Physics 234 Topics: • AC Circuits • Optics – Maxwell’s equations – EM waves – Diffraction/Interference – Optical instruments • Special Relativity – Time dilation – Length contraction – Relativity of simultaneity – E = mc2 – Relativistic collisions – Relativity and E&M Course Website www.csupomona.edu/~alrudolph/classes/phy234/ Lecture has often been described as the process of taking the information contained in the teachers notes and transferring them into the students notes without the information passing through the brains of either A mind is a fire to be kindled, not a vessel to be filled Plutarch It's not what the teacher does that matters; rather, it is what the students do Think-Pair-Share (TPS) Questions and Peer Instruction • Short (10-20 minute) lecture on topic • “Think-Pair-Share” Question posed • Students given time to think • Students record individual answers • Students discuss with their neighbors (peer instruction) • Students record revised answers • Instructor leads class discussion Adapted from Eric Mazur, “Peer Instruction: A user’s manual” A Simple Intelligence Test What is the best baseball team in Southern California? A. The Angels B. The Dodgers  The effect of Peer Instruction in the Classroom • Crouch & Mazur (2001) – Harvard Univ., calculus-based physics courses, started using peer instruction in 1991 Implementation C. Crouch & E. Mazur, “Peer Instruction: Ten years of experience and results,” Am. J. Phys. 69(9), 970-977 (2001). Avg. Score no phone – Avg. Score phone users = 4.7 ± 1.4 % Final Grade (percent) 90 3 Astronomy Classes (N=328) Spring 2012 85 80 75 70 65 60 Never 1-2 times 3-5 times Over 5 times Frequency of Cell Phone Use (per class) The magnitude of the instantaneous value of the emf represented by this phasor is A. B. C. D. constant. increasing. decreasing. It’s not possible to tell without knowing t. Resonance in an RLC circuit Low-pass and High-pass RC circuits R = 500  ; C = 2 nF A B C D E Waves • • • • • As the wave approaches the bird, the buoy bobs up-and-down The number of times/second is called the frequency (f) in Hz The time between crests (or troughs) is the period (T = 1/f) The spacing between the crests (or troughs) is the wavelength (λ) The speed of the wave is 1 wavelength per period (v = λ/T = λf) Wave active figure EM Waves • Light is electromagnetic (EM) waves • What is waving? Electric and magnetic fields. • c = 300,000 km/s for all EM radiation • Since c = f ✕ λ = constant for all EM waves, as frequency (f) increases, wavelength (λ) decreases, and vice versa f λ The Electromagnetic Spectrum • A prism shows visible light spread out into colors (ROY G. BIV) • Herschel showed (c. 1800) that there is energy outside the visible spectrum, by placing a thermometer beyond the red (infrared radiation) • EM radiation exists at all possible wavelengths and frequencies • Visible radiation runs from 400-700 nm, blue to red (1 nanometer = 10-9 m) f λ c Radio EM Waves Quiz I Put the following kinds of light in order, according to wavelength, short to long: a) Visible light, ultraviolet (UV), infrared (IR), radio, X rays, gamma rays b) Gamma rays, UV, visible, X-rays, IR, radio c) Gamma rays, X rays, UV, visible, IR, radio d) X rays, UV, visible, IR, radio, gamma rays e) UV, visible light, IR, gamma rays, X rays EM Waves Quiz II Which travels fastest? a) b) c) d) e) X rays Ultraviolet Visible Radio waves They all travel at the same speed An electromagnetic wave is traveling in the positive y-direction. The electric field at one instant of time is shown at one position. The magnetic field at this position points A. In the positive y-direction. B. In the negative y-direction. C. In the positive x-direction. D. In the negative x-direction. E. Away from the origin. k EM wave polarization EM wave polarization Polarizer When a ray of light is incident on two polarizers with their polarization axes perpendicular, no light is transmitted. If a third polarizer is inserted between these two with its polarization axis at an angle of 45° to the other two, does any light get through to point P? A. Yes B. No Reflected sunlight is polarized, so image on right has glare, but image on left is done with polarizing filter (no glare) Photos by Dr. Ching-Kuang Shene, posted at http://www.geocities.com/cokinfiltersystem/polarizer.htm More Glare Reduction The reflected light is polarized, so a filter that removes that polarization removes the reflection. http://www.centuryoptics.com/products/filters/polarizers/true_samples.htm 2-slit Diffraction Pattern (neglecting slit width) sinθ =  /d ϕ = kdsinθ sinθ = 2 /d Midterm exam • The midterm exam is next Friday, 2/7 - please come on time (or better yet, early) • It will cover the material covered in class through next Wednesday, 2/5, and on the first four homeworks • You may create a two-sided 8.5”x11” sheet of equations to use during the exam • I will be away that day: Dr. Kai Lam will be administering the exam • Good luck! Diffraction Grating If light contains waves with different wavelengths, each will experience constructive interference at different angles d = 2000 nm;  r = 700 nm;  b = 400 nm Grating demo A diffraction grating is illuminated with yellow light at normal incidence. The pattern seen on a screen behind the grating consists of three yellow spots, one at zero degrees (straight through) and one each at ±45°.You now add red light of equal intensity, coming in the same direction as the yellow light. The new pattern consists of A. B. C. D. red spots at 0° and ±45°. yellow spots at 0° and ±45°. orange spots at 0° and ±45°. an orange spot at 0°, yellow spots at ±45°, and red spots slightly farther out. E. an orange spot at 0°, yellow spots at ±45°, and red spots slightly closer in. Grating Diffraction Pattern Transmission grating spectrograph Reflection grating spectrograph Redshift of Galaxies Redshifts and Hubble’s Law H0 = 71 kms-1Mpc-1 Single Slit Diffraction Pattern Hubble Ultradeep Field Blue light of wavelength  passes through a single slit of width a and forms a diffraction pattern on a screen. If the blue light is replaced by red light of wavelength 2 , the original diffraction pattern is reproduced if the slit width is changed to A. B. C. D. E. a/4. a/2. No change is necessary. 2a. 4a. 2-slit Diffraction Pattern (including slit width) Circular Aperture Diffraction Pattern Telescopes are circular apertures Arecibo Radio Telescope Diameter is 305 m (1000 ft) Gemini North telescope Diameter = 8 m (26 ft) Can Edward save Bella? Edward has to save her Shoreline James has Bella trapped on a boat Fermat’s Principle of Least Time • Light rays take the path between any two points that requires the least time Sprinters on the Beach A group of sprinters gather at point P on a parking lot bordering a beach. They must run across the parking lot to a point Q on the beach as quickly as possible. Which path from P to Q takes the least time? Hint: You should consider the relative speeds of the sprinters on the hard surface of the parking lot and on loose sand.. A. B. C. D. E. F. a b c d e All paths take the same amount of time. Sprinters on the Beach 2 Suppose the sprinters wish to get from point Q on the beach to point P on the parking lot as quickly as possible. Which path takes the least time? A. B. C. D. E. F. a b c d e All paths take the same amount of time. Apparent depth Fish in the Water 1 A fish swims below the surface of the water at P. An observer at O sees the fish at A. a greater depth than it really is B. the same depth C. a smaller depth than it really is Fish in the Water 1 Fish in the Water 2 A fish swims below the surface of the water. Suppose an observer is looking at the fish from point O¢—straight above the fish. The observer sees the fish at A. a greater depth than it really is B. the same depth C. a smaller depth than it really is Fish in the Water 2 Fish’s view of the world Total Internal Reflection Total Internal Reflection