Part A Monochromatic light falls on a slit that is 2.50x10-3 mm wide. If the angle between the first dark fringes on either side of the central maximum is 27.0 ° (dark fringe to dark fringe), what is the wavelength of the light used? Express your answer to three significant figures and include the appropriate units. = Value Units

Part A Monochromatic light falls on a slit that is 2.50x10-3 mm wide. If the angle between the first dark fringes on either side of the central maximum is 27.0 ° (dark fringe to dark fringe), what is the wavelength of the light used? Express your answer to three significant figures and include the appropriate units. = Value Units

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Wave Optics

Section: Chapter Questions

Problem 5OQ

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Which of the following causes the fringes in a two-slit interference pattern to move farther apart? (a) decreasing the wavelength of the light (b) decreasing the screen distance L (c) decreasing the slit spacing d (d) immersing the entire apparatus in water
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.
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.
Monochromatic light of wavelength is incident on a pair of slits separated by 2.40 104m. and forms an interference pattern on a screen placed 1.80 m away from the slits. The first-order bright fringe is 4.52 mm from the center of the central maximum. (a) Draw a picture, labeling the angle and the legs of the right triangle associated with the first-order bright fringe. (b) Compute the tangent of the angle associated with the first-order bright fringe. (c) Find the angle corresponding to the first-order bright fringe and compute the sine of that angle. Are the sine and tangent of the angle comparable in value? Does your answer always hold true? (d) Calculate the wavelength of the light. (e) Compute the angle of the fifth-order bright fringe. (f) Find its position on the screen.
Monochromatic light of wavelength is incident on a pair of slits separated by 2.40 104m. and forms an interference pattern on a screen placed 1.80 m away from the slits. The first-order bright fringe is 4.52 mm from the center of the central maximum. (a) Draw a picture, labeling the angle and the legs of the right triangle associated with the first-order bright fringe. (b) Compute the tangent of the angle associated with the first-order bright fringe. (c) Find the angle corresponding to the first-order bright fringe and compute the sine of that angle. Are the sine and tangent of the angle comparable in value? Does your answer always hold true? (d) Calculate the wavelength of the light. (e) Compute the angle of the fifth-order bright fringe. (f) Find its position on the screen.
Two slits of width 2 m, each in an opaque material, are separated by a center-to-center distance of 6 m. A monochromatic light of wavelength 450 nm is incident on the double-slit. One finds a combined interference and diffraction pattern on the screen. (a) How many peaks of the interference will be observed in the central maximum of the diffraction pattern? (b) How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same? (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, 12 m, while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength 680 nm is used? (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)? (f) Does this ratio depend on the wavelength of the light? (g) Does this ratio depend on the width or separation of the slits?
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.
Monochromatic light of wavelength 530 nm passes through a horizontal single slit of width 1.5 m in an opaque plate. A screen of dimensions 2.0m2.0m is 1.2 m away from the slit. (a) Which way is the diffraction pattern spread out on the screen? (b) What are the angles of the minima with respect to the center? (c) What are the angles of the maxima? (d) How wide is the central bright fringe on the screen? (e) How wide is the next bright fringe on the screen?
Suppose Youngs double-slit experiment is performed in air using red light and then the apparatus is immersed in water. What happens to the interference pattern on the screen? (a) It disappears. (b) The bright and dark fringes stay in the same locations, but the contrast is reduced. (c) The bright fringes are closer together. (d) The bright fringes are farther apart. (e) No change happens in the interference pattern.
A 65-fringe shift results in a Michelson interferometer when a 42.0-µm film made of an unknown material is placed in one arm. The light source has wavelength 632.9 nm. Identify the material using the indices of refraction found in Table 1.1.
Blue light of wavelength 450 nm falls on a slit of width 0.25 mm. A converging lens of focal length 20 cm is placed behind the slit and focuses the diffraction pattern on a screen. (a) How far is the screen from the lens? (b) What is the distance between the first and the third minima of the diffraction pattern?
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)