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 46PQ
CASE STUDY Michelson’s interferometer played an important role in improving our understanding of light, and it has many practical uses today. For example, it may be used to measure precisely the indices of refraction of various media. Suppose an initially evacuated tube of length 6.50 cm is placed in one of the paths in Michelson’s interferometer. The tube is then filled slowly with a gas of an unknown index of refraction, and as a result 42 fringes shift. The laser light has a wavelength of 608.5 nm. You will find that the index of refraction is very close to 1. Give n – 1 to three significant figures.
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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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- CASE STUDY Michelsons interferometer played an important role in improving our understanding of light, and it has many practical uses today. For example, it may be used to measure distances precisely. Suppose the mirror labeled 1 in Figure 36.30 (page 1176) is movable. If the laser light has a wavelength of 632.5 nm, how many fringes will pass across the detector if mirror 1 is moved just 1.000 mm? If you can easily detect the passage of just one fringe, how accurately can you measure the displacement of the mirror?arrow_forwardIn Figure 38.4, assume the slit is in a barrier that is opaque to x-rays as well as to visible light. The photograph in Figure 38.4b shows the diffraction pattern produced with visible light. What will happen if the experiment is repeated with x-rays as the incoming wave and with no other changes? (a) The diffraction pattern is similar. (b) There is no noticeable diffraction pattern but rather a projected shadow of high intensity on the screen, having the same width as the slit. (c) The central maximum is much wider, and the minima occur at larger angles than with visible light. (d) No x-rays reach the screen.arrow_forwardTwo slits of width 2 m, each in an opaque material, are separated by a center-to-center distance of 6 m. A monochromatic light of wavelength 450 nm is incident on the double-slit. One finds a combined interference and diffraction pattern on the screen. (a) How many peaks of the interference will be observed in the central maximum of the diffraction pattern? (b) How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same? (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, 12 m, while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength 680 nm is used? (e) What is the value of the ratio of the intensity of the central peak to the intensity of the next bright peak in (a)? (f) Does this ratio depend on the wavelength of the light? (g) Does this ratio depend on the width or separation of the slits?arrow_forward
- Assume Figure 38.1 was photographed with red light of a single wavelength 0. The light passed through a single slit of width a and traveled distance L to the screen where the photograph was made. Consider the width of the central bright fringe, measured between the centers of the dark fringes on both sides of it. Rank from largest to smallest the widths of the central fringe in the following situations and note any cases of equality. (a) The experiment is performed as photographed. (b) The experiment is performed with light whose frequency is increased by 50%. (c) The experiment is performed with light whose wavelength is increased by 50%. (d) The experiment is performed with the original light and with a slit of width 2a. (e) The experiment is performed with the original light and slit and with distance 2L to the screen.arrow_forwardIn a Youngs double-slit experiment, a set of parallel slits with a separation of 0.100 mm is illuminated by light having a wave- length of 589 nm, and the interference pattern is observed on a screen 4.00 m from the slits, (a) What is the difference in path lengths from each of the slits to the location of a third-order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?arrow_forwardSlit 1 of a double-slit is wider than slit 2 so that the light from slit 1 has an amplitude exactly 3 times that of the light from slit 2. Show that Equation 36.9 is replaced by the following equation for this situation: I=Imax[1+3cos2(dsin)] Begin by assuming that the total magnitude of the electric field at point P on the screen in Figure 36.4 is the superposition of two waves, with electric field magnitudes E1=3E0sintE2=E0sin(t+) The phase angle in E2 is due to the extra path length traveled by the lower beam in Figure 36.4. You will need to evaluate the integral of the square of the sine function over one period. Refer to Figure 32.5 for an easy way to perform this evaluation. You might find the following trigonometric identities helpful: sinA+sinB=2sin(A+B2)cos(AB2)sin(A+B)=sinAcosB+cosAsinBcosA=2cos2(A2)1arrow_forward
- Figure 27.55 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit Width or the separation between slits? Explain your responses. Figure 27.55 This double slit interference pattern also shows signs of single slit interference. (credit: PASCO)arrow_forwardA student sets up a double-slit experiment using mono chromatic light of wavelength . The distance between the slits is equal to 25 . (a) Find the angles at which the m = 1, 2, and 3 maxima occur on the viewing screen. (b) At what angles do the first three dark fringes occur? (c) Why are the answers so evenly spaced? Is the spacing even for all orders? Explain.arrow_forwardMonochromatic light of wavelength is incident on a pair of slits separated by 2.40 104m. and forms an interference pattern on a screen placed 1.80 m away from the slits. The first-order bright fringe is 4.52 mm from the center of the central maximum. (a) Draw a picture, labeling the angle and the legs of the right triangle associated with the first-order bright fringe. (b) Compute the tangent of the angle associated with the first-order bright fringe. (c) Find the angle corresponding to the first-order bright fringe and compute the sine of that angle. Are the sine and tangent of the angle comparable in value? Does your answer always hold true? (d) Calculate the wavelength of the light. (e) Compute the angle of the fifth-order bright fringe. (f) Find its position on the screen.arrow_forward
- (a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 m. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.arrow_forwardA diffraction grating with 2000 lines per centimeter is used to measure the wavelengths emitted by a hydrogen gas discharge tube. (a) At what angles will you find the maxima of the two first-order blue lines of wavelengths 410 and 434 nm? (b) The maxima of two other first-order lines are found at 1=0.097 rad and 2=0.132 rad . What are the wavelengths of these lines?arrow_forwardAn intensity minimum is found for 450 nm light transmitted through a transparent film (n=1.20) in air. (a) What is minimum thickness of the film? (b) If this wavelength is the longest for which the intensity minimum occurs, what are the next three lower values of ? for which this happens?arrow_forward
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