2- EXAMPLE 24-3 Wavelengths from double-slit interference. White light passes through two slits 0.50 mm apart, and an interference pattern is observed on a screen 2.5 m away. The first-order fringe resembles a rainbow with violet and red light at opposite ends. The violet light is about 2.0 mm and the red 3.5 mm from the center of the central white fringe (Fig. 24-11). Estimate the wavelengths for the violet and red light. White 2.0 mm- 3.5 mm I FIGURE 24-11 First-order fringes for a double slit are a full spectrum, like a rainbow. Also Example 24-3.

2- EXAMPLE 24-3 Wavelengths from double-slit interference. White light passes through two slits 0.50 mm apart, and an interference pattern is observed on a screen 2.5 m away. The first-order fringe resembles a rainbow with violet and red light at opposite ends. The violet light is about 2.0 mm and the red 3.5 mm from the center of the central white fringe (Fig. 24-11). Estimate the wavelengths for the violet and red light. White 2.0 mm- 3.5 mm I FIGURE 24-11 First-order fringes for a double slit are a full spectrum, like a rainbow. Also Example 24-3.

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter27: Wave Optics

Section: Chapter Questions

Problem 18PE: Figure 27.56 shows a double slit located a distance x from a screen, with the distance from the...

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Show that the distribution of intensity in a double-slit pattern is given by Equation 36.9. Begin by assuming that the total magnitude of the electric field at point P on the screen in Figure 36.4 is the superposition of two waves, with electric field magnitudes E1=E0sintE2=E0sin(t+) The phase angle in in E2 is due to the extra path length traveled by the lower beam in Figure 36.4. Recall from Equation 33.27 that the intensity of light is proportional to the square of the amplitude of the electric field. In addition, the apparent intensity of the pattern is the time-averaged intensity of the electromagnetic wave. You will need to evaluate the integral of the square of the sine function over one period. Refer to Figure 32.5 for an easy way to perform this evaluation. You will also need the trigonometric identity sinA+sinB=2sin(A+B2)cos(AB2)
Suppose the single slit in Figure 38.4 is 6.00 cm wide and in front of a microwave source operating at 7.50 GHz. (a) Calculate the angle for the first minimum in the diffraction pattern. (b) What is the relative intensity l/lmax at 0 =- 15.0? (c) Assume two such sources, separated laterally by 20.0 cm, are behind the slit. What must be the maximum distance between the plane of the sources and the slit if the diffraction patterns are to be resolved? In this case, the approximation sin tan 8 is not valid because of the relatively small value of a/.
Measurements are made of the intensity distribution within the central bright fringe in a Youngs interference pattern (see Fig. 36.5). At a particular value of y, it is found that I/Imax = 0.810 when 600-nm light is used. What wavelength of light should be used to reduce the relative intensity at the same location to 64.0% of the maximum intensity?
A diffraction pattern is produced on a screen 1.40 m from a single slit, using monochromatic light of wavelength 5.00 102 nm. The distance from the center of the central maximum to the first-order maximum is 3.00 mm. Calculate the slit width. Hint: Assume that the first-order maximum is halfway between the first- and second-order minima.
An effect analogous to two-slit interference can occur with sound waves, instead of light. In an open field, two speakers placed 1.30 m apart are powered by a single-function generator producing sine waves at 1200-Hz frequency. A student walks along a line 12.5 m away and parallel to the line between the speakers. She hears an alternating pattern of loud and quiet, due to constructive and destructive interference. What is (a) the wavelength of this sound and (b) the distance between the central maximum and the first maximum (loud) position along this line?
A monochromatic light of unknown wavelength is incident on a slit of width 20 m. A diffraction pattern is seen at a screen 2.5 m away where the central maximum is spread over a distance of 10.0 cm. Find the wavelength.
Two coherent waves, coming from sources at different locations, move along the x axis. Their wave functions are E1=860sin[2x1650924t+6] and E2=860sin[2x2650924t+8] where E1 and E2 are in volts per meter, x1 and x2 are in nanometers, and t is in picoseconds. When the two waves are superposed, determine the relationship between x1, and x2 that produces constructive interference.
An American standard analog television picture (non-HDTV), also known as NTSC, is composed of approximately 485 visible horizontal lines of varying light intensity. Assume your ability to resolve the lines is limited only by the Rayleigh criterion, the pupils of your eyes are 5.00 min in diameter, and the average wavelength of the light coming from the screen is 550. nm. Calculate the ratio of the minimum viewing distance to the vertical dimension of the picture such that you will not be able to resolve the lines.
Figure 27.56 shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where sin, with in radians), the distance between fringes is given by y=x/d. Figure 27.56 The distance between adjacent fringes is y=x/d, assuming the slit separation d is large compared with .
A diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum be for 520-nm-wavelength green light?
If a diffraction grating produces a first-order maximum for the shortest wavelength of visible light at 30.0°, at what angle will the first-order maximum be for the largest wavelength of visible light?
Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.