A spy satellite orbits Earth at a height of 180 km. What is the maximum distance an observer can be and still resolve the lamps as two separate sources of light, if the resolution is affected solely by the diffraction of light entering the eye? Click here to let us know! Determine the intensities of three interference peaks other than the central peak in the central maximum of the diffraction, if possible, when a light of wavelength 500 nm is incident normally on a double slit of width 1000 nm and separation 1500 nm. 70. The grating provided in your optics kit has 600 lines (slits)/mm. At what angle does it produces its second minimum? (b) What is unreasonable about this result? 59. 68. 67. 44. 4. 96. For this case, what is the ratio of the slit width to the wavelength of the light? A rectangular slit is twice as wide as it is high. An opal such as that shown in Figure 4.15 acts like a reflection grating with rows separated by about \(\displaystyle 8μm.\) If the opal is illuminated normally, (a) at what angle will red light be seen and. Louisa Meshi; 2 Formation of electron diffraction and HRTEM image . To understand how to determine the intensity of the light associated with double slit interference How far apart must two objects be on the moon to be resolvable by the 8.1-m-diameter Gemini North telescope at Mauna Kea, Hawaii, if only the diffraction effects of the telescope aperture limit the resolution? Suppose you are looking down at a highway from a jetliner flying at an altitude of 6.0 km. (b) What is the highest-order minimum produced? This document is highly rated by NEET students and has been viewed 440 times. 118. A water break at the entrance to a harbor consists of a rock barrier with a 50.0-m-wide opening. (b) Take your result to be the practical limit for the eye. (b) Plot \(\displaystyle y=tanβ\) and \(\displaystyle y=β\) versus \(\displaystyle β\) and find the intersections of these two curves. If the wall is 1.50 m from the CD, and the first fringe is 0.600 m from the central maximum, what is the spacing of grooves on the CD? (This might be done to hit a corner reflector to measure the round-trip time and, hence, distance.). What is the maximum number of lines per centimeter a diffraction grating can have and produce a complete first-order spectrum for visible light? (b) When the specimen is immersed in oil, with index of refraction of 1.52? The distance between atoms in a molecule is about \(\displaystyle 10^{−8}cm\). Constructive interference occurs at point X. Assume that the pupil of the observer’s eye has a diameter of 5.0 mm. Use the intensity of the central spot to be \(\displaystyle 1mW/cm^2\). (d) How does your answer to (c) compare to details you normally observe in everyday circumstances? 20. Legal. Can it resolve the millimeter markings of a ruler placed 35 m away? Assume light enters the eye through a pupil of diameter 4.5 mm. (This will greatly reduce the intensity of the fifth maximum.) 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? 91. Assume λ=550nm.λ=550nm. Ocean waves of 20.0-m wavelength approach the opening straight on. 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. 41. 53. 3. Explain what ββ represents. A He-Ne laser beam is reflected from the surface of a CD onto a wall. 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. 54. (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)? Diffraction par une fente. 24. What image will one see if a hologram is recorded using monochromatic light but its image is viewed in white light? The limit to the eye’s acuity is actually related to diffraction by the pupil. Find the intensity at a \(\displaystyle 10°\) angle to the axis in terms of the intensity of the central maximum. 77. (a) What diameter mirror is needed to be able to see 1.00-m detail on a Jovian moon at a distance of \(\displaystyle 7.50×10^8km\) from Earth? Make waves with a dripping faucet, audio speaker, or laser! 34. (b) In actuality, it is just barely possible to discern that Pluto and Charon are separate bodies using a ground-based telescope. The interference pattern is observed on a screen 3.0 m away. If a diffraction grating produces a first-order maximum for the shortest wavelength of visible light at \(\displaystyle 30.0°\), at what angle will the first-order maximum be for the largest wavelength of visible light? (b) Repeat this calculation for a musical note of frequency 440 Hz (A above middle C). Why can lenses, mirrors, or apertures not be used to correct the spreading? Diffraction is a wave phenomenon and is also observed with water waves in a ripple tank. In 1801, Thomas Young attempted to prove that light was a wave by showing that it has the ability to diffract and interfere. 100. 46. Vocabulary Interference: When two waves overlap to produce one new wave. At what angle will the first-order maximum be for 520-nm-wavelength green light? Find the intensity in terms of \(\displaystyle I_o\) at \(\displaystyle θ=0.5°\), \(\displaystyle 1.0°, 1.5°, 3.0°,\) and \(\displaystyle 10.0°\). How narrow is a slit that produces a diffraction pattern on a screen 1.8 m away whose central peak is 1.0 m wide? 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 \(\displaystyle 30.0°\). According to the superposition principle, the net displacement is simply given by the vector or the algebraic sum of the individual displacements. shows how to the wavelength in a given medium, λnλn, is related to the wavelength in a vacuum, λλ, and the refractive index, n, of the medium. Is the central diffraction peak wider in the vertical direction or in the horizontal direction? (d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular width of the next maximum (which is the angle between the first and second minima). 40. 11. (Hint: The distance between adjacent fringes is \(\displaystyle Δy=xλ/d\), assuming the slit separation d is comparable to \(\displaystyle λ\).). Determine (a) the spacing between the reflecting planes, and (b) the unknown wavelength. 71. 47. (a) If a single slit produces a first minimum at \(\displaystyle 14.5°\), at what angle is the second-order minimum? (e) How wide is the next bright fringe on the screen? Objects viewed through a microscope are placed very close to the focal point of the objective lens. 3 Ewald sphere construction. Note that some of the bright spots are dim on either side of the center. (b) What slit width would place this minimum at \(\displaystyle 85.0°\)? 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? (c) What is the distance between two just-resolvable points held at an arm’s length (0.800 m) from your eye? The brightest spot is the reflected beam at an angle equal to the angle of incidence. (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, \(\displaystyle 12μm\), while keeping the widths of the slits same? Remember to answer all questions in your lab notebook in a neat and orderly fashion. 117. Two slits of width \(\displaystyle 2μm\), each in an opaque material, are separated by a center-to-center distance of \(\displaystyle 6μm\). 49. (b) At what angle will the second minimum be? Two lamps producing light of wavelength 589 nm are ﬁxed 1.0 m apart on a wooden plank. 1. (c) Discuss the relationship between integral reductions in lines per centimeter and the new angles of various order maxima. On a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of \(\displaystyle 27.1°\) relative to its surface, using an X-ray source of unknown wavelength. A screen of dimensions \(\displaystyle 2.0m×2.0m\) is 1.2 m away from the slit. The first-order Bragg angle for a certain crystal is \(\displaystyle 12.1°\). 78. 6) Describe how diffraction is related to an optical instrument’s resolution. 76. TWO identical loudspeakers, L 1 and are operated at the same frequency and in phase with each other. For example, the radio telescope in Penticton, BC in Canada, has a diameter of 26 m and can be operated at frequencies as high as 6.6 GHz. (a) Where are the first minima of the diffraction pattern? What is the minimum diameter mirror on a telescope that would allow you to see details as small as 5.00 km on the moon some 384,000 km away? 26. (a) At what angle is the first minimum for 550-nm light falling on a single slit of width \(\displaystyle 1.00μm\)? What did Thomas Young discover in 1801? What if it is viewed using light of exactly half the original wavelength? 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. Instead, Young observed many, bright and dark lines. Assume 550 nm for the wavelength of light and 400,000 km for the distance to the moon. A single slit of width \(\displaystyle 3.0μm\) is illuminated by a sodium yellow light of wavelength 589 nm. If the separation between the first and the second minima of a single-slit diffraction pattern is 6.0 mm, what is the distance between the screen and the slit? Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. 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. As an example of diffraction by apertures of everyday dimensions, consider a doorway of width 1.0 m. (a) What is the angular position of the first minimum in the diffraction pattern of 600-nm light? How many dots per inch (dpi) does this correspond to? 38. 110. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.30 m apart? What is the distance between lines on a diffraction grating that produces a second-order maximum for 760-nm red light at an angle of \(\displaystyle 60.0°\)? 7. [ "article:topic", "authorname:openstax", "license:ccby", "showtoc:no", "program:openstax" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FMap%253A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)%2F04%253A_Diffraction%2F4.0E%253A_4.E%253A_Diffraction_(Exercises), Creative Commons Attribution License (by 4.0). To understand the meaning of constructive and destructive interference 2. Why? At what angles to the incident direction are the boats inside the harbor most protected against wave action? (b) Would such a grating be useful for ultraviolet spectra? What is the wavelength of this X-ray? 14-3 Diffraction and Interference Vocabulary Diffraction: The spreading of a wave as it passes around an obstacle or through an opening. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). The central diffraction peak of the double-slit interference pattern contains exactly nine fringes. Electromagnetism & Light Interference & Diffraction Interference and Diffraction 33-1 Phase Difference and Coherence 33-2 Interference in Thin Films 33-3 Two-Slit Interference Pattern 33-4 Diffraction Pattern of a Single Slit 33-5 Using Phasors to Add Harmonic Waves 33-6 Fraunhofer and Fresnel Diffraction 33-7 Diffraction and Resolution 33-8 Diffraction Gratings … In Equation 4.4, the parameter ββ looks like an angle but is not an angle that you can measure with a protractor in the physical world. Because of diffraction, the waves leaving the two small slits, spread out as shown in Figure 1. Course Hero, Inc. Assume an average wavelength of 550 nm for the light received. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. 14. (a) By differentiating Equation 4.4, show that the higher-order maxima of the single-slit diffraction pattern occur at values of \(\displaystyle β\) that satisfy \(\displaystyle tanβ=β\). (b) How close together could these point sources be at the 2 million light-year distance of the Andromeda Galaxy? 37. Can an astronaut orbiting Earth in a satellite at a distance of 180 km from the surface distinguish two skyscrapers that are 20 m apart? 12. Explain. (Use \(\displaystyle λ=600nm\).) Title: Exercise: Indexing of the electron diffraction patterns 1 ExerciseIndexing of the electron diffraction patterns. (b) What is the longest wavelength for which it does produce a first-order maximum? The characters of a stadium scoreboard are formed with closely spaced lightbulbs that radiate primarily yellow light.