Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card, Single-Term
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ISBN: 9781337888745
Author: SERWAY, Raymond A., Jewett, John W.
Publisher: Cengage Learning
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Chapter 36, Problem 9P
Coherent light rays of wavelength λ strike a pair of slits separated by distance d at an angle θ1 with respect to the normal to the plane containing the slits as shown in Figure P36.9. The rays leaving the slits make an angle θ2 with respect to the normal, and an interference maximum is formed by those rays on a screen that is a great distance from the slits. Show that the angle θ2 is given by
where m is an integer.
Figure P36.9
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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 36 Solutions
Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card, Single-Term
Ch. 36.2 - Which of the following causes the fringes in a...Ch. 36.3 - Using Figure 36.6 as a model, sketch the...Ch. 36.5 - One microscope slide is placed on top of another...Ch. 36 - Two slits are separated by 0.320 mm. A beam of...Ch. 36 - Why is the following situation impossible? Two...Ch. 36 - A laser beam is incident on two slits with a...Ch. 36 - In a Youngs double-slit experiment, two parallel...Ch. 36 - Light of wavelength 620 nm falls on a double slit,...Ch. 36 - Light with wavelength 442 nm passes through a...Ch. 36 - A student holds a laser that emits light of...
Ch. 36 - A student holds a laser that emits light of...Ch. 36 - Coherent light rays of wavelength strike a pair...Ch. 36 - In Figure P36.10 (not to scale), let L = 1.20 m...Ch. 36 - You are working in an optical research laboratory....Ch. 36 - You are operating a new radio telescope that has...Ch. 36 - In the double-slit arrangement of Figure P36.13, d...Ch. 36 - Monochromatic light of wavelength is incident on...Ch. 36 - Prob. 15PCh. 36 - Show that the distribution of intensity in a...Ch. 36 - Green light ( = 546 nm) illuminates a pair of...Ch. 36 - Monochromatic coherent light of amplitude E0 and...Ch. 36 - A material having an index of refraction of 1.30...Ch. 36 - A soap bubble (n = 1.33) floating in air has the...Ch. 36 - A film of MgF2 (n = 1.38) having thickness 1.00 ...Ch. 36 - An oil film (n = 1.45) floating on water is...Ch. 36 - When a liquid is introduced into the air space...Ch. 36 - You are working as an expert witness for an...Ch. 36 - Astronomers observe the chromosphere of the Sun...Ch. 36 - A lens made of glass (ng = 1.52) is coated with a...Ch. 36 - Mirror M1 in Figure 36.13 is moved through a...Ch. 36 - Radio transmitter A operating at 60.0 MHz is 10.0...Ch. 36 - In an experiment similar to that of Example 36.1,...Ch. 36 - In the What If? section of Example 36.2, it was...Ch. 36 - Two coherent waves, coming from sources at...Ch. 36 - Raise your hand and hold it flat. Think of the...Ch. 36 - In a Youngs double-slit experiment using light of...Ch. 36 - Review. A flat piece of glass is held stationary...Ch. 36 - Figure P36.35 shows a radio-wave transmitter and a...Ch. 36 - Figure P36.35 shows a radio-wave transmitter and a...Ch. 36 - In a Newtons-rings experiment, a plano-convex...Ch. 36 - Measurements are made of the intensity...Ch. 36 - A plano-concave lens having index of refraction...Ch. 36 - Why is the following situation impossible? A piece...Ch. 36 - Interference fringes are produced using Lloyds...Ch. 36 - A plano-convex lens has index of refraction n. The...Ch. 36 - Prob. 43APCh. 36 - Prob. 44APCh. 36 - Astronomers observe a 60.0-MHz radio source both...Ch. 36 - Prob. 46CPCh. 36 - Our discussion of the techniques for determining...Ch. 36 - The condition for constructive interference by...Ch. 36 - Both sides of a uniform film that has index of...Ch. 36 - Slit 1 of a double-slit is wider than slit 2 so...
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