Concept explainers
The Very Large Array (VLA) is a set of 27 radio telescope dishes in Catron and Socorro counties, New Mexico (Fig. P37.37). The antennas can be moved apart on railroad tracks, and their combined signals give the resolving power of a synthetic aperture 36.0 km in diameter. (a) If the detectors are tuned to a frequency of 1.40 GHz, what is the angular resolution of the VLA? (b) Clouds of interstellar hydrogen
Figure P37.37
(a)
Answer to Problem 38.59AP
Explanation of Solution
Given info: The diameter of the aperture is
The formula to calculate the angular resolution is,
Here,
First calculate
Here,
Substitute
Thus, the wavelength is
From equation (3), substitute
Convert
Conclusion:
Therefore, the angular resolution is
(b)
Answer to Problem 38.59AP
Explanation of Solution
Given info: The distance between the clouds is
The formula to calculate the minimum separation between the clouds so that they can be well resolved is,
Here,
Substitute
Conclusion:
Therefore, the minimum separation between the two clouds required to have resolved image is
(c)
Answer to Problem 38.59AP
Explanation of Solution
Given info: The wavelength of the light to which hawk’s eye is sensitive is green light. The wavelength of the green light is
From equation (1) the formula to calculate the angular resolution is,
Here,
Substitute
Convert
Conclusion:
Therefore, angular resolution of the hawk’s eyes is
(d)
Answer to Problem 38.59AP
Explanation of Solution
Given info: The distance between the hawk and the mouse is
The formula to calculate the minimum separation between the mouse whiskers so that they can be well resolved is,
Here,
Substitute
Conclusion:
Therefore, the minimum separation between the two mouse whiskers so that hawk cans e them is
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Chapter 38 Solutions
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