PHYSICS:F/SCI.+ENGRS.,V.1
10th Edition
ISBN: 9781337553575
Author: SERWAY
Publisher: CENGAGE L
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Chapter 35, Problem 4P
Two plane mirrors stand facing each other, 3.00 m apart, and a woman stands between them. The woman looks at one of the mirrors from a distance of 1.00 m and holds her left arm out to the side of her body with the palm of her hand facing the closer mirror. (a) What is the apparent position of the closest image of her left hand, measured perpendicularly from the surface of the mirror in front of her? (b) Does it show the palm of her hand or the back of her hand? (c) What is the position of the next closest image? (d) Does it show the palm of her hand or the back of her hand? (e) What is the position of the third closest image? (f) Does it show the palm of her hand or the back of her hand? (g) Which of the images are real and which are virtual?
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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]
Chapter 35 Solutions
PHYSICS:F/SCI.+ENGRS.,V.1
Ch. 35.1 - You are standing approximately 2 m away from a...Ch. 35.2 - You wish to start a fire by reflecting sunlight...Ch. 35.2 - Consider the image in the mirror in Figure 35.14....Ch. 35.3 - Prob. 35.4QQCh. 35.3 - Prob. 35.5QQCh. 35.4 - What is the focal length of a pane of window...Ch. 35.6 - Two campers wish to start a fire during the day....Ch. 35 - (a) Does your bathroom mirror show you older or...Ch. 35 - Two flat mirrors have their reflecting surfaces...Ch. 35 - A periscope (Fig. P35.3) is useful for viewing...
Ch. 35 - Two plane mirrors stand facing each other, 3.00 m...Ch. 35 - An object is placed 50.0 cm from a concave...Ch. 35 - An object is placed 20.0 cm from a concave...Ch. 35 - An object of height 2.00 cm is placed 30.0 cm from...Ch. 35 - Why is the following situation impossible? At a...Ch. 35 - A large hall in a museum has a niche in one wall....Ch. 35 - A concave spherical mirror has a radius of...Ch. 35 - An object 10.0 cm tall is placed at the zero mark...Ch. 35 - You are training to become an opticians assistant....Ch. 35 - A certain Christmas tree ornament is a silver...Ch. 35 - Review. A ball is dropped at t = 0 from rest 3.00...Ch. 35 - You unconsciously estimate the distance to an...Ch. 35 - A convex spherical mirror has a focal length of...Ch. 35 - One end of a long glass rod (n = 1.50) is formed...Ch. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Figure P35.20 (page 958) shows a curved surface...Ch. 35 - To dress up your dorm room, you have purchased a...Ch. 35 - You are working for a solar energy company. Your...Ch. 35 - An object located 32.0 cm in front of a lens forms...Ch. 35 - An objects distance from a converging lens is 5.00...Ch. 35 - A contact lens is made of plastic with an index of...Ch. 35 - A converging lens has a focal length of 10.0 cm....Ch. 35 - A converging lens has a focal length of 10.0 cm....Ch. 35 - Suppose an object has thickness dp so that it...Ch. 35 - An object is placed 10.0 cm from a diverging lens...Ch. 35 - In Figure P35.30, a thin converging lens of focal...Ch. 35 - You are working for an electronics company that...Ch. 35 - Prob. 32PCh. 35 - Two rays traveling parallel to the principal axis...Ch. 35 - Josh cannot see objects clearly beyond 25.0 cm...Ch. 35 - Figure 35.34 diagrams a cross section of a camera....Ch. 35 - The refracting telescope at the Yerkes Observatory...Ch. 35 - The distance between the eyepiece and the...Ch. 35 - What are (a) the maximum angular magnification...Ch. 35 - A patient has a near point of 45.0 cm and far...Ch. 35 - The intensity I of the light reaching the CCD in a...Ch. 35 - A certain childs near point is 10.0 cm; her far...Ch. 35 - Astronomers often take photographs with the...Ch. 35 - A simple model of the human eye ignores its lens...Ch. 35 - A real object is located at the zero end of a...Ch. 35 - The distance between an object and its upright...Ch. 35 - Prob. 46APCh. 35 - Andy decides to use an old pair of eyeglasses to...Ch. 35 - Two converging lenses having focal lengths of f1 =...Ch. 35 - Two lenses made of kinds of glass having different...Ch. 35 - Prob. 50APCh. 35 - An object is placed 12.0 cm to the left of a...Ch. 35 - An object is placed a distance p to the left of a...Ch. 35 - In a darkened room, a burning candle is placed...Ch. 35 - In many applications, it is necessary to expand or...Ch. 35 - Why is the following situation impossible?...Ch. 35 - A zoom lens system is a combination of lenses that...Ch. 35 - Consider the lensmirror arrangement shown in...Ch. 35 - A floating strawberry illusion is achieved with...
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