Concept explainers
(a)
The limiting resolution of the microscope.
(a)
Answer to Problem 7PQ
The limiting resolution of the microscope is
Explanation of Solution
Write the expression for the limit of resolution of the optical system.
Here,
Conclusion:
Substitute
Therefore, the limiting resolution of the microscope is
(b)
The wavelength that will produce the smallest angle of resolution.
(b)
Answer to Problem 7PQ
The smallest angle of resolution is produced by violet light of
Explanation of Solution
The range of the visible light is from red
From the equation (I), the angle of resolution is proportional to the
Conclusion:
Therefore, the smallest angle of resolution is produced by violet light of
(c)
The angular resolution of the microscope.
(c)
Answer to Problem 7PQ
The angular resolution of the microscope is
Explanation of Solution
Conclusion:
Substitute
Therefore, the angular resolution of the microscope is
(d)
The angular resolution of the microscope if the microscope is inserted in water.
(d)
Answer to Problem 7PQ
The angular resolution of the microscope is
Explanation of Solution
Conclusion:
Substitute
Therefore, the angular resolution of the microscope is
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Chapter 36 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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- A parallel X-ray beam is diffracted by sodium chloride. Strong first-order is obtained when the Bragg angle (the angle between the crystal planes and the emerging beam) is 6º 50’. The distance between the planes that are in the reflection position in the crystal is 2,8 Å. 1 angstron = 1 Å = 0,1 nm. a) What is the wavelength of X-rays?arrow_forwardThe Very Large Array (VLA) is a set of 27 radio telescope dishes in Catron and Socorro counties, New Mexico (as shown). The antennas can be moved apart on railroad tracks, and their combined signals give the resolvingpower 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 radiate at the frequency used in part (a). What must be the separation distance of two clouds at the center of the galaxy, 26 000 light-years away, if they are to be resolved? (c) What If? As the telescope looks up, a circling hawk looks down. Assume the hawk is most sensitive to green light having a wavelength of 500 nm and has apupil of diameter 12.0 mm. Find the angular resolution of the hawk’s eye. (d) A mouse is on the ground 30.0 m below. By what distance must the mouse’s whiskers be separated if the hawk can resolve them?arrow_forwardRecall from class that the resolution is limited due to the nature of light. More specifically, since light diffracts as it goes through a small opening, it becomes difficult to differentiate two light sources when the diffraction central peak from one source overlaps with the first minimum of the second source, as shown in the figure below. (a) The pupil of the human eye has an aperture of around 5mm, and visible light has wavelengths peaked around 500nm. Estimate the angular resolution of the human eye (that is, the smallest angle for which you could distinguish that light was coming from two different directions). (b) Suppose two point sources of light were separated by a distance x, and you are standing one meter away from them. Estimate the smallest distance x for which you could tell that there were two point sources (rather than just one).arrow_forward
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