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Question 1

An important theme in military technology is the reduction of the visibility of an aircraft to enemv radars. One {partial} solution is to cover the socalled stealth aircraft with a coating of dielectric material. If the radar's wavelength is 2.40 cm, what is the minimum desired thickness of the coating in centimeters. assuming that the index of refraction of the dielectric coating is n = 1.86 and the aircraft surface induces a 11' phase shift on reflected electromagnetic waves? A coating of R1 = 1.29 material is to be added to 112 = 1.49 glass. in order to make it \"iridescent." 10a Iridescence is associated with multiple colors being reflected. What is the thinnest layer of material {in nanometers} that will have a reflection maximum for normalincidence Light at both A1 = 400 and A2 = 600 nm (vacuum) wavelengths? 10b This thickness will have a reflection minimum at some {vacuum} waveLength between 400 and 6'30 nm. What is the wavelength in nanometers of the reflection minimum? 11 In a Young's interference experiment, the two slits are separated by 0.154 mm. and the incident Light includes light of wavelengths A1 = 540.0 nm and A2 = 450.0 nm. The overlapping interference patterns are formed on a screen 1.34 m from the slits. Calculate the minimum distance in centimeters from the center of the screen to the point where a bright line of the A1 light coincides with a bright line of the A2 light. Use the small angle approximation. 2 A wide beam of light from a laser with a wavelength of 500. nm is incident on a long narrow opening that is 0.150 mm wide. What will be the width, in mm, of the central maximum on a screen 2.50 m from the opening (i.e what will be the distance between the nodes adjacent to the central maximum?) (Use the small angle approximation, and give your result in millimeters.)You are looking into the headlights of a distant vehicle on an autoroute in France. The driver has shown his resistance to the Europeanization of Europe by resolutely continuing to use yellow headlights [wavelength 550 nm]. 3a What is the theoretical limit of angular resolution of your eyes for these headlights when your iris has a diameter of 4.00 mm? {Express your answer in mrad.) 3h If the headlights of the car are separated by 1.40 m, with this resolution at what distance wouLd Iyou be just be abLe to tell that the vehicLe had. in fact, two headLights? {Express your answer in km] Two slits separated by a distance of d = 0.140 mm are located at a distance of D = 890. mm from a screen. The screen is oriented parallel to the plane of the slits. The slits are illuminated by a coherent Light source with a wavelength of A = 522 x 10?3 mm. The interference pattern shows a peak at the center of the screen [ m = D} and then alternating minima and maxima. 4a What is the path length difference in millimeters between the two waves from the two slits at the rst i m = 1] maximum on the screen? 4b What is the path length difference in millimeters between the two waves from the two slits at the first ( m = 0) minimum on the screen?4c Calculate the distance on the screen between the central maximum (m = 0) and the first (m = 1) maximum. You can assume sin 0 ~ tan 0 / 0, with 0 expressed in radians. Give your answer in millimeters.A xylophone has a set of vibrating bars. A bar with a frequency of 344 Hz is struck. A very short time later, a second bar is also sounded, and one hears the volume of the xylophone increase and decrease 5 times each second (called beats). What are the possible frequencies of the second bar (in Hz)? (Select all that are possible) 349 Hz 339 Hz 334 Hz 354 Hz 350. Hz6 A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. Two successive resonances are heard at 53.1 Hz and 68.3 Hz. How deep is the well in meters? (Use 343m/s for the speed of sound)7 A 60 year old person has a threshold of hearing at f = 10 kHz of 95.0 dB. In contrast, a typical young adult's threshold at 10 kHz is only = 43.0 dB. If the young adult can just barely hear a 10 kHz tone, by what factor must the intensity of the sound wave be amplified so that it is heard by the older person?8 As you stand by a railroad track, a train approaches with its whistLe bLowing. As the train passes {i.e. as it goes from approaching you to speeding away from you). you hear a frequency shift equalto 28.0% of the restframe frequency of the whistle [i.e. 28.0% of the frequency heard by passengers on the train). How fast is the train moving? Express your answer in kmfhr. [Note that the speed of sound that day is 331.4 mfs.) You decide to circumvent the tvrannv of the twelve eventempered semitone musical scale of Western civilization by introducing your own 1? tone scale to cover the octave in equal percentage steps. How close can you get to the interval which in Western music is called the "fourth [1.333 J"? {Express your answer as a percentage deviation of the upper note from the just value, keeping the sign and rounding it off to the nearest tenth of a percent.)