EBK COLLEGE PHYSICS, VOLUME 2
11th Edition
ISBN: 9781337514644
Author: Vuille
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Textbook Question
Chapter 22, Problem 39P
A light ray is incident normally to the long face (the hypotenuse) of a 45°–45°–90° prism surrounded by air, as shown m Figure 22.26b. Calculate the minimum index of refraction of the prism for which the ray will totally internally reflect at each of the two sides making the tight angle.
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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 22 Solutions
EBK COLLEGE PHYSICS, VOLUME 2
Ch. 22.2 - Which part of Figure 22.3, (a) or (b), better...Ch. 22.2 - Prob. 22.2QQCh. 22.3 - A material has an index of refraction that...Ch. 22.3 - As light travels from a vacuum (n = 1) to a medium...Ch. 22 - Prob. 1CQCh. 22 - A ray of light passes from one material into a...Ch. 22 - Prob. 3CQCh. 22 - Prob. 4CQCh. 22 - Determine whether each of the following statements...Ch. 22 - A type of mirage called a pingo is often observed...
Ch. 22 - In dispersive materials, the angle of refraction...Ch. 22 - The level of water in a clear, colorless glass can...Ch. 22 - Prob. 9CQCh. 22 - Light in medium A undergoes a total internal...Ch. 22 - Prob. 11CQCh. 22 - Try this simple experiment on your own. Take two...Ch. 22 - Prob. 13CQCh. 22 - Prob. 14CQCh. 22 - A light ray containing both blue and red...Ch. 22 - During the Apollo XI Moon landing, a...Ch. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Find the speed of light in (a) water, (b) crown...Ch. 22 - A ray of light travels from air into another...Ch. 22 - Prob. 8PCh. 22 - An underwater scuba diver sees the Sun at an...Ch. 22 - Prob. 10PCh. 22 - A laser beam is incident at an angle of 30.0 to...Ch. 22 - Light containing wavelengths of 400. nm, 500. nm,...Ch. 22 - A ray of light is incident on the surface of a...Ch. 22 - Prob. 14PCh. 22 - The light emitted by a helium-neon laser has a...Ch. 22 - Figure P22.16 shows a light ray traveling in a...Ch. 22 - Prob. 17PCh. 22 - A ray of light strikes a flat, 2.00-cm-thick block...Ch. 22 - Prob. 19PCh. 22 - Prob. 20PCh. 22 - A man shines a flashlight from a boat into the...Ch. 22 - A narrow beam of ultra-sonic waves reflects off...Ch. 22 - A person looking into an empty container is able...Ch. 22 - Prob. 24PCh. 22 - Prob. 25PCh. 22 - Prob. 26PCh. 22 - An opaque cylindrical tank with an open top has a...Ch. 22 - A certain kind of glass has an index of refraction...Ch. 22 - The index of refraction for red light in water is...Ch. 22 - The index of refraction for crown glass is 1.512...Ch. 22 - A light beam containing red and violet wavelengths...Ch. 22 - Prob. 32PCh. 22 - A ray of light strikes the midpoint of one face of...Ch. 22 - For light of wavelength 589 nm. calculate the...Ch. 22 - Repeat Problem 34, but this time assume the...Ch. 22 - A beam of light is incident from air on the...Ch. 22 - Prob. 37PCh. 22 - Prob. 38PCh. 22 - A light ray is incident normally to the long face...Ch. 22 - Prob. 40PCh. 22 - A room contains air in which the speed of sound is...Ch. 22 - Prob. 42PCh. 22 - The light beam in Figure P22.43 strikes surface 2...Ch. 22 - Prob. 44PCh. 22 - A layer of ice having parallel sides floats on...Ch. 22 - A ray of light is incident at an angle 30.0 on a...Ch. 22 - When a man stands near the edge of an empty...Ch. 22 - Prob. 48APCh. 22 - Refraction causes objects submerged in water to...Ch. 22 - A narrow beam of light is incident from air onto a...Ch. 22 - Prob. 51APCh. 22 - Endoscopes are medical instruments used to examine...Ch. 22 - A piece of wire is bent through an angle . The...Ch. 22 - Prob. 54APCh. 22 - Prob. 55APCh. 22 - Prob. 56APCh. 22 - Prob. 57APCh. 22 - Students allow a narrow beam of laser light to...Ch. 22 - Prob. 59APCh. 22 - Three sheets of plastic have unknown indices of...Ch. 22 - A person swimming underwater on a bright day and...Ch. 22 - Prob. 62AP
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