College Physics 11E Global Edition
11th Edition
ISBN: 9781337620338
Author: SERWAY/VUILLE
Publisher: CENGAGE Learning Custom Publishing
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Chapter 24, Problem 32P
A student and his lab partner create a single slit by carefully aligning two razor blades to a separation of 0.500 mm. When a helium-neon laser at 633 nm illuminates the slit, a diffraction pattern is observed on a screen 1.25 m beyond the slit. Calculate (a) the angle θdark to the first minimum in the diffraction pattern and (b) the width of the central maximum.
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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 24 Solutions
College Physics 11E Global Edition
Ch. 24.2 - In a two-slit interference pattern projected on a...Ch. 24.2 - if the distance between the slits is doubled in...Ch. 24.2 - A Youngs double-slit experiment is performed with...Ch. 24.4 - Suppose Youngs experiment is carried out in air,...Ch. 24.7 - In a single-alit diffraction experiment, as the...Ch. 24.8 - If laser light is reflected from a phonograph...Ch. 24 - Your automobile has two headlights. What sort of...Ch. 24 - A plane monochromatic light wave is incident on a...Ch. 24 - A plane monochromatic light wave is incident on a...Ch. 24 - If a Youngs experiment carried out in air is...
Ch. 24 - Sodiums emission lines at 589.0 nm and 589.6 nm...Ch. 24 - Count the number of 180 phase reversals for the...Ch. 24 - Figure CQ24.7 shows rays with wavelength incident...Ch. 24 - Fingerprints left on a piece of glass such as a...Ch. 24 - In everyday experience, why are radio waves...Ch. 24 - Suppose reflected while light is used to observe a...Ch. 24 - Would it be possible to place a nonreflective...Ch. 24 - Certain sunglasses use a polarizing material to...Ch. 24 - Why is it so much easier to perform interference...Ch. 24 - A soap film is held vertically in air and is...Ch. 24 - Consider a dark fringe in an interference pattern...Ch. 24 - Holding your hand at arms length, you can readily...Ch. 24 - A laser beam is incident on two slits with a...Ch. 24 - In a Youngs double-slit experiment, a set of...Ch. 24 - Light at 633 nm from a helium-neon laser shines on...Ch. 24 - Light of wavelength 620. nm falls on a double...Ch. 24 - In a location where the speed of sound is 354 m/s....Ch. 24 - A double slit separated by 0.058 0 mm is placed...Ch. 24 - Two radio antennas separated by d = 3.00 102 cm....Ch. 24 - Prob. 8PCh. 24 - Monochromatic light falls on a screen 1.75 m from...Ch. 24 - A pair of parallel slits separated by 2.00 104 m...Ch. 24 - A riverside warehouse has two open doors, as in...Ch. 24 - A student sets up a double-slit experiment using...Ch. 24 - Radio waves from a star, of wavelength 2.50 102...Ch. 24 - Monochromatic light of wavelength is incident on...Ch. 24 - Waves from a radio station have a wavelength of...Ch. 24 - A soap bubble (n = 1.33) having a wall thickness...Ch. 24 - A thin layer of liquid methylene iodide (n =...Ch. 24 - A thin film of oil (n = 1.25) is located on...Ch. 24 - A thin film of glass (n = 1.52) of thickness 0.420...Ch. 24 - A transparent oil with index of refraction 1.29...Ch. 24 - A possible means for making an airplane invisible...Ch. 24 - An oil film (n = 1.45) floating on water is...Ch. 24 - Astronomers observe the chromosphere of the Sun...Ch. 24 - A spacer is cut from a playing card of thickness...Ch. 24 - An investigator finds at a fiber at a crime scene...Ch. 24 - A plano-convex lens with radius of curvature R =...Ch. 24 - A thin film of oil (n = 1.45) of thickness 425 nm...Ch. 24 - Prob. 28PCh. 24 - A thin film of glycerin (n = 1.173) of thickness...Ch. 24 - Prob. 30PCh. 24 - Light of wavelength 5.40 102 nm passes through a...Ch. 24 - A student and his lab partner create a single slit...Ch. 24 - Light of wavelength 587.5 nm illuminates a slit of...Ch. 24 - Microwaves of wavelength 5.00 cm enter a long,...Ch. 24 - A beam of monochromatic light is diffracted by a...Ch. 24 - A screen is placed 50.0 cm from a single slit that...Ch. 24 - A slit of width 0.50 mm is illuminated with light...Ch. 24 - The second-order dark fringe in a single-slit...Ch. 24 - Three discrete spectral lines occur at angles of...Ch. 24 - Intense white light is incident on a diffraction...Ch. 24 - The hydrogen spectrum has a red line at 656 nm and...Ch. 24 - Prob. 42PCh. 24 - A helium-neon laser ( = 632.8 nm) is used to...Ch. 24 - Prob. 44PCh. 24 - Prob. 45PCh. 24 - White light is incident on a diffraction grating...Ch. 24 - Sunlight is incident on a diffraction grating that...Ch. 24 - Monochromatic light at 577 nm illuminates a...Ch. 24 - Light of wavelength 5.00 102 nm is incident...Ch. 24 - Prob. 50PCh. 24 - The angle of incidence of a light beam in air onto...Ch. 24 - Unpolarized light passes through two Polaroid...Ch. 24 - The index of retraction of a glass plate is 1.52....Ch. 24 - At what angle above the horizon is the Sun if...Ch. 24 - Prob. 55PCh. 24 - The critical angle for total internal reflection...Ch. 24 - Equation 24.14 assumes the incident light is in...Ch. 24 - Prob. 58PCh. 24 - Three polarizing plates whose planes are parallel...Ch. 24 - Light of intensity I0 is polarized vertically and...Ch. 24 - Light with a wavelength in vacuum of 546.1 nm...Ch. 24 - Light from a helium-neon laser ( = 632.8 nm) is...Ch. 24 - Laser light with a wavelength of 632.6 nm is...Ch. 24 - In a Youngs interference experiment, the two slits...Ch. 24 - Light of wavelength 546 nm (the intense green line...Ch. 24 - The two speakers are placed 35.0 cm apart. A...Ch. 24 - Interference effects are produced at point P on a...Ch. 24 - Prob. 68APCh. 24 - Figure P24.69 shows a radio-wave transmitter and a...Ch. 24 - Three polarizers, centered on a common axis and...Ch. 24 - Prob. 71APCh. 24 - A plano-convex lens (flat on one side, convex on...Ch. 24 - A diffraction pattern is produced on a screen 1.40...Ch. 24 - Prob. 74AP
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