilation A clock moving past an observer appears to run slow ts = proper time (time measured when at rest with respect to clock) tm = dilated time

Length Contractions Since observers must agree on relative velocities, length must change based on the frame of reference. Lm = Length between points A and B where A and B are moving with velocity v Ls = Length between points A and B where A and B are stationary

Paradoxes The Curious Case of the Muon The Twin Paradox Muon’s are elementary particles that are produced when our upper atmosphere is bombarded by cosmic rays The Muon’s lifetime is very short (2.2 x 10^-6 s) According to Newtonian mechanics even traveling at high speeds Muon’s should not get to the surface of the Earth The Muon’s clock is running slow so it seems to last longer In the Muon’s frame of reference the distance is contracted The Twin Paradox The twin that leaves ages at a slower rate than the twin that stays on Earth The symmetry that we have seen is ruined because the twin in the shuttle has to accelerate High acceleration causes your clock to run slower - MUCH slower The Ladder in the Barn How can one observer say that the ladder fits into the barn and the other says it doesn’t? For one observer both ends are simultaneously inside the barn The other observer does not see both ends inside the barn simultaneously

Pg 572 1. Are airline pilots’ watches running slow in comparison with clocks on the ground? Why or why not? 2. A beam of unknown elementary particles travels at a speed of 2.0 x 108 m/s. Their average lifetime in the beam is measured to be 1.6 x 10-8 s. Calculate their average lifetime when at rest. [1.2 x 10-8 s] 3. A Vulcan spacecraft has a speed of 0.600c with respect to Earth. The Vulcans determine 32.0 h to be the time interval between two events on Earth. What value would they determine for this time interval if their ship had a speed of 0.940c with respect to Earth? [75.0 h] 4. The K+ meson, a subatomic particle, has an average rest lifetime of 1.0 x 10-8 s. If the particle travels through the laboratory at 2.6 x 108 m/s, by how much has its lifetime, relative to the laboratory, increased? [2x] 2. 1.2 x 10-8 s 3. 75.0 h 4. 2x

Pg 576 5. A spaceship passes you at the speed of 0.90c. You measure its length to be 50.0 m. What is its length when at rest? [115 m] 6. You are a space traveller, moving at 0.60c with respect to Earth, on your way to a star that is stationary relative to Earth. You measure the length of your trajectory to be 8.0 light-years (ly). Your friend makes the same journey at 0.80c with respect to Earth. What does your friend measure the length of the trajectory to be? [6.0 ly] 7. A spacecraft travels along a space station platform at 0.65c relative to the platform. An astronaut on the spacecraft determines the platform to be 3.00 x 102 m long. What is the length of the platform as measured by an observer on the platform? [3.95 x 102 m] 5. 115 m 6. 6.0 ly 7. 3.95 x 102 m

12.1 The Photoelectric Effect Textbook: 12.1 Homework: pg. 597 – 598 # 1 – 5 pg. 604 # 7 – 15

Planck’s Constant In 1900, German physicist Max Planck suggested that light travels in packets called quanta. These packets define the amount of energy transferred by a given frequency of light. E = hf h = 6.63 x 10-34 Js The main postulate of quantum mechanical theory: E is the smallest amount or quantum of energy (in joules) that can be transferred for a given wavelength of electromagnetic radiation. Pg. 597 #2

The Photoelectric Effect Einstein received the Nobel Prize in physics in 1921 Current flows if frequency of light is greater than threshold frequency (f0) Work function, W, is the minimum amount of energy needed for the electrons to be emitted from metal surface.

Photons Light is made of particles called photons Ephoton = hf h = 6.63 x 10-34 Js 1eV = 1.6 x 10-19 J = 1V Electron requires energy to escape surface of metal, left over energy provides Ek Ek = hf - W W = Work Function Pg. 604 #11, 13, 14

What wavelength of light is required for ejecting photoelectrons from a tungsten surface (Wf = 4.52 eV) if the maximum kinetic energy of the electrons is 1.68 eV? Light of frequency 8.0 x 1014 Hz illuminates a surface whose work function is 1.2 eV. What is the maximum speed with which an electron reaches the plate? 2.00 x 102 nm 6.3 x 105 m/s

21. (a) Calculate the energy of a single microwave quantum of wavelength of 10.0 cm. (b) Calculate how many quanta of 10.0-cm microwave energy would be required to raise the temperature of 250.0 mL of water from 20°C to the boiling point, given that the specific heat capacity of water is 4.2 x103 J/kg?°C. 2 x 10-23J 4.2 x 1027

Applications Solar panels Photo-resistors Digital cameras charge-coupled device (CCD) a semiconductor chip with an array of light-sensitive cells, used for converting light images into electrical signals

Textbook: pg 580 – 583 Homework: pg. 583 # 1 – 6 11.3 Mass and Energy: E = mc2 Textbook: pg 580 – 583 Homework: pg. 583 # 1 – 6

Relativistic Energy Conservation of mass-energy

Calculate how much energy can be produced by the complete annihilation of 1.0 kg of mass. Calculate the energy required to accelerate a proton from rest to 0.90c. (mp = 1.673 x10-27 kg) 9 x 1016J, 1.95 x 10-10 J

Probability versus Determinism Textbook: 12.6 Homework: Read: pg 650 – 653

The de Broglie wavelength The wave nature of matter is mathematically expressed by the de Broglie equation: λ = wavelength (m h = Planck’s constant (6.63 x 10-34 Js) m = mass (kg) v = speed (m/s)

Momentum of a Photon: The Compton Effect 1923: American physicist A.H. Compton directed a beam of high energy X-ray photons at a thin metal foil Compton effect: the scattering of lower – frequency photons by high-energy photons

Heisenberg’s Uncertainty Principle If Δx is the uncertainty in a particle’s position, and Δp is the uncertainty in its momentum, then