College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Textbook Question
Chapter 25, Problem 14CQ
It can he argued that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are d1 and d0 related?
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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 25 Solutions
College Physics For Ap® Courses
Ch. 25 - Using the law of reflection, explain how powder...Ch. 25 - Diffusion by reflection from a rough surface is...Ch. 25 - Why is the index of refraction always greater than...Ch. 25 - Does the fact that the light flash from lightning...Ch. 25 - Will light change direction toward or away from...Ch. 25 - Explain why an object in water always appears to...Ch. 25 - Explain why a person’s legs appeal very short when...Ch. 25 - Why is the front surface of a thermometer curved...Ch. 25 - Suppose light were incident from air onto a...Ch. 25 - A ring with a colorless gemstone is dropped into...
Ch. 25 - A high-quality diamond may be quite clear and...Ch. 25 - Is it possible that total internal reflection...Ch. 25 - The most common type at mirage is an illusion that...Ch. 25 - It can he argued that a flat piece of glass, such...Ch. 25 - You can often see a reflection when looking at a...Ch. 25 - When you focus a camera, you adjust the distance...Ch. 25 - A thin lens has two focal points, one on either...Ch. 25 - Will the focal length of a lens change when it is...Ch. 25 - What are the differences between teal and virtual...Ch. 25 - Can you see a virtual image? Can you photograph...Ch. 25 - Is it necessary to project a real image onto a...Ch. 25 - At what distance is an image always locatedat do,...Ch. 25 - Under what circumstances will an image be located...Ch. 25 - What is meant by a negative magnification? 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In crown glass?Ch. 25 - Calculate the index of refraction for a medium in...Ch. 25 - In what substance in Table 25.1 is the speed of...Ch. 25 - There was a major collision of an asteroid with...Ch. 25 - A scuba diver training in a pool looks at his...Ch. 25 - Components of some computers communicate with each...Ch. 25 - (a) Using information in Figure 25.53, find the...Ch. 25 - Suppose you have an unknown clear substance...Ch. 25 - On the Moon’s surface, lunar astronauts placed a...Ch. 25 - Suppose Figure 25.54 represents a ray of light...Ch. 25 - Figure 25.54 shows a ray of light passing from one...Ch. 25 - Unreasonable Results Suppose light travels from...Ch. 25 - Construct Your Own Problem Consider sunlight...Ch. 25 - Unreasonable Results Light traveling from water to...Ch. 25 - Verify that the critical angle for light going...Ch. 25 - (a) At the end of Example 25.4, it was stated that...Ch. 25 - An optical fiber uses flint glass clad with crown...Ch. 25 - At what minimum angle will you get total internal...Ch. 25 - Suppose you are using total internal reflection to...Ch. 25 - You can determine me index of refraction of a...Ch. 25 - A ray of light, emitted beneath the surface of an...Ch. 25 - A light ray entering an optical fiber surrounded...Ch. 25 - (a) What is me ratio of the speed of red light to...Ch. 25 - A beam of white light goes from air into water at...Ch. 25 - By how much do the critical angles for red (660...Ch. 25 - (a) A narrow beam of light containing yellow (580...Ch. 25 - A parallel beam of light containing orange (610...Ch. 25 - A ray of 610 nm light goes from air into fused...Ch. 25 - A narrow beam of light containing red (660 nm) and...Ch. 25 - A narrow beam of white light enters a prism made...Ch. 25 - What is the power in diopters at a camera lens...Ch. 25 - Your camera's zoom lens has an adjustable focal...Ch. 25 - What is the focal length of 1.75 D reading glasses...Ch. 25 - You note that your prescription for new eyeglasses...Ch. 25 - How far from the lens must the film in a camera...Ch. 25 - A certain slide projector has a 100 mm focal...Ch. 25 - A doctor examines a mole with a 15.0 cm focal...Ch. 25 - How far from a piece of paper must you hold your...Ch. 25 - A camera with a 50.0 mm focal length lens is being...Ch. 25 - A camera lens used for taking close-up photographs...Ch. 25 - Suppose your 50.00 mm local length camera lens is...Ch. 25 - (a) What is the focal length of a magnifying glass...Ch. 25 - What magnification will be produced by a lens of...Ch. 25 - In Example 25.7, the magnification of a book held...Ch. 25 - Suppose a 200 mm focal length telephoto lens is...Ch. 25 - A camera with a 100 mm focal length lens is used...Ch. 25 - Combine thin lens equations to show that the...Ch. 25 - What is the focal length of a makeup mirror that...Ch. 25 - Some telephoto cameras use a mirror rather than a...Ch. 25 - (a) Calculate the focal length of the mirror...Ch. 25 - Find the magnification of the heater element in...Ch. 25 - What is the focal length of a makeup mirror that...Ch. 25 - A shopper standing 3.00 m from a convex security...Ch. 25 - An object 1.50 cm high is held 3.00 cm from a...Ch. 25 - Ray tracing for a flat mirror shows that the image...Ch. 25 - Show that for a flat mirror hi= ho, knowing that...Ch. 25 - Use the law of reflection to prove that the focal...Ch. 25 - Referring to the electric room heater considered...Ch. 25 - Consider a 250-W heat lamp fixed to the ceiling in...
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