Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 35.6, Problem 35.6CE
To determine
The wavelength that will produce the broadest central maximum.
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Two radio antennas 60 m apart broadcast a synchronized signal with a frequency of 100 MHz. Imagine that we have a detector 5.0 km from the antennas.
(a) At this distance, what is the separation between adjacent "bright spots" in the interference pattern along a line parallel to the line between the antennas? Draw a sketch of this situation (schematic diagram) that accurately illustrates what are the known quantities and what is the quantity you are looking to find.
(b) Do "bright spots" mean where the radio signal is stronger or weaker? Explain why.
draw diagram
According to the principles of quantum mechanics, every particle acts like a wave. To demonstrate this, a helium nucleus is shown to exhibit interference as it passes through a double-slit. The helium nucleus has a mass of 6.64 x 10^-27 kg and its speed is 500.0 m/s when is passes through the slits.
a. What is the wavelength of the wave associated with the helium nucleus in nanometers?
b. If the slits are seperated by 1.00 nm and the distance from the slits to the detector (effectively, the "screen") is 15.0 cm, what is the distance, in centimeters, from the central maximum to the first-order maximum of constructive interference?
c. If the uncertainty in the velocity of the helium nucleus is 18 m/s, what is the uncertainty in its position, assuming a simultaneous measurement?
If we treat a double slit experiment as a point-like source where distances from
the slits are measured by r₁ and r2 respectively, a plane wave from each slit would
Ae-i where ;=kr; -wt+do and 01 - 02=
take the form ₁
Ae-i1 and 2:
=
=
k(r₁ r₂).
1. Solve for the probability density ₁+ 22 in terms of A, k, r₁ and r2.
-
Chapter 35 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 35.1 - Perhaps Newton never observed a diffraction...Ch. 35.1 - Prob. 35.2CECh. 35.2 - Prob. 35.3CECh. 35.3 - Prob. 35.4CECh. 35.4 - When we studied Youngs double-slit experiment, we...Ch. 35.6 - Prob. 35.6CECh. 35 - Light Is a Wave C As shown in Figure P35.1, spray...Ch. 35 - Sound Wave Interference Revisited Draw two...Ch. 35 - Prob. 3PQCh. 35 - You are seated on a couch equidistant between two...
Ch. 35 - Prob. 5PQCh. 35 - Prob. 6PQCh. 35 - A student shines a red laser pointer with a...Ch. 35 - Monochromatic light is incident on a pair of slits...Ch. 35 - Prob. 9PQCh. 35 - In a Youngs double-slit experiment with microwaves...Ch. 35 - A beam from a helium-neon laser with wavelength...Ch. 35 - Prob. 12PQCh. 35 - Prob. 13PQCh. 35 - Prob. 14PQCh. 35 - Light from a sodium vapor lamp ( = 589 nm) forms...Ch. 35 - Prob. 16PQCh. 35 - Prob. 17PQCh. 35 - Prob. 18PQCh. 35 - Prob. 19PQCh. 35 - Prob. 20PQCh. 35 - Prob. 21PQCh. 35 - Prob. 22PQCh. 35 - Prob. 23PQCh. 35 - Figure P35.24 shows the diffraction patterns...Ch. 35 - Prob. 25PQCh. 35 - Prob. 26PQCh. 35 - A thread must have a uniform thickness of 0.525...Ch. 35 - Prob. 28PQCh. 35 - Prob. 29PQCh. 35 - A radio wave of wavelength 21.5 cm passes through...Ch. 35 - Prob. 31PQCh. 35 - Prob. 32PQCh. 35 - A single slit is illuminated by light consisting...Ch. 35 - Prob. 34PQCh. 35 - Prob. 35PQCh. 35 - Prob. 36PQCh. 35 - Prob. 37PQCh. 35 - Prob. 38PQCh. 35 - Prob. 39PQCh. 35 - Prob. 40PQCh. 35 - Prob. 41PQCh. 35 - Prob. 42PQCh. 35 - Prob. 43PQCh. 35 - Prob. 44PQCh. 35 - Prob. 45PQCh. 35 - Prob. 46PQCh. 35 - Prob. 47PQCh. 35 - Prob. 48PQCh. 35 - Figure P35.49 shows the intensity of the...Ch. 35 - Prob. 50PQCh. 35 - Prob. 51PQCh. 35 - Prob. 52PQCh. 35 - Light of wavelength 750.0 nm passes through a...Ch. 35 - Prob. 54PQCh. 35 - Prob. 55PQCh. 35 - Prob. 56PQCh. 35 - Light of wavelength 515 nm is incident on two...Ch. 35 - Light of wavelength 515 nm is incident on two...Ch. 35 - A Two slits are separated by distance d and each...Ch. 35 - Prob. 60PQCh. 35 - Prob. 61PQCh. 35 - If you spray paint through two slits, what pattern...Ch. 35 - Prob. 63PQCh. 35 - Prob. 64PQCh. 35 - Prob. 65PQCh. 35 - Prob. 66PQCh. 35 - Prob. 67PQCh. 35 - Prob. 68PQCh. 35 - Prob. 69PQCh. 35 - Prob. 70PQCh. 35 - Prob. 71PQCh. 35 - Prob. 72PQCh. 35 - Prob. 73PQCh. 35 - Prob. 74PQCh. 35 - Prob. 75PQCh. 35 - Prob. 76PQCh. 35 - Prob. 77PQCh. 35 - Another way to construct a double-slit experiment...Ch. 35 - Prob. 79PQCh. 35 - Prob. 80PQCh. 35 - Table P35.80 presents data gathered by students...Ch. 35 - Prob. 82PQCh. 35 - Prob. 83PQCh. 35 - Prob. 84PQCh. 35 - Prob. 85PQCh. 35 - Prob. 86PQCh. 35 - Prob. 87PQCh. 35 - Prob. 88PQCh. 35 - A One of the slits in a Youngs double-slit...Ch. 35 - Prob. 90PQ
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- Ex. 6: In Young's experiment, the wavelength of monochromatic light used is 6000 A. U. The optical path difference between the rays from the two coherent sources at point P on the screen is 0.0075 mm and at a point Q on the screen is 0.0015 mm. How many bright and dark bands are observed between the two points P and Q? (points P and Q are on the opposite sides of central bright band).arrow_forwardMichelson's interferometer played an important role in improving our understanding of light, and it has many practical uses today. For example, it may be used to measure distances precisely. Suppose the mirror labeled 1 in the figure below is movable. If the laser light has a wavelength of 654.0 nm, how many fringes will pass across the detector if mirror 1 is moved just 1.960 (mm)? If you can easily detect the passage of just one fringe, how accurately can you measure the displacement of the mirror(nm)?arrow_forwardHW1 : If an X - ray diffraction pattern for a powder sample of Cr ( crystal system : body - centered cubic and lattice parameter a = 0.2000 nm) is measured using a conventional diffractometer , we will obtain six diffraction peaks corresponding to (110),( 200),(211),(220), ( 310), and ( 222) planes . Compute the Lorentz - polarization factor using Cu - K, radiation Lamda = 1.545 nm . Hint : make a table for indexing pattern analysis . e 5:44 /arrow_forward
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