4. Green light has a wavelength of approximately 540 nm. When green light is diffracted through a single slit with a width of 2.7 x 10-5 m, the distance on the screen from the centre to the first bright fringe is 2.34 cm. a) Determine the distance between the slit and the screen for this observation to have been made. b) Keeping the same distance between slit and screen, and using the same green light, what width of slit would be needed to double the distance to the first bright fringe.

4. Green light has a wavelength of approximately 540 nm. When green light is diffracted through a single slit with a width of 2.7 x 10-5 m, the distance on the screen from the centre to the first bright fringe is 2.34 cm. a) Determine the distance between the slit and the screen for this observation to have been made. b) Keeping the same distance between slit and screen, and using the same green light, what width of slit would be needed to double the distance to the first bright fringe.

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter37: Wave Optics

Section: Chapter Questions

Problem 37.44P: One leg of a Michelson interferometer contains an evacuated cylinder of length L, having glass...

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In a Youngs double-slit experiment, a set of parallel slits with a separation of 0.100 mm is illuminated by light having a wave- length of 589 nm, and the interference pattern is observed on a screen 4.00 m from the slits, (a) What is the difference in path lengths from each of the slits to the location of a third-order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?
In a Youngs double-slit experiment, a set of parallel slits with a separation of 0.100 mm is illuminated by light having a wave- length of 589 nm, and the interference pattern is observed on a screen 4.00 m from the slits, (a) What is the difference in path lengths from each of the slits to the location of a third-order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?
In Figure 38.4, assume the slit is in a barrier that is opaque to x-rays as well as to visible light. The photograph in Figure 38.4b shows the diffraction pattern produced with visible light. What will happen if the experiment is repeated with x-rays as the incoming wave and with no other changes? (a) The diffraction pattern is similar. (b) There is no noticeable diffraction pattern but rather a projected shadow of high intensity on the screen, having the same width as the slit. (c) The central maximum is much wider, and the minima occur at larger angles than with visible light. (d) No x-rays reach the screen.
(a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20.0 m. (b) What slit width would place this minimum at 85.0°? Explicitly show how you follow the steps in Problem-Solving Strategies for Wave Optics
(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 m. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.
What If? Suppose light strikes a single slit of width a at an angle from the perpendicular direction as shown in Figure P37.6. Show that Equation 37.1, the condition for destructive interference, must be modified to read sindark=masinm=1,2,3,
(a) What is the minimum width of a single slit (in multiples of ) that will produce a first minimum for a wavelength ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?
In Figure P27.7 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4?
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.
(a) If the first-order maximum for pure-wavelength light falling on a double slit is at an angle of 10.0°, at what angle is the second-order maximum? (b) What is the angle of the first minimum? (c) What is the highest-order maximum possible here?
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.
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)