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Lecture27

# Lecture27 - Physics 344 Foundations of 21st Century Physics...

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Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 2 and 3 in Six Ideas that Shaped Physics, Unit Q Announcement: Homework 10 due Friday. Next week, homework 11 will overlap.

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Interference and the Wave Model of Light Last time, we predicted the intensity of light reaching a distant screen from two sources oscillating in phase by considering points on the screen one at a time and focusing on the difference in the length of the paths to the chosen point from each of the sources. Q2. What is the path difference, Δ l = d sin θ , if the chosen point C is located at the first place the intensity falls to zero as you move it away from the central maximum of the interference pattern? A) λ /4 B) λ /2 C) 3 λ /4 D) λ E) 2 λ Q1. What is the path difference, Δ l = d sin θ , if the chosen point C is located at the first place the intensity falls to zero as you move it away from the central maximum of the interference pattern? A) λ /4 B) λ /2 C) 3 λ /4 D) λ * *
Interference and the Wave Model of Light d (N-1)d θ In recitation, we used the same approach to conclude that the principal interference fringes produced by a diffraction grating ( N sources oscillating in phase) are much narrower than in the 2-source case. L λ = / 2 λ With 2 sources, the first interference zero occurs when l = λ /2 = d sin θ . With N sources, it occurs when L = λ = (N – 1)dsin θ N , since this means that first and middle sources are out of phase and since all the remaining sources can be paired with a similarly out of phase partner. The principal (brightest) fringes occur when all of the sources are in phase, so, at the same angles as the 2-source fringes. Since their location depends on λ the narrow fringes of a grating efficiently separate light by color, sending different λ s in different directions

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x z L d << L 1 k arrowrightnosp 1 2 2 k arrowrightnosp Interference Revisited Last time, we also realized that we were going to have to develop a more sophisticated photon model of light to explain the appearance of interference fringes in the low- intensity version of the 2-slit experiments we discussed. screen To do that we must have a model of the “beam” of light that reaches the screen in such experiments, not simply a prediction of where the fringes are. Since the screen is far from the sources, the electromagnetic field is a superposition of two essentially plane waves with the same frequency and nearly parallel wave vectors in the neighborhood of screen’s center, where we’ve located the origin of our coordinate system.
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