6. Light is incident on a diffraction grating with 7600 lines/cm and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam consists of two wavelengths 2, = 4.4 x 107 m and 22 = 6.8 x 107 m. Calculate the linear distance between the first -order bright fringes of these two wavelengths on the screen.

6. Light is incident on a diffraction grating with 7600 lines/cm and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam consists of two wavelengths 2, = 4.4 x 107 m and 22 = 6.8 x 107 m. Calculate the linear distance between the first -order bright fringes of these two wavelengths on the screen.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter36: Applications Of The Wave Model

Section: Chapter Questions

Problem 42PQ

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Coherent light of wavelength 501.5 nm is sent through two parallel slits in an opaque material. Each slit is 0.700 m wide. Their centers are 2.80 m apart. The light then falls on a semicylindrical screen, with its axis at the midline between the slits. We would like to describe the appearance of the pattern of light visible on the screen. (a) Find the direction for each two-slit interference maximum on the screen as an angle away from the bisector of the line joining the slits. (b) How many angles are there that represent two-slit interference maxima? (c) Find the direction for each single-slit interference minimum on the screen as an angle away from the bisector of the line joining the slits. (d) How many angles are there that represent single-slit interference minima? (e) How many of the angles in part (d) are identical to those in part (a)? (f) How many bright fringes are visible on the screen? (g) If the intensity of the central fringe is Imax, what is the intensity of the last fringe visible on the screen?
(a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20.0 m. (b) What slit width would place this minimum at 85.0°? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics
(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of 20.0°? (b) At what angle will the fourth line of the Balmer series appear in first order? (c) At what angle will the second-order maximum be for the first line?
In 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?
(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.
In 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.
Unreasonable Results Red light of wavelength of 700 nm falls on a double slit separated by 400 nm. (a) At what angle is the first-order maximum in the diffraction pattern? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
You are working in an optical research laboratory. One of your projects involves the use of a double slit through which you pass orange laser light of wavelength 590 nm. Unfortunately, because of budget cuts, there are a lot of researchers in the same room, with lots of equipment stuffed in the room, and, in particular, lots of laser beams flying around the room. One day, you find that a second laser beam of unknown origin and different color is entering your double slit along with your orange beam and you are seeing an interference pattern that is the sum of those due to the two beams. You notice that the combined pattern is pretty much a mess, but wait! The m = 3 maximum of your orange laser beam pattern is pure; there is absolutely no mixture of the other color at that point. From this fact, you determine the wavelength of the offending laser light so that you can figure out which other researcher to ask to modify the aiming of his laser.
The laser in a compact disc player must precisely follow the spiral track on CD, along which the distance between one loop of the spiral and the next is only about 1.25 m. Figure P38.29 (page 1186) shows how a diffraction grating is used to provide information to keep the beam on track. The laser light passes through a diffraction grating before it reaches the CD. The strong central maximum of the diffraction pattern is used to read the information in the track of pits. The two first-order side maxima are designed to fall on the flat surfaces on both sides of the information track and are used for steering. As long as both beams are reflecting from smooth, nonpitted .surfaces, they are detected with constant high intensity. If the main beam wanders off the track, however, one of the side beams begins to strike pits on the information track and the reflected light diminishes. This change is used with an electronic circuit to guide the beam back to the desired location. Assume the laser light has a wavelength of 780 11m and the diffraction grating is positioned 6.90 m from tike disk. Assume the first-order beams are to fall on the CD 0.400 m on either side of the information track. What should be the number of grooves per millimeter in the grating?
Suppose Youngs double-slit experiment is performed in air using red light and then the apparatus is immersed in water. What happens to the interference pattern on the screen? (a) It disappears. (b) The bright and dark fringes stay in the same locations, but the contrast is reduced. (c) The bright fringes are closer together. (d) The bright fringes are farther apart. (e) No change happens in the interference pattern.
Monochromatic coherent light of amplitude E0 and angular frequency passes through three parallel slits, each separated by a distance d from its neighbor. (a) Show that the time-averaged intensity as a function of the angle is I()=Imax[1+2cos(2dsin)]2 (b) Explain how this expression describes both the primary and the secondary maxima. (c) Determine the ratio of the intensities of the primary and secondary maxima. Hint: See Problem 16.
From Equation 37.2, find an expression for the sine of the angles at which the minimum intensity occurs in a single-slit diffraction pattern. Compare the result to Equation 37.1.