Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 36, Problem 47CP
To determine
The minimum thickness for the constructive interference of sodium light.
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White light is incident normally on a glass lens (n=1.52) that is coated with a film of MgF2 (n=1.38). For what minimum thickness of the film will the reflections at the two interfaces result in total destructive interference of yellow light of wavelength 580 nm (in air)?
White light is incident normally on a glass lens (n=1.52) that is coated with a film of MgF2(n=1.38). For what minimum thickness of the film will the reflections at the two interfacesresult in total destructive interference of yellow light of wavelength 580 nm (in air)?
Our 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.
Chapter 36 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 36.2 - Which of the following causes the fringes in a...Ch. 36.3 - Using Figure 36.6 as a model, sketch the...Ch. 36.5 - One microscope slide is placed on top of another...Ch. 36 - Two slits are separated by 0.320 mm. A beam of...Ch. 36 - Prob. 2PCh. 36 - A laser beam is incident on two slits with a...Ch. 36 - Prob. 4PCh. 36 - Prob. 5PCh. 36 - Light with wavelength 442 nm passes through a...Ch. 36 - Prob. 7P
Ch. 36 - A student holds a laser that emits light of...Ch. 36 - Coherent light rays of wavelength strike a pair...Ch. 36 - In Figure P36.10 (not to scale), let L = 1.20 m...Ch. 36 - Prob. 11PCh. 36 - Prob. 12PCh. 36 - In the double-slit arrangement of Figure P36.13, d...Ch. 36 - Monochromatic light of wavelength is incident on...Ch. 36 - Prob. 15PCh. 36 - Show that the distribution of intensity in a...Ch. 36 - Prob. 17PCh. 36 - Monochromatic coherent light of amplitude E0 and...Ch. 36 - Prob. 19PCh. 36 - Prob. 20PCh. 36 - Prob. 21PCh. 36 - Prob. 22PCh. 36 - When a liquid is introduced into the air space...Ch. 36 - Prob. 24PCh. 36 - Prob. 25PCh. 36 - Prob. 26PCh. 36 - Prob. 27PCh. 36 - Prob. 28APCh. 36 - Prob. 29APCh. 36 - Prob. 30APCh. 36 - Prob. 31APCh. 36 - Prob. 32APCh. 36 - In a Youngs double-slit experiment using light of...Ch. 36 - Prob. 34APCh. 36 - Figure P36.35 shows a radio-wave transmitter and a...Ch. 36 - Prob. 36APCh. 36 - In a Newtons-rings experiment, a plano-convex...Ch. 36 - Prob. 38APCh. 36 - A plano-concave lens having index of refraction...Ch. 36 - Prob. 40APCh. 36 - Interference fringes are produced using Lloyds...Ch. 36 - A plano-convex lens has index of refraction n. The...Ch. 36 - Prob. 43APCh. 36 - Prob. 44APCh. 36 - Prob. 45APCh. 36 - Prob. 46CPCh. 36 - Prob. 47CPCh. 36 - Prob. 48CPCh. 36 - Prob. 49CPCh. 36 - Prob. 50CP
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- Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at λ2 and an intensity maximum is observed at λ1, where λ1 > λ2. (a) Assuming no intensity minima are observed between λ1 and λ2, find an expression for the integer m in Equations 27.13 and 27.14 in terms of the wavelengths λ1 and λ2. (b) Assuming n = 1.40, λ1 = 500 nm, and λ2 = 370 nm, determine the best estimate for the thickness of the film.arrow_forwardConsider a single-slit diffraction pattern for =589 nm, projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?arrow_forwardTo keep unwanted light from reflecting from the surface of eyeglasses or other lenses, a thin film of a material with an index of refraction n = 1.38 iscoated onto the plastic lens (n = 1.55). What is the thinnest film that will minimize reflection for λ = 550 nm, the middle of the visible-light spectrum?arrow_forward
- The rhinestones in costume jewelry are glass with index of refraction 1.50. To make them more reflective, they are often coated with a layer of silicon monoxide of index of refraction 2.00.What is the minimum coating thickness needed to ensure that light of wavelength 560 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference?arrow_forwardLaser light of wavelength 460 nmnm is traveling in air and shines at normal incidence onto the flat end of a transparent plastic rod that has nn = 1.30. The end of the rod has a thin coating of a transparent material that has refractive index 1.75. a)What is the minimum (nonzero) thickness of the coating for which there is maximum transmission of the light into the rod? b)What is the minimum (nonzero) thickness of the coating for which transmission into the rod is minimized?arrow_forwardConsider the perpendicular reflection of light of wavelength 520 nm in air from a soap film with refractive index 1.32 that has air on both sides. Find the thickness, in nanometers, of the thinnest soap film that will cause constructive interference for the reflected light. t =?arrow_forward
- A thin layer of liquid methylene iodide (n = 1.756) is sandwiched between two flat, parallel plates of glass (n = 1.50). What must be the thickness of the liquid layer if normally incident light with ? = 339 nm in air is to be strongly reflected?arrow_forwardIt is desired to apply an anti-reflection coating on a glass lens used in air, by coating the lens with a thin film of magnesium fluoride of refractive index nf = 1.37; (assume the glass has refractive index larger than nfd ). Write down the formula for optical path difference between waves reflected at top and bottom of the film, and use this to calculate the minimum required thickness of the coating to give a reflectance minimum for normal-incidence green light of wavelength 550 nm in air.arrow_forwardA thin film, with a thickness of 272.7 nm and with air on both sides, is illuminated with a beam of white light. The beam is perpendicular to the film and consists of the full range of wavelengths for the visible spectrum. In the light reflected by the film, light with a wavelength of 600.0 nm undergoes fully constructive interference. At what wavelength does the reflected light undergo fully destructive interference? (Hint: You must make a reasonable assumption about the index of refraction.)arrow_forward
- A thin layer of a transparent material that has an index of refraction of 1.25 is used as a nonreflective coating on the surface of glass that has an index of refraction of 1.50. What should the minimum thickness of the material be for the material to be nonreflecting for light that has a wavelength of 578 nm?arrow_forwardA piece of glass with a refractive index of n=1.5 has its top surface inclined by an angle a relative to its bottom surface, as shown. The horizontal length of the glass is L=2cm, and the thickness t of the thinner left side is not zero. The glass, which is surrounded by air, is illuminated from above with red light with a wavelength of 600nm in air. (a) What is a if there are bright constructive reflection peaks on the left edge and right edge of the piece of glass, and none in between? (b) What are the 3 smallest possible thicknesses t for the thin left side of the glass for the conditions and answer for aarrow_forwardGiven solution A&B A) What is the longest wavelength of light that will experience constructive interference when viewed from directly above if the layer of mineral oil is 120 nm thick? a) 240 nm b) 350 nm c) 480 nm d) 640 nm e) 700 nm B) If the layer of mineral oil stretches out and becomes thinner as it does so the above answer: a) increases b) decreases c) remains the samearrow_forward
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