COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Textbook Question
Chapter 26, Problem 19PE
Repeat the previous problem for glasses that are 1.75 cm from the eyes.
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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 26 Solutions
COLLEGE PHYSICS
Ch. 26 - If the lens of a person’s eye is removed because...Ch. 26 - A cataract is cloudiness in the lens of the eye....Ch. 26 - When laser light is shone into a relaxed...Ch. 26 - How does the power of a dry contact lens compare...Ch. 26 - Why is your vision so blurry when you open your...Ch. 26 - It has become common to replace the...Ch. 26 - If the cornea is to be reshaped (this can be done...Ch. 26 - If there is a fixed percent uncertainty in LASIK...Ch. 26 - A person with presbyopia has lost some or all of...Ch. 26 - A pure red object on a black background seems to...
Ch. 26 - What is color constancy, and what are its...Ch. 26 - There are different types of color blindness...Ch. 26 - Propose a way to study the function of the rods...Ch. 26 - Geometric optics describes the interaction of...Ch. 26 - The image produced by the microscope in Figure...Ch. 26 - Why not have the objective at a microscope form a...Ch. 26 - What advantages do oil immersion objectives offer?Ch. 26 - How does the NA of a microscope compare wi1h the...Ch. 26 - If you want your microscope or telescope to...Ch. 26 - List the various types of aberrations. What causes...Ch. 26 - What is the power of the eye when viewing an...Ch. 26 - Calculate the power at the eye when viewing an...Ch. 26 - (a) The print in many books averages 3.50 mm in...Ch. 26 - Suppose a certain person’s visual acuity is such...Ch. 26 - People who do very detailed work close up, such as...Ch. 26 - What is the far point of a person whose eyes have...Ch. 26 - What is the near point of a person whose eyes have...Ch. 26 - (a) A laser vision correction reshaping the cornea...Ch. 26 - In a LASIK vision correction, the power of a...Ch. 26 - What was the previous far point of a patient who...Ch. 26 - A severely myopic patient has a far point of 5.00...Ch. 26 - A student’s eyes, while reading the blackboard,...Ch. 26 - The power of a physician’s eyes is 53.0 D while...Ch. 26 - A young woman with normal distant vision has a...Ch. 26 - The far point of a myopic administrator is 50.0...Ch. 26 - A very myopic man has afar point of 20.0 cm. What...Ch. 26 - Repeat the previous problem for eyeglasses held...Ch. 26 - A myopic person sees that her contact lens...Ch. 26 - Repeat the previous problem for glasses that are...Ch. 26 - The contact lens prescription for a mildly...Ch. 26 - A nearsighted man cannot see objects clearly...Ch. 26 - A mother sees that her child's contact lens...Ch. 26 - Repeat the previous problem for glasses that are...Ch. 26 - The contact lens prescription for a nearsighted...Ch. 26 - Unreasonable Results A boy has a near point of 50...Ch. 26 - A microscope with an overall magnification of 800...Ch. 26 - (a) What magnification is produced by a 0.150 cm...Ch. 26 - (a) Where does an object need to be placed...Ch. 26 - You switch from a 1.40NA60X oil immersion...Ch. 26 - An amoeba is 0.305 cm away from the 0.300 cm focal...Ch. 26 - You are using a standard microscope with a...Ch. 26 - Unreasonable Results Your friends show you an...Ch. 26 - What is the angular magnification of a telescope...Ch. 26 - Find the distance between the objective and...Ch. 26 - A large reflecting telescope has an objective...Ch. 26 - A small telescope has a concave mirror with a 2.00...Ch. 26 - A 7.5x binocular produces an angular magnification...Ch. 26 - Construct Your Own Problem Consider a telescope of...Ch. 26 - Integrated Concepts (a) During laser vision...Ch. 26 - Prob. 1TPCh. 26 - Prob. 2TPCh. 26 - Prob. 3TPCh. 26 - Prob. 4TPCh. 26 - Prob. 5TPCh. 26 - Prob. 6TPCh. 26 - Prob. 7TPCh. 26 - Prob. 8TPCh. 26 - Prob. 9TPCh. 26 - Prob. 10TPCh. 26 - Prob. 11TP
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