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p2020chap13 - PHYS-2020 General Physics II Course Lecture...

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PHYS-2020: General Physics II Course Lecture Notes Section XIII Dr. Donald G. Luttermoser East Tennessee State University Edition 3.3
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Abstract These class notes are designed for use of the instructor and students of the course PHYS-2020: General Physics II taught by Dr. Donald Luttermoser at East Tennessee State University. These notes make reference to the College Physics, 9th Edition (2012) textbook by Serway and Vuille.
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XIII. Wave Optics A. Wave Interference and Young’s Double Slit Experiment. 1. We have already discussed wave interference (see VII.E.2 on Page VII-15 and VIII.E on Page VIII-12). In this section we will ex- pand upon the physics of interference. 2. In order to carry out experiments concerning constructive or de- structive interference of waves of two or more sources, the waves from the sources must be coherent . a) This means that the waves they emit must maintain a constant phase with respect to each other. b) In addition to this, the waves must have identical wave- lengths to be coherent. i) Both of these conditions require the sources to emit a single emission-line spectrum. ii) A laser ( l ight a mplification of s timulated e mission of r adiation) is a good source of coherent radiation. c) Most ordinary light sources produce a continuous spec- trum, hence produce incoherent light. Incoherent light can be converted to coherent light through the use of two “pinholes” or “slits” at a specific separation as described below. 3. In 1801, Thomas Young first demonstrated interference in light waves from two sources produced from a single source of light passing through two pinholes in a screen as shown in Figure 24.1 XIII–1
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XIII–2 PHYS-2020: General Physics II in your textbook. (From this point forward, we will describe this experiment with slits instead of pinholes.) a) This experiment showed that the resulting wavefronts from the two slits produced as series of bright and dark parallel bands called fringes . b) In order for the wavefronts ( i.e. , wavecrests) of the light from the two different slits to arrive on a projection screen at the same time at the same place, the following equation must be true δ = r 2 - r 1 = d sin θ , (XIII-1) where r 1 is the distance that the wavefront traveled from slit 1, r 2 the distance traveled from slit 2, δ is the path difference between r 2 and r 1 , d the distance between the slits, and θ is the angle shown in the figure below. S 2 Q S 1 d slit plane Source L viewing screen O P y r 2 r 1 δ = r 2 - r 1 = d sin θ θ θ
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Donald G. Luttermoser, ETSU XIII–3 c) The “bright fringes” correspond to regions of construc- tive interference . This will occur at a position on the viewing screen when δ = ± : δ = d sin θ bright = mλ , m = 0 , ± 1 , ± 2 , . . . (XIII-2) i) The number m is called the order number .
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