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Announcements HW set 9 due this week; covers Ch 23 and Ch 24.1-4 Office hours: My office hours Th 2 -3 pm or make an appointment Come to class April 19 course and instructor evaluation 8 bonus HITT points Always check out http://www.phys.ufl.edu/courses/phy2054/spring11/ for more announcementshttp://www.phys.ufl.edu/courses/phy2054/spring11/ QUESTIONS? PLEASE ASK!

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From last time… Thin Lenses Converging, diverging Magnification Lens equation Remember the sign conventions! (Table 23.3) Lens maker’s equation Ray tracing Converging lenses Diverging lenses

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Chapter 24 Wave Optics http://www.exploratorium.edu/ronh/bubbles/bubble_colors.html http://www.ligo.org/ http://upload.wikimedia.org/wikipedia/commons/5/5d/ Michelson_Interferometer_Green_Laser_Interference.jpg http://fuff.org/interference/two_sources_interference.gif

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Wave Optics: Coherence and Interference The wave nature of light Interference, diffraction, polarization To produce interference – sources must be coherent (maintain a constant phase w.r.t. each other) (waves should have identical wavelengths) Coherent sources Old days: Single Slit + Double slit Young ’ s double slit Today: Lasers! http://www.black-holes.org/gwa4.html sciencecity.oupchina.com.hk

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Young ’ s Double Slit Experiment Light incident on a screen with a narrow slit, S o Light emerging from S o arrive at a second screen that contains two narrow, parallel slits, S 1 and S 2 Light waves emerging from S 1 and S 2 originate from the same wave front and therefore are always in phase The light from the two slits form a visible pattern on a screen The pattern consists of a series of bright and dark parallel bands called fringes Constructive interference occurs where a bright fringe appears Destructive interference results in a dark fringe DEMO

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Interference Patterns Constructive interference (again) Destructive interference Question: What is the difference in the path length (distance) that the two waves travel of the above pictures ?

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Interference Equations δ = r 2 – r 1 = d sin θ assumes the paths are parallel, a very good approximation since L >> d Bright fringe (constructive interference) δ must be either zero or some integral multiple of the wavelength, λ δ = d sin θ bright = m λ m = 0, ±1, ±2, … m is called the order number Dark fringe (destructive interference) δ must be an odd half wavelength δ = d sin θ dark = (m + ½) λ m = 0, ±1, ±2, …

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Interference Equations The positions of the fringes can be measured vertically from the zeroth order maximum y = L tan θ L sin θ L>>d>>λ θ << 1 For bright fringes (constructive interference) For dark fringes (destructive interference)

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Phase Changes Due To Reflection An electromagnetic wave undergoes a 180° phase change upon reflection from a medium of higher index of refraction than the one in which it was traveling Analogous to a reflected pulse on a string There is no phase change when the wave is reflected from a boundary leading to a medium of lower index of refraction Analogous to a pulse in a string reflecting from a free support

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Problem 23.13, p 818 Radio waves from a star, of wavelength 250 m, reach a radio telescope by two separate paths as shown in the figure. One is a direct path to the receiver, which is situated on the edge of a cliff. The second is by reflection off the water. The first minimum of destructive interference occurs when the star is is 25° above the horizon. Find the height of the cliff. (Assume no phase change on reflection.)

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Interference in Thin Films Interference is due to the interaction of the waves reflected from both surfaces of the film Ray 1 - phase change of 180° with respect to the incident ray Ray 2 - no phase change with respect to the incident wave Ray 2 travels an additional physical distance of 2t in the film The wavelength λ is reduced by n in the film the optical path length is 2 n t Constructive interference 2 n t = (m + ½ ) λ m = 0, 1, 2 … takes into account both the difference in optical path length for the two rays and the 180° phase change Destructive interference 2 n t = m λ m = 0, 1, 2 … DEMO

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Handling thin films problems Identify the thin film causing the interference Determine the indices of refraction in the film and the media on either side of it Determine the number of phase reversals: zero, one or two Interference is constructive if the path difference is an integral multiple of λ and destructive if the path difference is an odd half multiple of λ NOTE: The conditions are reversed if one of the waves undergoes a phase change on reflection Equation1 phase reversal 0 or 2 phase reversals 2nt = (m + ½) constructivedestructive 2nt = m destructiveconstructive

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Problem 24.26, p 819 A plano-convex lens with a radius of curvature R = 3.0 m is in contact with a flat plate of glass. A light source and the observer ’ s eye are both close to normal, as shown below. The radius of the 50 th bright Newton ’ s ring is found to be 9.8 mm from the center. What is the wavelength of the light produced by the source?

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Anti-reflection coatings on solar cells

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Answer to 23.13

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Answer to 23.26

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