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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
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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 announcements • QUESTIONS? PLEASE ASK!
From last time… Converging lenses • Thin Lenses • Converging, diverging • Magnification • Lens equation • Remember the sign conventions! (Table 23.3) • Lens maker’s equation • Ray tracing Diverging lenses
Chapter 24 http://upload.wikimedia.org/wikipedia/commons/5/5d/ Michelson_Interferometer_Green_Laser_Interference.jpg http://www.exploratorium.edu/ronh/bubbles/bubble_colors.html Wave Optics http://www.ligo.org/ http://fuff.org/interference/two_sources_interference.gif
Wave Optics: Coherence and Interference http://www.black-holes.org/gwa4.html • 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! sciencecity.oupchina.com.hk
Young’s Double Slit Experiment • Light incident on a screen with a narrow slit, So • Light emerging from So arrive at a second screen that contains two narrow, parallel slits, S1 and S2 • Light waves emerging from S1 and S2 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
Interference Patterns Constructive interference Constructive interference (again) Destructive interference Question: What is the difference in the path length (distance) that the two waves travel of the above pictures ?
Interference Equations • δ = r2 – r1 = 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 θbright = 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 θdark = (m + ½) λ • m = 0, ±1, ±2, …
Interference Equations • The positions of the fringes can be measured vertically from the zeroth order maximum • y = L tan θL sin θ • L>>d>>λ • θ << 1 • For bright fringes (constructive interference) • For dark fringes (destructive interference)
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
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.)
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
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
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 50th 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?
