College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Chapter 25, Problem 27PE
A light ray entering an optical fiber surrounded by air is first refracted and then reflected as shown in Figure 25.55. Show than if the fiber is made from crown glass, any incident ray will be totally internally reflected.
Figure 25.55 A light ray enters the end of a fiber, the−surface of which is perpendicular to its sides. Examine the conditions under which it may be totally internally reflected.
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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)…
How does boiling point of water decreases as the altitude increases?
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? What is...Ch. 25 - Can a case 1 image be larger than the object even...Ch. 25 - Figure 25.49 shows a light bulb between two...Ch. 25 - Devise an arrangement of mirrors allowing you to...Ch. 25 - If you wish to see your entire body in a flat...Ch. 25 - It can be argued than a flat mirror has an in?nite...Ch. 25 - Why are diverging mirrors often used for rear-view...Ch. 25 - Suppose a man stands in front of a mirror as shown...Ch. 25 - Show that when light reflects from two mirrors...Ch. 25 - Light shows staged with lasers use moving mirrors...Ch. 25 - A flat minor is neither converging nor diverging....Ch. 25 - What is the speed of light in water? In glycerine?Ch. 25 - What is the speed of light in air? 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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