Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 30, Problem 59P
To determine
Show that
ϕ = 4 sin − 1 ( sin θ n ) − 2 θ
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Question 3 of 17
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X
L
L
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0.5/
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?
xcom
L
2
(b) What is the y coordinate of the system's center of mass?
Ycom
45
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Q Search
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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 30 Solutions
Essential University Physics
Ch. 30.1 - Prob. 30.1GICh. 30.2 - The figure shows the path of a light ray through...Ch. 30.3 - The glass prism in Fig. 30.11 has n = 1.5 and is...Ch. 30.4 - Prob. 30.4GICh. 30 - Prob. 1FTDCh. 30 - Why does a spoon appear bent when its in a glass...Ch. 30 - Prob. 3FTDCh. 30 - Prob. 4FTDCh. 30 - You send white light through two identical glass...Ch. 30 - In glass, which end of the visible spectrum has...
Ch. 30 - Prob. 7FTDCh. 30 - Why are polarizing sunglasses better than glasses...Ch. 30 - Under what conditions will the polarizing angle be...Ch. 30 - Through what angle should you rotate a mirror so...Ch. 30 - Prob. 12ECh. 30 - To what angular accuracy must two ostensibly...Ch. 30 - Prob. 14ECh. 30 - In which substance in Table 30.1 does the speed of...Ch. 30 - Information in a compact disc is stored in pits"...Ch. 30 - Light is incident on an air-glass interface, and...Ch. 30 - A light ray propagates in a transparent material...Ch. 30 - Light propagating in the glass (n = 1.52) wall of...Ch. 30 - Prob. 20ECh. 30 - Find the refractive index of a material for which...Ch. 30 - Find the critical angle for total internal...Ch. 30 - A drop of water is trapped in a block of ice....Ch. 30 - What is the critical angle for light propagating...Ch. 30 - Total internal reflection occurs at an interface...Ch. 30 - Blue and red laser beams strike an air-glass...Ch. 30 - White light propagating in air is incident at 45...Ch. 30 - Example 30.2: Take the slab in Fig 30.6 to be...Ch. 30 - Example 30.2: Take θ1 = 32.5° in Fig 30.6. (a) If...Ch. 30 - Prob. 30ECh. 30 - Prob. 31ECh. 30 - Prob. 32ECh. 30 - Prob. 33ECh. 30 - Prob. 34ECh. 30 - Prob. 35ECh. 30 - Suppose the 60 angle in Fig. 30.18 is changed to...Ch. 30 - The refractive index of a human cornea is 1.40. If...Ch. 30 - Two plane mirrors make an angle . A light ray...Ch. 30 - An unlabeled bottle of liquid has spilled, and...Ch. 30 - A meter stick lies on the bottom of the...Ch. 30 - Prob. 41PCh. 30 - At the aquarium where you work, a fish has gone...Ch. 30 - Prob. 43PCh. 30 - You've dropped your car keys at night off the end...Ch. 30 - Laser eye surgery uses ultraviolet light with...Ch. 30 - Prob. 46PCh. 30 - Where and in what direction would the main beam...Ch. 30 - Find the speed of light in a material for which...Ch. 30 - Prob. 49PCh. 30 - For the interface between air (refractive index 1)...Ch. 30 - A scuba diver sets off a camera flash at depth h...Ch. 30 - Suppose the red and blue beams of Exercise 26 are...Ch. 30 - In cataract surgery, ophthalmologists replace the...Ch. 30 - In a ruby laser, light is produced in a solid rod...Ch. 30 - An optical fiber with circular cross section has...Ch. 30 - A cylindrical tank 2.4 m deep is full to the brim...Ch. 30 - For what diameter tank in Problem 50 will sunlight...Ch. 30 - Prob. 58PCh. 30 - Prob. 59PCh. 30 - (a) Differentiate the result of Problem 55 to show...Ch. 30 - Prob. 61PCh. 30 - Show that a three-dimensional corner reflector...Ch. 30 - Fermat's principle states that a light ray's path...Ch. 30 - Prob. 64PCh. 30 - A slab of transparent material has thickness d and...Ch. 30 - For common materials like glass, the wavelength...Ch. 30 - Figure 30.25a depicts lights path over a hot road,...Ch. 30 - Prob. 68PPCh. 30 - Figure 30.25b shows how continuous refraction in...Ch. 30 - The refractive index in the ionosphere is strongly...
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