INTRODUCTORY PHYSICS HUNTER COLLEGE LABORATORY EXERCISE #9 Interference and Diffraction Objective: To understand the destructive interference for the phenoma of diffraction when plane waves of light illuminate a single narrow slit. To show this, calculate the minimum angular spreading of a flashlight beam that is originally 5.00 cm in diameter with an average wavelength of 600 nm. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.800 m wide and the speed of sound is 340 m/s? Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. 4. Ocean waves of 20.0-m wavelength approach the opening straight on. Two lamps producing light of wavelength 589 nm are fixed 1.0 m apart on a wooden plank. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 101. 52. A water break at the entrance to a harbor consists of a rock barrier with a 50.0-m-wide opening. 113. −θ r d +- +-θ r m =5 m =-5 θ i=0 90 Figure 3: Grating geometry for problem 1. where m is the di↵raction order, is the wavelength, d is the groove (slit) spacing, i is the incident angle, and r is the di↵racted angle. As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change? The angular width of the central peak is found to be \(\displaystyle 25°\). If diffraction occurs for any finite aperture, we must revisit our ideas about multiple-slit interference. Determine (a) the spacing between the reflecting planes, and (b) the unknown wavelength. A grating with 4000 lines per centimeter is used to diffract light that contains all wavelengths between 400 and 650 nm. For Exercise 3. blue red Figure 25.29: An interference pattern set up in a room by two speakers broadcasting identical single-frequency waves. Why can lenses, mirrors, or apertures not be used to correct the spreading? Chapter 25 – Interference and Diffraction Page 25 - 19 Figure 25.28: The graph shows sinθ as a function of wavelength for different orders of light shining on a diffraction grating. Experiment with diffraction through elliptical, rectangular, or irregular apertures. The characters of a stadium scoreboard are formed with closely spaced lightbulbs that radiate primarily yellow light. 67. 90. (b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the moon, assuming a lunar distance of \(\displaystyle 3.84×10^8m\). 124. The number of regions of destructive interference in an interference pattern depends on the wavelength of the waves and. The 305-m-diameter Arecibo radio telescope pictured in Figure 4.20 detects radio waves with a 4.00-cm average wavelength. Put up a barrier to explore single-slit diffraction and double-slit interference. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. 102. Have questions or comments? (b) Where is the first minimum for 700-nm red light? (a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam? What is the minimum diameter of the objective lens in a telescope that must be used to resolve columns of troops marching 2.0 m apart? 51. 91. (Hint: The distance between adjacent fringes is \(\displaystyle Δy=xλ/d\), assuming the slit separation d is comparable to \(\displaystyle λ\).). (a) What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm? The equation is useful for calcu Is higher resolution obtained in a microscope with red or blue light? For a double-slit configuration where the slit separation is four times the slit width, how many interference fringes lie in the central peak of the diffraction pattern? The width of the central peak in a single-slit diffraction pattern is 5.0 mm. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? Find the ratio of the width of the slits to the separation between them, if the first minimum of the single-slit pattern falls on the fifth maximum of the double-slit pattern. \[x=\frac{1.22λf_0}{D},\]. Textbook Authors: Walker, James S. , ISBN-10: 0-32190-308-0, ISBN-13: 978-0-32190-308-2, Publisher: Pearson It's generally guided by Huygen's Principle, which states: every point on a wave front acts as a source of tiny wavelets that move forward with the same speed as the wave; the wave front at a later instant is the surface that is tangent to the wavelets. The interference fringes produced by the double-slit experiment can be detected, by moving a detector across the fringes. 123. (a) Where are the first minima of the diffraction pattern? The light wavelength is 500 nm and the slit width is 0.16 mm. (a) Show that a 30,000 line per centimeter grating will not produce a maximum for visible light. What image will one see if a hologram is recorded using monochromatic light but its image is viewed in white light? A diffraction grating has 2000 lines per centimeter. A monochromatic light of wavelength 589 nm incident on a double slit with slit width \(\displaystyle 2.5μm\) and unknown separation results in a diffraction pattern containing nine interference peaks inside the central maximum. 39. For Exercise 4. If a microscope can accept light from objects at angles as large as \(\displaystyle α=70°\), what is the smallest structure that can be resolved when illuminated with light of wavelength 500 nm and. Find the intensity in terms of \(\displaystyle I_o\) at \(\displaystyle θ=0.5°\), \(\displaystyle 1.0°, 1.5°, 3.0°,\) and \(\displaystyle 10.0°\). 77. 59. 38. A diffraction grating produces a second maximum that is 89.7 cm from the central maximum on a screen 2.0 m away. A converging lens of focal length 20 cm is placed behind the slit and focuses the diffraction pattern on a screen. How many interference fringes lie in the central peak of the diffraction pattern? What is the ratio of the slit separation to the slit width? 29. Diffraction spreading for a flashlight is insignificant compared with other limitations in its optics, such as spherical aberrations in its mirror. How can you tell that a hologram is a true three-dimensional image and that those in three-dimensional movies are not? (b) Repeat this calculation for a musical note of frequency 440 Hz (A above middle C). 74. 24. 17. Objects viewed through a microscope are placed very close to the focal point of the objective lens. Note that 90 degrees is the angle 116. (b) The maxima of two other first-order lines are found at \(\displaystyle θ_1=0.097\)rad and \(\displaystyle θ_2=0.132\)rad. To explore the phenomena of intereference as observed in Young's double-slit, For Fall 2020 distance learning, the Wave Interference simulation is from the PhET, Interference: Young's double-slit experiment. (a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width \(\displaystyle 20.0μm\). 121. What did Thomas Young discover in 1801? A He-Ne laser beam is reflected from the surface of a CD onto a wall. 18. 17. (b) At what angle will the second minimum be? A microwave of an unknown wavelength is incident on a single slit of width 6 cm. Additionally, when illuminated with a different, this time of known wavelength 0.137 nm, a second-order maximum is detected at \(\displaystyle 37.3°\). What are the reasons for this? Diffraction is a phenomenon which envolves the bending of waves around obstacles. What is the second-order angle? Show that a diffraction grating cannot produce a second-order maximum for a given wavelength of light unless the first-order maximum is at an angle less than \(\displaystyle 30.0°\). About This Quiz & Worksheet. When a monochromatic light of wavelength 430 nm incident on a double slit of slit separation \(\displaystyle 5μm\), there are 11 interference fringes in its central maximum. Thomas Young's double-slit experiment is the first evidence for the wave nature of light. This preview shows page 1 - 3 out of 8 pages. (This will greatly reduce the intensity of the fifth maximum.) (b) Find the wavelength of light that has its first minimum at \(\displaystyle 62.0°\). Discuss the practicality of the device in terms of being able to discern between wavelengths of interest. The grating provided in your optics kit has 600 lines (slits)/mm. 3 Ewald sphere construction. The pattern is actually a combination of single- and double-slit interference. On a bright clear day, you are at the top of a mountain and looking at a city 12 km away. diffraction_fente_simple2.swf: File Size: 19 kb: File Type: swf: Télécharger le fichier. Assume that the pupil of the observer’s eye has a diameter of 5.0 mm. Exercise Discussion for DC Pandey Optics and Modern Physics Solutions Chapter 28: Interference and Diffraction of Light There is only one Introductory Exercise in this chapter that comprises 8 questions in which you will be required to calculate the fringe width, maxima and minima of the intensities, etc. 11. At what angle does a diffraction grating produce a second-order maximum for light having a first-order maximum at \(\displaystyle 20.0°\)? 65. (a) Assume that the maxima are halfway between the minima of a single-slit diffraction pattern. Consider plane waves of light of a single wavelength falling on a double slits, s, as shown, in Figure 1. 62. 112. A monochromatic light of wavelength 450 nm is incident on the double-slit. Propulsé par Créez votre propre site Web unique avec des modèles personnalisables. If you and a friend are on opposite sides of a hill, you can communicate with walkie-talkies but not with flashlights. Microwaves of wavelength 10.0 mm fall normally on a metal plate that contains a slit 25 mm wide. (a) What is the wavelength corresponding to this frequency? How far would you place a screen from the slit of the previous problem so that the second minimum is a distance of 2.5 mm from the center of the diffraction pattern?   Terms. Louisa Meshi; 2 Formation of electron diffraction and HRTEM image . What if it is viewed using light of exactly half the original wavelength? There are two tall towers 20.0 m apart in the city. A screen of dimensions \(\displaystyle 2.0m×2.0m\) is 1.2 m away from the slit. What is the spacing between structures in a feather that acts as a reflection grating, giving that they produce a first-order maximum for 525-nm light at a \(\displaystyle 30.0°\) angle? (c) What is the greatest number of line per centimeter a diffraction grating can have and produce a complete second-order spectrum for visible light? A monochromatic light of unknown wavelength is incident on a slit of width \(\displaystyle 20μm\). 32. X-rays of wavelength 0.103 nm reflects off a crystal and a second-order maximum is recorded at a Bragg angle of \(\displaystyle 25.5°\). 12. 71. where \(\displaystyle f_0\) is the focal length and D is the diameter of the objective lens as shown below. A spy satellite is reputed to be able to resolve objects 10. cm apart while operating 197 km above the surface of Earth. 117. The total path length OYX is B c D E 414 mm 421 mm 442 mm 456 mm 463 mm. (a) What is the angle between two just-resolvable point sources for this telescope? 35. Calcite crystals contain scattering planes separated by 0.30 nm. If the grating has 600 lines per centimeter, what is the wavelength of the light that produces the diffraction pattern? 119. For an N-slit diffraction grating, the distance from a maxima to a minima at order p is given by ... Browse other questions tagged homework-and-exercises optics double-slit-experiment interference diffraction or ask your own question. (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)? 6. 16. Determine the angular width of the central peak. Interference and Diffraction 141 Diffraction Grating (Day 2) The logical end to the progression of slits you have been studying is a diffraction grating consisting of a large number of equal-width slits spaced close together at regular intervals. Find the ratio of the width of the slits to the separation between them, if the first minimum of the single slit pattern falls on the fifth maximum of the double slit pattern. 98. Because radio waves have much longer wavelengths than visible light, the diameter of a radio telescope must be very large to provide good resolution.