Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 35, Problem 74PQ
To determine
The angular position for the first-order location of silence.
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In your summer job at an optics company, you are asked to measure the wavelength λ of the light that is produced by a laser. To do so, you pass the laser light through two narrow slits that are separated by a distance d. You observe the interference pattern on a screen that is 0.900 m from the slits and measure the separation ∆y between adjacent bright fringes in the portion of the pattern that is near the center of the screen. Using a microscope, you measure d. But both ∆y and d are small and difficult to measure accurately, so you repeat the measurements for several pairs of slits, each with a different value of d. Your results are shown in Fig. P35.50, where you have plotted ∆y versus 1/d. The line in the graph is the best-fit straight line for the data. (a) Explain why the data points plotted this way fall close to a straight line. (b) Use Fig. to calculate λ.
A two-slit Young’s interference experiment is arranged with the wavelength of the light source λ = 0.5 μm. When a thin film of transparent material is put in front of one of the slits, the zero order fringe moves to the position previously occupied by the 4th order bright fringe. The index of refraction of the film is n = 1.2. Calculate the thickness of the film.
Coherent microwave light with a frequency f= 2.0*1010 Hz is incident on a d=5.0 cm double slit barrier, producing an interference pattern of a number of maxima and minima. A detector is free to swing around the full 180 degrees in order to find the presence of intereference maxima and minima. How many different minima will this detector detect, as it is allowed to swing around the full 180 degrees? Include minima on both sides of the centerkine in your count.
Chapter 35 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 35.1 - Perhaps Newton never observed a diffraction...Ch. 35.1 - Prob. 35.2CECh. 35.2 - Prob. 35.3CECh. 35.3 - Prob. 35.4CECh. 35.4 - When we studied Youngs double-slit experiment, we...Ch. 35.6 - Prob. 35.6CECh. 35 - Light Is a Wave C As shown in Figure P35.1, spray...Ch. 35 - Sound Wave Interference Revisited Draw two...Ch. 35 - Prob. 3PQCh. 35 - You are seated on a couch equidistant between two...
Ch. 35 - Prob. 5PQCh. 35 - Prob. 6PQCh. 35 - A student shines a red laser pointer with a...Ch. 35 - Monochromatic light is incident on a pair of slits...Ch. 35 - Prob. 9PQCh. 35 - In a Youngs double-slit experiment with microwaves...Ch. 35 - A beam from a helium-neon laser with wavelength...Ch. 35 - Prob. 12PQCh. 35 - Prob. 13PQCh. 35 - Prob. 14PQCh. 35 - Light from a sodium vapor lamp ( = 589 nm) forms...Ch. 35 - Prob. 16PQCh. 35 - Prob. 17PQCh. 35 - Prob. 18PQCh. 35 - Prob. 19PQCh. 35 - Prob. 20PQCh. 35 - Prob. 21PQCh. 35 - Prob. 22PQCh. 35 - Prob. 23PQCh. 35 - Figure P35.24 shows the diffraction patterns...Ch. 35 - Prob. 25PQCh. 35 - Prob. 26PQCh. 35 - A thread must have a uniform thickness of 0.525...Ch. 35 - Prob. 28PQCh. 35 - Prob. 29PQCh. 35 - A radio wave of wavelength 21.5 cm passes through...Ch. 35 - Prob. 31PQCh. 35 - Prob. 32PQCh. 35 - A single slit is illuminated by light consisting...Ch. 35 - Prob. 34PQCh. 35 - Prob. 35PQCh. 35 - Prob. 36PQCh. 35 - Prob. 37PQCh. 35 - Prob. 38PQCh. 35 - Prob. 39PQCh. 35 - Prob. 40PQCh. 35 - Prob. 41PQCh. 35 - Prob. 42PQCh. 35 - Prob. 43PQCh. 35 - Prob. 44PQCh. 35 - Prob. 45PQCh. 35 - Prob. 46PQCh. 35 - Prob. 47PQCh. 35 - Prob. 48PQCh. 35 - Figure P35.49 shows the intensity of the...Ch. 35 - Prob. 50PQCh. 35 - Prob. 51PQCh. 35 - Prob. 52PQCh. 35 - Light of wavelength 750.0 nm passes through a...Ch. 35 - Prob. 54PQCh. 35 - Prob. 55PQCh. 35 - Prob. 56PQCh. 35 - Light of wavelength 515 nm is incident on two...Ch. 35 - Light of wavelength 515 nm is incident on two...Ch. 35 - A Two slits are separated by distance d and each...Ch. 35 - Prob. 60PQCh. 35 - Prob. 61PQCh. 35 - If you spray paint through two slits, what pattern...Ch. 35 - Prob. 63PQCh. 35 - Prob. 64PQCh. 35 - Prob. 65PQCh. 35 - Prob. 66PQCh. 35 - Prob. 67PQCh. 35 - Prob. 68PQCh. 35 - Prob. 69PQCh. 35 - Prob. 70PQCh. 35 - Prob. 71PQCh. 35 - Prob. 72PQCh. 35 - Prob. 73PQCh. 35 - Prob. 74PQCh. 35 - Prob. 75PQCh. 35 - Prob. 76PQCh. 35 - Prob. 77PQCh. 35 - Another way to construct a double-slit experiment...Ch. 35 - Prob. 79PQCh. 35 - Prob. 80PQCh. 35 - Table P35.80 presents data gathered by students...Ch. 35 - Prob. 82PQCh. 35 - Prob. 83PQCh. 35 - Prob. 84PQCh. 35 - Prob. 85PQCh. 35 - Prob. 86PQCh. 35 - Prob. 87PQCh. 35 - Prob. 88PQCh. 35 - A One of the slits in a Youngs double-slit...Ch. 35 - Prob. 90PQ
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- Consider a single-slit diffraction pattern for =589 nm, projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?arrow_forwardThe interference figure of a set of double slits is measured at a stop. The experiment is performed with a laser with a wavelength of 450nm (approach the speed of light to 300,000 km/s in this situation) and it is measured that the interference maximum m=2 is 10mm away from the main maximum.Then, 2 pieces of glass are placed in front of each of the slits. The piece of glass P1 causes a delay in the wave (in relation to a wave that propagates in the air) of 7.5x10^(-16)sThe piece of P2 glass causes a delay of 3.75x10^(-16)s. How many mm will the main maximum be shifted from the initial position?a)1.25 towards P1b)1.25 towards P2c)1.50 towards P1d)1.50 towards P2e)1.75 towards P1f)1.75 towards P2g)2.00 towards P1h)2.00 towards P2i)2.25 towards P1j)2.25 towards P2arrow_forwardThe analysis of any two-point source interference pattern and a successful determination of wavelength demands an ability to sort through the measured information and equating the values with the symbols in Young's equation. Apply your understanding by interpreting the following statements and identifying the values of y, d, m and L. Finally, perform some conversions of the given information such that all information share the same unit. Two sources separated by 0.500 mm produce an interference pattern 525 cm away. The fifth and the second antinodal line on the same side of the pattern are separated by 98 mm. y= ________ d=________ m=_______ L=________arrow_forward
- In a Young's interference experiment, the two slits are separated by 0.145 mm and the incident light includes two wavelengths: ?1 = 540 nm (green) and ?2 = 450 nm (blue). The overlapping interference patterns are observed on a screen 1.22 m from the slits.(a) Find a relationship between the orders m1 and m2 that determines where a bright fringe of the green light coincides with a bright fringe of the blue light. (The order m1 is associated with ?1, and m2 is associated with ?2.) m2/m1= (b) Find the minimum values of m1 and m2 such that the overlapping of the bright fringes will occur.m1 = m2 = Find the position of the overlap on the screen. ________cm from the central maximumarrow_forwardIn a realistic two‑slit experiment, you see two interference effects described in this chapter. There is the large‑scale interference pattern from diffraction that depends on the width of each slit, and within that pattern there is the small‑scale interference pattern that depends on the separation distance between the slits. For a slit width of 0.040 mm and a slit separation of 0.50 mm,what is the number n1 of bright two‑slit interference fringes that fit inside the central bright fringe of the diffraction pattern (from the first dark fringe on one side of the center to the first dark fringe on the other side) if the laser has a wavelength of 700 nm? n1 = ? For the same slit width and slit separation, what is the number n2 of bright two‑slit interference fringes that fit inside the central bright fringe of the diffraction pattern if the laser has a wavelength of 490 nm? n2 = ?arrow_forwardThe double slit experiment is a quintessential wave experiment in physics. Given a third order fringe 5.00 cm away from the central fringe, a double slit with a separation of 0.0510 mm, and a distance between the slits and the fringes of 1.50 m, find the following. (a) wavelength 56E-9 X For a double slit, how is the distance from the central maximum to any constructive interference site (bright fringe) related to the separation of the slits, distance between the slits and the interference pattern, and the wavelength of the light? nm (b) separation between adjacent fringes cm Additional Materials Readingarrow_forward
- In a Young’s interference experiment, the two slits are separated by 0.150 mm and the incident light includes two wavelengths: λ1 = 540 nm (green) and λ2 = 450 nm (blue). The overlapping interference patterns are observed on a screen 1.40 m from the slits. (a) Find a relationship between the orders m1 and m2 that determines where a bright fringe of the green light coincides with a bright fringe of the blue light. (The order m1 is associated with λ1 , and m2 is associated with λ2.) (b) Find the minimum values of m1 and m2 such that the overlapping of the bright fringes will occur and find the position of the overlap on the screen.arrow_forwardLight of wavelength λ = 580 nm is incident upon two thin slits that are separated by a distance d = 25 μm. The light hits a screen L = 1.5 m from the screen. It is observed that at a point y = 5.5 mm from the central maximum the intensity of the light is I = 55 W/m2. What is the intensity of the light at the two slits (I0) in watts per square meter?arrow_forwardIn a Young's interference experiment, the two slits are separated by 0.175 mm and the incident light includes two wavelengths: λ1 = 540 nm (green) and λ2 = 450 nm (blue). The overlapping interference patterns are observed on a screen 1.46 m from the slits. (a) Find a relationship between the orders m1 and m2 that determines where a bright fringe of the green light coincides with a bright fringe of the blue light. (The order m1 is associated with λ1, and m2 is associated with λ2.) m2 m1 = (b) Find the minimum values of m1 and m2 such that the overlapping of the bright fringes will occur. m1 = m2 = Find the position of the overlap on the screen. cm from the central maximumarrow_forward
- Light of wavelength λ = 410 nm is incident upon two thin slits that are separated by a distance d = 25 μm. The light hits a screen L = 2.4 m from the screen. It is observed that at a point y = 4.8 mm from the central maximum the intensity of the light is I = 85 W/m2. Part (a) Write an equation for the phase shift between the light from the two slits at the observation point in terms of the given variables. Part (b) For the given data, what is the phase shift, in radians, between the light from the two slits at the observation point? Part (c) What is the intensity of the light at the two slits (I0) in watts per square meter?arrow_forwardYoung's experiment is performed with light from excited helium atoms λ = 500 nm. Fringes are measured carefully on a screen 1.2 m away from the double slit, and the center of the 20th bright fringe is found to be 10.6 mm from the center of the central bright fringe and at an angle above the central axis. is given by (CONSIDER THAT IS SMALL): a) b) 0 0.0106 1.2 d 1.2 0.0106 Calculate , in SI units. Ay = c) the >rture Assume 0 = 0.28°. Find the separation distance d between the two slits of the aperture screen, in SI units. + + O1.2 x 500 x 10 -9 d -Assume d = 5.4 x 10-3 m. What is the distance Ay between the second and third dark lines of interference pattern on the screen, in SI units?arrow_forwardIn a laboratory, light from a particular spectrum line of helium passes through a diffraction grating and the second-order maximum is at 18.9° from the center of the central bright fringe. The same grating is then used for light from a distant galaxy that is moving away from the earth with a speed of 2.65 x 107 m/s. For the light from the galaxy, what is the angular location of the second-order maximum for the same spectral line as was observed in the lab?arrow_forward
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