EM Waves, Optics: Poynting Vector, Polarization, Mirrors, Lenses, Relativity - Prof. James, Study notes of Physics

Download EM Waves, Optics: Poynting Vector, Polarization, Mirrors, Lenses, Relativity - Prof. James and more Study notes Physics in PDF only on Docsity! Chapter 33 – Electromagnetic Waves EM Waves: E = Em sin(kx – wt) and B = Bmsin(kx – wt) c = E/B = 1/sqrt(µo * εo) Energy Flow: The rate per unit area at which energy is transported via an EM wave = Poynting Vector: S -> = (1/ µo)* E -> x B-> Direction of S is perpendicular to the directions of E and B. Intensity from a point source: I = (PS)/(4πrπrr 2) Radiation Pressure: F = IA/c Polarization: 1st filter = I = 0.5Io 2 nd filter = I = Iocos(θ)) If θ) = 90 o then no light is let through Reflection: θ)1 = θ) ’ 1 Refraction: n1sin(θ)1) = n2sin(θ)2) <- Snell’s Law n = c/v sin(θ)2) = (n1/n2)*sin(θ)1) θ)2 = sin -1((n1/n2)*sin(θ)1)) Total Internal Reflection: θ)c = sin -1(n2/n1) <- Critical Angle where a wave encountering a body will experience TIR Chapter 34 – Images Terminology: p = Object Distance q = Image Distance Magnification = Image height / Object height = h’/h Plane Mirrors: can reflect light in one direction instead of scattering or absorbing it = flat mirror = p = q M = 1 Concave Spherical Mirrors: A real image is formed. Mirror Type Object Location Image Sign Location Type Orientation f r m Plane Anywhere opposite virtual erect N/A to inf. 1 Concave Inside F opposite virtual erect + + + Outside F same real inverted + + - Convex Anywhere opposite virtual erect - - + Lens Type Object Location Image Sign Location Type Orientation f r m Converging Inside F same virtual erect + + + Outside F opposite real inverted + + - Diverging Anywhere same virtual erect - - + Refractive Index for Apparent Depth: n = sin(i)/sin(r) = depth/apparent depth width of fringe = s = 2Ltan(θ)) Single Slit Diffraction: Minimum: sin(θ)) = λ/(width of slit) Other Minimums: sin(θ)) = nλ/(width of slit) Intensity: I(θ)) = Iosinc 2(dsin(θ))/λ) sinc(x) = sin(πrx)/(πrx) Diffraction Grating: dsind(θ)) = mλ m=1,2,3… Thin Films: dsind(θ)) = 2t RELATIVITY: Twin Paradox: One travels at light speed to visit her friend. She comes back in 3 years at γ = 2. When she returns, she is three years older but two is 6 years older (3*2). Moving at speed of light keeps you young. Postulates: 1. Relativity Postulate: The laws of physics are the same for observers in all inertial reference frames. No one frame is preferred over any other. 2. Speed of Light Postulate: The speed of light in vacuum has the same value c in all directions and in all inertial reference frames. Ultimate Speed: c = 2997924πr58 m/s Simultaneity: If two observers are in relative motion, they will not, in general, agree as to whether two events are simultaneous. If one observer finds them to be simultaneous, the other generally will not. Simultaneity is not an absolute concept but rather a relative one, depending on the motion of the observer. Relativity of Time: The time interval between two events depends on how far apart they occur in both space and time; that is, their spatial and temporal separations are entangled. ∆t = ∆to / sqrt(1 – (v/c)^2) = γ∆to γ = 1/sqrt(1-β^2) β = speed parameter = its always less than 1. ∆to = smallest time ∆t > ∆to in this respect. DISTANCE TRAVELED = velocity * ∆t EX: We are standing beside the railroad tracks when a train goes by with a hobo inside, shining a laser out the end of the boxcar. Our measurement of the speed of light is the same as that measures by the hobo. His measurement is NOT the flight time of the pulse a proper time. The start and end of the flight are spatially separated. Our measurements cannot be related by the equation above because his measurement is not a proper time. Relativity of Length: The length Lo of an object measured in the rest frame of the object is its proper length or rest length. Measurements of the length from any reference frame that is in relative motion parallel to that length are always s less than the proper length. L = Lo*sqrt(1 - β^2) = Lo/ γ velocity = (Loc)/(sqrt(c * ∆t)^2 + Lo^2)