Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 36, Problem 12PQ
To determine
The conditions for constructive and destructive interference produced by the transmitted light.
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A plane wave of monochromatic light is incident normally on a uniform thin film of oil that covers a glass plate. The wavelength of the source can be varied continuously. Fully destructive interference of the reflected light is observed for wavelengths of 500 and 700 nm and for no wavelengths in between. If the index of refraction of the oil is 1.30 and that of the glass is 1.50, find the thickness of the oil film.
A thin film suspended in air is 0.410 mm thick and is illuminated with white light incident perpendicularly on its surface. The index of refraction of the film is 1.50. At what wavelength will visible light that is reflected from the two surfaces of the film undergo fully constructive interference?
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: Foundations and Connections
Ch. 36.2 - Prob. 36.1CECh. 36.3 - Prob. 36.2CECh. 36.4 - Prob. 36.3CECh. 36.5 - Prob. 36.4CECh. 36.5 - Prob. 36.5CECh. 36 - Many circular apertures are adjustable, such as...Ch. 36 - Many of the images we regularly look at are...Ch. 36 - The hydrogen line at 1420.4 MHz corresponds to the...Ch. 36 - Prob. 4PQCh. 36 - Estimate the diffraction-limited resolution of the...
Ch. 36 - Prob. 6PQCh. 36 - Prob. 7PQCh. 36 - Prob. 8PQCh. 36 - Prob. 9PQCh. 36 - Prob. 10PQCh. 36 - Prob. 11PQCh. 36 - Prob. 12PQCh. 36 - Prob. 13PQCh. 36 - Prob. 14PQCh. 36 - Prob. 15PQCh. 36 - Prob. 16PQCh. 36 - Prob. 17PQCh. 36 - Prob. 18PQCh. 36 - Prob. 19PQCh. 36 - Prob. 20PQCh. 36 - Prob. 21PQCh. 36 - Prob. 22PQCh. 36 - Prob. 23PQCh. 36 - Prob. 24PQCh. 36 - Light of wavelength 566 nm is incident on a...Ch. 36 - Prob. 26PQCh. 36 - Prob. 27PQCh. 36 - Prob. 28PQCh. 36 - Prob. 29PQCh. 36 - Prob. 30PQCh. 36 - A light source emits a mixture of wavelengths from...Ch. 36 - Prob. 32PQCh. 36 - Prob. 33PQCh. 36 - Prob. 34PQCh. 36 - Prob. 35PQCh. 36 - Prob. 36PQCh. 36 - Prob. 37PQCh. 36 - Prob. 38PQCh. 36 - Prob. 39PQCh. 36 - Prob. 40PQCh. 36 - Prob. 41PQCh. 36 - Prob. 42PQCh. 36 - Prob. 43PQCh. 36 - Prob. 44PQCh. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - Prob. 47PQCh. 36 - Prob. 48PQCh. 36 - Problems 49 and 50 are paired. C Optical flats are...Ch. 36 - Optical flats are flat pieces of glass used to...Ch. 36 - Prob. 51PQCh. 36 - Prob. 52PQCh. 36 - Figure P36.53 shows two thin glass plates...Ch. 36 - Viewed from above, a thin film of motor oil with...Ch. 36 - Newtons rings, discovered by Isaac Newton, are an...Ch. 36 - Prob. 56PQCh. 36 - What is the radius of the beam of an argon laser...Ch. 36 - Prob. 58PQCh. 36 - A diffraction grating with 428 rulings per...Ch. 36 - How many rulings must a diffraction grating have...Ch. 36 - Prob. 61PQCh. 36 - White light is incident on a diffraction grating...Ch. 36 - X-rays incident on a crystal with planes of atoms...Ch. 36 - Prob. 64PQCh. 36 - Prob. 65PQCh. 36 - Prob. 66PQCh. 36 - The fringe width b is defined as the distance...Ch. 36 - The fringe width is defined as the distance...Ch. 36 - Prob. 69PQ
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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 l 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 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_forwardWhite light is sent downward onto a horizontal thin film that is sandwiched between two materials. The indexes of refraction are 1.80 for the top material, 1.70 for the thin film, and 1.50 for the bottom material. The film thickness is 5.00* 10-7 m. Of the visible wavelengths (400 to 700 nm) that result in fully constructive interference at an observer above the film, which is the (a) longer and (b) shorter wavelength? The materials and film are then heated so that the film thickness increases. (c) Does the light resulting in fully constructive interference shift toward longer or shorter wavelengths?arrow_forward
- A thin layer of oil with index of refraction no = 1.47 is floating above the water. The index of refraction of water is nw = 1.3. The index of refraction of air is na = 1. A light with wavelength λ = 325 nm goes in from the air to oil and water. Part (a) Express the wavelength of the light in the oil, λo, in terms of λ and no. Part (b) Express the minimum thickness of the film that will result in destructive interference, tmin, in terms of λo. Part (c) Express tmin in terms of λ and no. Part (d) Solve for the numerical value of tmin in nm.arrow_forwardA thin film of oil (n = 1.17) is located on smooth, wet pavement. When viewed from a direction perpendicular to the pavement, the film reflects most strongly red light at 640 nm and reflects no light at 512 nm. (b) Let m1 correspond to the order of the constructive interference and m2 to the order of destructive interference. Obtain a relationship between m1 and m2 that is consistent with the given data.arrow_forwardWhite light is reflected from a thin film suspended in air (e.g. a soap film) with an angle of incidence, as measured in the air, of 0. If the refractive index of the film relative to air is n, and its thickness is d, show that the condition for destructive (a) interference is: mà = 2d (n? - sin² 0)arrow_forward
- A puddle of water is covered with an oil film that has an index of refraction with an unknown value. However, it is known that the unknown value is greater than that of water. The thickness of the oil film is such that it is the minimum thickness possible for normally incident infrared radiation with a wavelength of 836 nm to experience destructive interference in the reflected radiation. When white light is incident normal to the oil film, what wavelengths in the visible range (400 nm-700 nm) will experience constructive interference?arrow_forwardWhen white light illuminates an oil film on water and the reflected light is viewed perpendicular to the surface of the water, no green light at 512 nm is reflected but there is a strong presence of red light with a wavelength of 640 nm. Determine the thickness of the oil film. Take the index of refraction of oil to be 1.28.arrow_forwardA 3.04-kHz tone is being produced by a speaker with a diameter of 0.207 m. The air temperature changes from 0 to 28 oC. Assuming air to be an ideal gas, find the change in the diffraction angle θ.arrow_forward
- One way to determine the index of refraction of a gas is to use an interferometer. As shown below, one of the beams of an interferometer passes through a glass container that has a length of L = 1.8 cm. Initially the glass container is a vacuum. When gas is slowly allowed into the container, a total of 6894 dark fringes move past the reference line. The laser has a wavelength of 635 nm (this is the wavelength when the light from the laser is moving through a vacuum). A.) Determine how many wavelengths will fit into the glass container when it is a vacuum. Since the light passes through the container twice, you need to determine how many wavelengths will fit into a glass container that has a length of 2L.number of wavelengths (vacuum) = B.) The number of dark fringes is the difference between the number of wavelengths that fit in the container (length of 2L) when it has gas and the number of wavelengths that fit in the container (length of 2L) when it is a vacuum. Use this knowledge to…arrow_forwardExpress the minimum thickness of the film, t, that results in constructive interference, in terms of n and λ. A soap bubble film with index of refraction n = 1.33 is illuminated perpendicularly with a light of wavelength λ = 350 nm.arrow_forwardWhite light, with a uniform intensity across the visible wavelength range of 400 nm to 720 nm, is perpendicularly incident on a glass film, of index of refraction ng 340 nm, , suspended in air. At what wavelength A is the light reflected by the film brightest to an = 1.52 and thickness d = observer?arrow_forward
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