Option 1: Red light of wavelength 6.50 x 10 m passes through two parallel slits. Nodal lines are produced on a screen 3.00 m away. The distance between the 1" and the 10th dark fringe is 5.00 cm. (a) Include a sketch of the interference pattern. (b) Calculate the separation of the two slits. Is this a realistic number? (c) How would the distance between the fringes be affected if you had used green light?

Option 1: Red light of wavelength 6.50 x 10 m passes through two parallel slits. Nodal lines are produced on a screen 3.00 m away. The distance between the 1" and the 10th dark fringe is 5.00 cm. (a) Include a sketch of the interference pattern. (b) Calculate the separation of the two slits. Is this a realistic number? (c) How would the distance between the fringes be affected if you had used green light?

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 37.27P: The intensity on the screen at a certain point in a double- slit interference pattern is 64.0% of...

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In Figure P36.10 (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? Figure P36.10
In the What If? section of Example 36.2, it was claimed that overlapping fringes in a two-slit interference pattern for two different wavelengths obey the following relationship even for large values of the angle : mm= (a) Prove this assertion. (b) Using the data in Example 36.2, find the nonzero value of y on the screen at which the fringes from the two wavelengths first coincide.
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)
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.
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?
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.
The intensity on the screen at a certain point in a double- slit interference pattern is 64.0% of the maximum value. (a) What minimum phase difference (in radians) between sources produces this result? (b) Express this phase difference as a path difference for 486.1-nm light.
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?
Suppose you perform Youngs double-slit experiment with the slit separation slightly smaller than the wavelength of the light. As a screen, you use a large half-cylinder with its axis along the midline between the slits. What interference pattern will you see on the interior surface of the cylinder? (a) bright and dark fringes so closely spaced as to be indistinguishable (b) one central bright fringe and two dark fringes only (c) a completely bright screen with no dark fringes (d) one central dark fringe and two bright fringes only (e) a completely dark screen with no bright fringes
A diffraction pattern is formed on a screen 120 cm away from a 0.400-mm-wide slit. Monochromatic 546.1-nm light is used. Calculate the fractional intensity I/Imax at a point on the screen 4.10 mm from the center of the principal maximum.
A double slit separated by 0.058 0 mm is placed 1.50 m from a screen. (a) If yellow light of wavelength 588 nm strikes the double slit, what is the separation between the zeroth-order and first-order maxima on the screen? (b) If blue light of wavelength 412 nm strikes the double slit, what is the separation between the second-order and fourth-order maxima?
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?