Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 11.3, Problem 3dT
To determine
To Discuss: The interference pattern with four and five slits.
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Question 3 of 17
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In the figure above, three uniform thin rods, each of length L, form
an inverted U. The vertical rods each have a mass m; the horizontal
rod has a mass 3m.
NOTE: Express your answer in terms of the variables given.
(a) What is the x coordinate of the system's center of mass?
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(b) What is the y coordinate of the system's center of mass?
Ycom
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Sketch the harmonic on graphing paper.
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Chapter 11 Solutions
Tutorials in Introductory Physics
Ch. 11.1 - Prob. 1TCh. 11.1 - Prob. 2aTCh. 11.1 - Prob. 2bTCh. 11.1 - Prob. 2cTCh. 11.1 - The representation that we have been using...Ch. 11.1 - Prob. 2eTCh. 11.1 - Prob. 2gTCh. 11.1 - Each of the photographs at right shows a part of a...Ch. 11.1 - Obtain a piece of paper and a transparency with...Ch. 11.2 - Obtain a pan of water and form a barrier in it...
Ch. 11.2 - Prob. 2aTCh. 11.2 - Obtain an enlargement of the diagram at right that...Ch. 11.2 - Suppose that the width of one of the slits were...Ch. 11.2 - Red light from a distant point source is incident...Ch. 11.2 - Compare the situation in part II (in which a...Ch. 11.2 - For each of the lettered points, determine D (in...Ch. 11.2 - Suppose that one of the slits were covered. At...Ch. 11.2 - The pattern produced by red light passing through...Ch. 11.2 - Consider point B, the first maximum to the left of...Ch. 11.3 - Red light from a distant point source is incident...Ch. 11.3 - In a previous homework, you found an expression...Ch. 11.3 - Suppose that the screen were semicircular, as...Ch. 11.3 - Consider a point M on the distant screen where...Ch. 11.3 - Consider a point N on the screen where there is a...Ch. 11.3 - Obtain a set of transparencies of sinusoidal...Ch. 11.3 - Suppose that coherent red light were incident on a...Ch. 11.3 - Generalize your results from the 2-slit, 3-slit,...Ch. 11.3 - Coherent red light is incident on a mask with two...Ch. 11.3 - Prob. 3dTCh. 11.4 - Red light from a distant point source is incident...Ch. 11.4 - Suppose that point X marks the location of the...Ch. 11.4 - Suppose that only slit 1 is uncovered, and all...Ch. 11.4 - Show how you could group all ten slits into five...Ch. 11.4 - Suppose that the number of slits is doubled and...Ch. 11.4 - If we continued to add slits in this way (i.e.,...Ch. 11.4 - How is this pattern different from what you would...Ch. 11.4 - Consider the following dialogue: Student 1: "l...Ch. 11.4 - The photograph at right shows the diffraction...Ch. 11.4 - The photograph at right shows the diffraction...Ch. 11.4 - Describe what you would see on the screen if the...Ch. 11.4 - If a diffraction pattern has several minima (like...Ch. 11.4 - In part A, you drew a diagram that showed how find...Ch. 11.4 - Use the model that we have developed to write an...Ch. 11.5 - The minima that occur in the case of a single slit...Ch. 11.5 - Consider the following dispute between two physics...Ch. 11.5 - A second slit, identical in size to the first, is...Ch. 11.5 - Both slits are now uncovered. For what angles will...Ch. 11.5 - Suppose that the width of both slit, a, were...Ch. 11.5 - Suppose instead that the distance between the...Ch. 11.5 - The four graphs from part C that show relative...Ch. 11.5 - Consider the relative intensity graph shown at...Ch. 11.5 - Consider the following comment made by a student:...Ch. 11.5 - You may have already noticed that the maxima are...Ch. 11.6 - Prob. 1TCh. 11.6 - Prob. 2aTCh. 11.6 - When comparing two materials of different indices...Ch. 11.6 - Consider light incident on a thin soap film, as...Ch. 11.6 - Light of frequency f=7.51014Hz is incident on the...Ch. 11.6 - Suppose that an observer were located on the left...Ch. 11.6 - Observer A is looking at the part of the film that...Ch. 11.6 - Observer B is looking at the part of the film that...Ch. 11.6 - Observer C is looking at the thinnest part of the...Ch. 11.6 - Describe the appearance of the film as a whole.Ch. 11.6 - What are the three smallest film thickness for...Ch. 11.6 - The thickness of the film is 1650 nm at the bottom...Ch. 11.7 - Look at the room lights through one of the...Ch. 11.7 - Hold a second polarizing filter in front of the...Ch. 11.7 - Do the room lights produce polarized light?...Ch. 11.7 - Suppose that you had two marked polarizers (i.e.,...Ch. 11.7 - Suppose that you had a polarizer with its...Ch. 11.7 - Prob. 2dTCh. 11.7 - An observer is looking at a light source through...Ch. 11.7 - Consider a beam of unpolarized light that is...
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