Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 27, Problem 58P
To determine
Obtain the condition for constructive interference in the given situation.
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In your research lab, a very thin, flat piece of glass with refractive index 1.40 and uniform thickness covers the opening of a chamber that holds a gas sample. The refractive indexes of the gases on either side of the glass are very close to unity. To determine the thickness of the glass, you shine coherent light of wavelength l0 in vacuum at normal incidence onto the surface of the glass. When l0 = 496 nm, constructive interference occurs for light that is reflected at the two surfaces of the glass. You find that the next shorter wavelength in vacuum for which there is constructive interference is 386 nm. (a) Use these measurements to calculate the thickness of the glass. (b) What is the longest wavelength in vacuum for which there is constructive interference for the reflected light?
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Chapter 27 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 27.3 - Which of the following causes the fringes in a...Ch. 27.5 - In a laboratory accident, you spill two liquids...Ch. 27.5 - Prob. 27.3QQCh. 27.6 - Prob. 27.4QQCh. 27.7 - Suppose you are observing a binary star with a...Ch. 27.8 - Ultraviolet light of wavelength 350 nm is incident...Ch. 27 - Consider a wave passing through a single slit....Ch. 27 - Prob. 2OQCh. 27 - Suppose Youngs double-slit experiment is performed...Ch. 27 - Prob. 4OQ
Ch. 27 - Prob. 5OQCh. 27 - Prob. 6OQCh. 27 - A monochromatic beam of light of wavelength 500 nm...Ch. 27 - A film of oil on a puddle in a parking lot shows a...Ch. 27 - Prob. 9OQCh. 27 - A Fraunhofer diffraction pattern is produced on a...Ch. 27 - Prob. 11OQCh. 27 - Prob. 12OQCh. 27 - Why is it advantageous to use a large-diameter...Ch. 27 - Prob. 1CQCh. 27 - Prob. 2CQCh. 27 - Prob. 3CQCh. 27 - Prob. 4CQCh. 27 - Why is the lens on a good-quality camera coated...Ch. 27 - Prob. 6CQCh. 27 - Prob. 7CQCh. 27 - Prob. 8CQCh. 27 - A laser beam is incident at a shallow angle on a...Ch. 27 - Prob. 10CQCh. 27 - Prob. 11CQCh. 27 - Prob. 12CQCh. 27 - John William Strutt, Lord Rayleigh (1842–1919),...Ch. 27 - Prob. 1PCh. 27 - Youngs double-slit experiment underlies the...Ch. 27 - Two radio antennas separated by d = 300 m as shown...Ch. 27 - Prob. 4PCh. 27 - Prob. 5PCh. 27 - Prob. 6PCh. 27 - In Figure P27.7 (not to scale), let L = 1.20 m and...Ch. 27 - Prob. 8PCh. 27 - Prob. 9PCh. 27 - Prob. 10PCh. 27 - Two slits are separated by 0.180 mm. An...Ch. 27 - Prob. 12PCh. 27 - A pair of narrow, parallel slits separated by...Ch. 27 - Coherent light rays of wavelength strike a pair...Ch. 27 - Prob. 15PCh. 27 - Prob. 16PCh. 27 - A riverside warehouse has several small doors...Ch. 27 - Prob. 18PCh. 27 - Prob. 19PCh. 27 - Astronomers observe the chromosphere of the Sun...Ch. 27 - Prob. 21PCh. 27 - Prob. 22PCh. 27 - A beam of 580-nm light passes through two closely...Ch. 27 - Prob. 24PCh. 27 - An air wedge is formed between two glass plates...Ch. 27 - Prob. 26PCh. 27 - Prob. 27PCh. 27 - Prob. 28PCh. 27 - Prob. 29PCh. 27 - Prob. 30PCh. 27 - Prob. 31PCh. 27 - Prob. 32PCh. 27 - A beam of monochromatic green light is diffracted...Ch. 27 - Prob. 34PCh. 27 - Prob. 35PCh. 27 - Prob. 36PCh. 27 - Prob. 37PCh. 27 - Prob. 38PCh. 27 - Prob. 39PCh. 27 - White light is spread out into its spectral...Ch. 27 - Prob. 41PCh. 27 - Prob. 42PCh. 27 - Prob. 43PCh. 27 - Prob. 44PCh. 27 - Prob. 45PCh. 27 - Prob. 46PCh. 27 - Prob. 47PCh. 27 - Prob. 48PCh. 27 - Prob. 49PCh. 27 - Prob. 50PCh. 27 - Prob. 51PCh. 27 - A wide beam of laser light with a wavelength of...Ch. 27 - Prob. 53PCh. 27 - Prob. 54PCh. 27 - Prob. 55PCh. 27 - Prob. 56PCh. 27 - Prob. 57PCh. 27 - Prob. 58PCh. 27 - Prob. 59PCh. 27 - Prob. 60PCh. 27 - Prob. 61PCh. 27 - Prob. 62PCh. 27 - Both sides of a uniform film that has index of...Ch. 27 - Prob. 64PCh. 27 - Light of wavelength 500 nm is incident normally on...Ch. 27 - Prob. 66PCh. 27 - A beam of bright red light of wavelength 654 nm...Ch. 27 - Iridescent peacock feathers are shown in Figure...Ch. 27 - Prob. 69PCh. 27 - Prob. 70PCh. 27 - Figure CQ27.4 shows an unbroken soap film in a...
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- Two identical horizontal sheets of glass have a thin film of air of thickness t between them. The glass has refractive index 1.40. The thickness t of the air layer can be varied. Light with wavelength l in air is at normal incidence onto the top of the air film. There is constructive interference between the light reflected at the top and bottom surfaces of the air film when its thickness is 650 nm. For the same wavelength of light the next larger thickness for which there is constructive interference is 910 nm. (a) What is the wavelength λ of the light when it is traveling in air? (b) What is the smallest thickness t of the air film for which there is constructive interference for this wavelength of light?arrow_forwardA thin film of glass (n 1.52) of thickness 0.420 um is viewed under white light at near normal incidence. What wavelength of visible light is most strongly reflected by the film when sur- rounded by air?arrow_forwardA flat piece of glass is held stationary and horizontal above the highly polished, flat top end of a 12.0-cm-long vertical metal rod that has its lower end rigidly fixed. The thin film of air between the rod and glass is observed to be bright by reflected light when it is illuminated by light of wavelength 490 nm. As the temperature is slowly increased by 21.5°C, the film changes from bright to dark and back to bright 200 times. What is the coefficient of linear expansion of the metal? °C-1arrow_forward
- Problem 8 :We wish to coat a flat slab of glass (n 1.5) with a %3D transparent material (n-1.25) so that light of wavelength 620nm (in vacuum) incident normally is not reflected. What should be the minimum thickness of the coating? Air=1 Film= Glass=1.5 1.25 a 111arrow_forwardA thin film of a liquid floats on ( therefore it is less dense) on a surface of water with n= 1.33. A maximum reflection occurs at a wavelength in air of 410.0 nm. You are able to determine the thickness of the film to be 97.0 nm. What is the index of refraction of the unknown liquid? Consider n to be 1.00 for air.arrow_forwardOur discussion of the techniques for determining constructive and destructive interference by reflection from a thin film in air has been confined to rays striking the film at nearly normal incidence. What If? Assume a ray is incidentat an angle of 30.0° (relative to the normal) on a film with index of refraction 1.38 surrounded by vacuum. Calculate the minimum thickness for constructive interference of sodium light with a wavelength of 590 nm.arrow_forward
- A bubble is formed by a soap film with index of refraction n=1.3 and a thickness of 325nm. When illuminated by white light and viewed directly (perpendicular to the surface), what wavelength in the visible spectrum (375nm to 725nm) will be strongly reflected?arrow_forwardTwo flat plates of glass with parallel faces are on a table, one plate on the other. Each plate is 11.0 cm long and has a refractive index of 1.55. A very thin sheet of metal foil is inserted under the end of the upper plate to raise it slightly at that end. When you view the glass plates from above with reflected white light, you observe that, at 1.15 mm from the line where the sheets are in contact, the violet light of wavelength 400.0 nm is enhanced in this reflected light, but no visible light is enhanced closer to the line of contact. (a) How far from the line of contact will green light (of wavelength 550.0 nm) and orange light (of wavelength 600.0 nm) first be enhanced? (b) How far from the line of contact will the violet, green, and orange light again be enhanced in the reflected light? (c) How thick is the metal foil holding the ends of the plates apart?arrow_forwardWhite light reflects at normal incidence from the top and bottom surfaces of a glass plate 1n = 1.522. There is air above and below the plate. Constructive interference is observed for light whose wavelength in air is 477.0 nm. What is the thickness of the plate if the next longer wavelength for which there is constructive interference is 540.6 nm?arrow_forward
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