COLLEGE PHYSICS (LL W/WEBASSIGN)
11th Edition
ISBN: 9781337741644
Author: SERWAY
Publisher: CENGAGE L
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Textbook Question
Chapter 23, Problem 4CQ
Construct ray diagrams to determine whether each of the following statement is true (T) or false (F). (a) For an object at a concave mirror’s center of curvature, the image is real and inverted. (b) As an object approaches the focal point of a concave mirror, the image size shrinks to zero. (c) For an object in front of a convex mirror, the image is always virtual and upright.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 23 Solutions
COLLEGE PHYSICS (LL W/WEBASSIGN)
Ch. 23.1 - In the overhead view if Figure 23.3, the image of...Ch. 23.3 - A person spearfishing from a boat sees a fish...Ch. 23.3 - True or False: (a) The image of an object placed...Ch. 23.5 - A clear plastic sandwich bag filled with water can...Ch. 23.5 - In Figure 23.25a, the blue object arrow is...Ch. 23.5 - An object is placed to the left of a converging...Ch. 23 - Tape a picture of yourself on a bathroom mirror....Ch. 23 - Prob. 2CQCh. 23 - The top row of Figure CQ23.3 shows three ray...Ch. 23 - Construct ray diagrams to determine whether each...
Ch. 23 - Construct ray diagrams to determine whether each...Ch. 23 - Prob. 6CQCh. 23 - Suppose you want to use a converging lens to...Ch. 23 - Lenses used in eyeglasses, whether converging or...Ch. 23 - In a Jules Verne novel, a piece of ice is shaped...Ch. 23 - If a cylinder of solid glass or clear plastic is...Ch. 23 - Prob. 11CQCh. 23 - Prob. 12CQCh. 23 - Why does the focal length of a mirror not depend...Ch. 23 - A person spear fishing from a boat sees a...Ch. 23 - An object represented by a gray arrow, is placed...Ch. 23 - (a) Does your bathroom mirror show you older or...Ch. 23 - Suppose you stand in front of a flat mirror and...Ch. 23 - Prob. 3PCh. 23 - In a church choir loft, two parallel walls are...Ch. 23 - A periscope (Fig. P23.5) is useful for viewing...Ch. 23 - A dentist uses a mirror to examine a tooth that is...Ch. 23 - A convex spherical mirror, whose focal length has...Ch. 23 - To fit a contact lens to a patient's eye, a...Ch. 23 - A virtual image is formed 20.0 cm from a concave...Ch. 23 - While looking at her image in a cosmetic minor,...Ch. 23 - Prob. 11PCh. 23 - A dedicated sports car enthusiast polishes the...Ch. 23 - A concave makeup mirror it designed to that a...Ch. 23 - A 1.80-m-tall person stands 9.00 m in front of a...Ch. 23 - A man standing 1.52 m in front of a shaving mirror...Ch. 23 - Prob. 16PCh. 23 - At an intersection of hospital hallways, a convex...Ch. 23 - The mirror of a solar cooker focuses the Suns rays...Ch. 23 - A spherical mirror is to be used to form an image,...Ch. 23 - Prob. 20PCh. 23 - A cubical block of ice 50.0 cm on an edge is...Ch. 23 - A goldfish is swimming inside a spherical bowl of...Ch. 23 - A paperweight is made of a solid hemisphere with...Ch. 23 - The top of a swimming pool is at ground level. If...Ch. 23 - A transparent sphere of unknown composition is...Ch. 23 - A man inside a spherical diving bell watches a...Ch. 23 - A jellyfish is floating in a water-filled aquarium...Ch. 23 - Figure P23.28 shows a curved surface separating a...Ch. 23 - A contact lens is made of plastic with an index of...Ch. 23 - A thin plastic lens with index of refraction n =...Ch. 23 - A converging lens has a local length of 10.0 cm....Ch. 23 - Prob. 32PCh. 23 - A diverging lens has a focal length of magnitude...Ch. 23 - A diverging lens has a focal length of 20.0 cm....Ch. 23 - Prob. 35PCh. 23 - The nickels image in Figure P23.36 has twice the...Ch. 23 - An object of height 8.00 cm it placed 25.0 cm to...Ch. 23 - An object is located 20.0 cm to the left of a...Ch. 23 - A converging lens is placed 30.0 cm to the right...Ch. 23 - (a) Use the thin-lens equation to derive an...Ch. 23 - Two converging lenses, each of focal length 15.0...Ch. 23 - A converging lens is placed at x = 0, a distance d...Ch. 23 - A 1.00-cm-high object is placed 4.00 cm to the...Ch. 23 - Two converging lenses having focal length of f1 =...Ch. 23 - Lens L1 in figure P23.45 has a focal length of...Ch. 23 - An object is placed 15.0 cm from a first...Ch. 23 - Prob. 47APCh. 23 - Prob. 48APCh. 23 - Prob. 49APCh. 23 - Prob. 50APCh. 23 - The lens and the mirror in figure P23.51 are...Ch. 23 - The object in Figure P23.52 is mid-way between the...Ch. 23 - Prob. 53APCh. 23 - Two rays travelling parallel to the principal axis...Ch. 23 - To work this problem, use the fact that the image...Ch. 23 - Consider two thin lenses, one of focal length f1...Ch. 23 - An object 2.00 cm high is placed 10.0 cm to the...Ch. 23 - Prob. 58APCh. 23 - Figure P23.59 shows a converging lens with radii...Ch. 23 - Prob. 60APCh. 23 - The lens-makers equation for a lens with index n1...Ch. 23 - An observer to the right of the mirror-lens...Ch. 23 - The lens-markers equation applies to a lens...Ch. 23 - Prob. 64APCh. 23 - A glass sphere (n = 1.50) with a radius of 15.0 cm...Ch. 23 - An object 10.0 cm tall is placed at the zero mark...
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