1. Figure below shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. The slits are illuminated by light of wavelength A. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Using the small angle approximation (where sine0, with 0 in radians), calculate the distance between fringes in terms of A and the variables shown below. Ym+1 Ут Om+1 d. Answer symbollically using: x,d, and A. Use the orange square root symbol box to enter variables and greek symbols. Ay= Using the result of part (a), calculate the distance between fringes for 646 -nm light falling on double slits separated by 0.09 mm, located 2 m from a screen as in Figure. Ду: cm

1. Figure below shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. The slits are illuminated by light of wavelength A. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Using the small angle approximation (where sine0, with 0 in radians), calculate the distance between fringes in terms of A and the variables shown below. Ym+1 Ут Om+1 d. Answer symbollically using: x,d, and A. Use the orange square root symbol box to enter variables and greek symbols. Ay= Using the result of part (a), calculate the distance between fringes for 646 -nm light falling on double slits separated by 0.09 mm, located 2 m from a screen as in Figure. Ду: cm

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter36: Wave Optics

Section: Chapter Questions

Problem 14P: Monochromatic light of wavelength is incident on a pair of slits separated by 2.40 104 m and forms...

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Figure 27.55 shows the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of single slit and double slit interference. Note that the bright spots are evenly spaced. Is this a double slit or single slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single slit or double slit characteristic? Which is smaller, the slit Width or the separation between slits? Explain your responses. Figure 27.55 This double slit interference pattern also shows signs of single slit interference. (credit: PASCO)
Monochromatic light of wavelength is incident on a pair of slits separated by 2.40 104 m and forms an interference pattern on a screen placed 1.80 m from the slits. The first-order bright fringe is at a position ybright = 4.52 mm measured from the center of the central maximum. From this information, we wish to predict where the fringe for n = 50 would be located. (a) Assuming the fringes are laid out linearly along the screen, find the position of the n = 50 fringe by multiplying the position of the n = 1 fringe by 50.0. (b) Find the tangent of the angle the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum. (c) Using the result of part (b) and Equation 36.2, calculate the wavelength of the light. (d) Compute the angle for the 50th-order bright fringe from Equation 36.2. (e) Find the position of the 50th-order bright fringe on the screen from Equation 36.5. (f) Comment on the agreement between the answers to parts (a) and (e).
In Figure 37.7, show mathematically how many interference maxima are enclosed by the central diffraction maximum in the pattern. Notice that the diagram is generated by using 650-nm light to illuminate two 3.0-m slits separated by 18 m. Figure 37.7 The combined effects of two-slit and single-slit interference. This pattern is produced when 650-nm light waves pass through two 3.0-m slits that are 18 m apart.
Light at 633 nm from a helium-neon laser shines on a pair of parallel slits separated by 1.45 105 m and an interference pattern is observed on a screen 2.00 m from the plane of the slits. (a) Find the angle from the central maximum to the First bright fringe. (b) At what angle from the central maximum does the second dark fringe appear? (c) Find the distance from the central maximum to the first bright fringe.
(a) If a single slit produces a first minimum at 14.5°, at what angle is the second-order minimum? (b) What is the angle of the third-order minimum? (c) Is there a fourth-order minimum? (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).
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.
Light with wavelength 442 nm passes through a double-slit system that has a slit separation d = 0.400 mm. Determine how far away a screen must be placed so that dark fringes appear directly opposite both slits, with only one bright fringe between them.
Determine what happens to the double-slit interference pattern if one of the slits is covered with a thin, transparent film whose thickness is /[2(n1)] , where ? is the wavelength of the incident light and n is the index of refraction of the film.
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? The light wavelength is 500 nm and the slit width is 0.16 mm.
A chamber 5.0 cm long with flat, parallel windows at the ends is placed in one arm of a Michelson interferometer (see below). The light used has a wavelength of 500 nm in a vacuum. While all the air is being pumped out of the chamber, 29 fringes pass by a point on the observation screen. What is the refractive index of the air?
A plane monochromatic light wave is incident on a double-slit as illustrated in Figure 24.4. As the slit separation decreases, what happens to the separation between the interference fringes on the screen? (a) It decreases, (b) It increases, (c) It remains the same, (d) It may increase or decrease, depending on the wave-length of the light, (e) More information is required.
At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?