A Jamin interferometer is a device for measuring or for comparing the indices of refraction of gases. A beamof monochromatic light is split into two parts, each of which is directed along the axis of a separate cylindricaltube before being recombined into a single beam that is viewed through a telescope. Suppose we are given thefollowing,•Length of each tube is L = 0.4 m.• λ= 598 nm.Both tubes are initially evacuated, and constructive interference is observed in the center of the field of view. Asair is slowly let into one of the tubes, the central field of view changes dark and back to bright a total of 198times.(a) What is the index of refraction for air?(b) If the fringes can be counted to ±0.25 fringe, where one fringe is equivalent to one complete cycle ofintensity variation at the center of the field of view, to what accuracy can the index of refraction of air bedetermined by this experiment?

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Answered: A Jamin interferometer is a device for…

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 58P: A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The...

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How far apart must two objects be on the moon to be distinguishable by eye if only the diffraction effects of the eye’s pupil limit the resolution? Assume 550 nm for the wavelength of light, the pupil diameter 5.0 mm, and 400,000 km for the distance to the moon.
While using a Michelson interferometer (shown in Fig. 37.13), you see a dark circle at the center of the interference pattern, (i) As you gradually move the light source toward the central mirror M0, through a distance /2, what do you see? (a) There is no change in the pattern, (b) The dark circle changes into a bright circle. (c) The dark circle changes into a bright circle and then back into a dark circle. (d) The dark circle changes into a bright circle, then into a dark circle, and then into a bright circle. (ii) As you gradually move the moving mirror toward the central mirror M0, through a distance /2, what tit) you see? Choose from the same possibilities.
When dots are placed on a page from a laser printer, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh’s criterion. Take the pupil of the eye to be 3.0 mm and the distance from the paper to the eye of 35 cm; find the minimum separation of two dots such that they cannot be resolved. How many dots per inch (dpi) does this correspond to?
Suppose you are looking down at a highway from a jetliner flying at an altitude of 6.0 km. How far apart must two cars be if you are able to distinguish them? Assume that =550 nm and that the diameter of your pupils is 4.0 mm.
Check Your Understanding What is the angular resolution of the Arecibo telescope shown in Figure 4.20 when operated at 21-cm wavelength? How does it compare to the resolution of the Hubble Telescope? Figure 4.20 A 305-m-diameter paraboloid at Arecibo in Puerto Rico is lined with reflective material, making it into a radio telescope. It is the largest curved focusing dish in the world. Although D for Arecibo is much larger than for the Hubble Telescope, it detects radiation of a much longer wavelength and its diffraction limit is significantly poorer than Hubble’s. The Arecibo telescope is still very useful, because important information is carried by radio waves that is not carried by visible light. (credit: Jeff Hitchcock)
The limit to the eye’s acuity is actually related to diffraction by the pupil. (a) What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm? (b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.30 m apart? (c) What is the distance between two just-resolvable points held at an arm’s length (0.800 m) from your eye? (d) How does your answer to (c) compare to details you normally observe in everyday circumstances?
Check Your Understanding Suppose the slit width in Example 4.1 is increased to 1.8106 m. What are the new angular positions for the first, second, and third minima? Would a fourth minimum exist?
What is the distance moved by the traveling mirror of a Michelson interferometer that corresponds to 1500 fringes passing by a point of the observation screen? Assume that the interferometer is illuminated with a 606 nm spectral line of krypton-86.
A light ray of wavelength 461.9 nm emerges from a 2-mm circular aperture of a krypton ion laser. Due to diffraction, the beam expands as it moves out. How large is the central bright spot at (a) 1 m, (b) 1 km, (c) 1000 km, and (d) at the surface of the moon at a distance of 400,000 km from Earth.
Check Your Understanding in Example 1.6, we had n1n2. If n2were decreased such thatn1n2and the speed of light in medium 2 is faster than in medium 1, what would happen to the length of AA’ ? What would happen to the wave front A’B and the direction of the refracted ray?
An experimenter detects 251 fringes when the movable mirror in a Michelson interferometer is displaced. The light source used is a sodium lamp, wavelength 589 nm. By what distance did the movable mirror move?
The thickness of an aluminum foil is measured using a Michelson interferometer that has its movable mirror mounted on a micrometer. There is a difference of 27 fringes in the observed interference pattern when the micrometer clamps down on the foil compared to when the micrometer is empty. Calculate the thickness of the foil?

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