Concept explainers
Slit 1 of a double-slit is wider than slit 2 so that the light from slit 1 has an amplitude exactly 3 times that of the light from slit 2. Show that Equation 36.9 is replaced by the following equation for this situation:
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
The phase angle ϕ in E2 is due to the extra path length traveled by the lower beam in Figure 36.4. 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 might find the following trigonometric identities helpful:
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Chapter 36 Solutions
Physics for Scientists and Engineers
- For fun, a student constructs a four-slit interference experiment. If the light from each of the four slits arrives in phase at the central maximum, then how will the intensity I compare to the intensity I1 from a single slit? a. I1 b. 4I1 c. 8I1 d. 16I1arrow_forwarda double slit is seperated by 0.0574 mm is placed 1.65 m from the screen. A. if yellow light of wavelength 589nm 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 410 nm strikes the double slit, what is the seperation between the second-rder and the fourth-order maxima?arrow_forwardIn a Young's double-slit experiment, a set of parallel slits with a separation of 0.108 mm is illuminated by light having a wavelength of 584 nm and the interference pattern observed on a screen 3.50 m from the slits. (a) What is the difference in path lengths from the two slits to the location of a third order bright fringe on the screen? answer in ?m (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? answer in ?marrow_forward
- In a Young's double-slit experiment, a set of parallel slits with a separation of 0.114 mm is illuminated by light having a wavelength of 587 nm and the interference pattern observed on a screen 4.50 m from the slits. (a) What is the difference in path lengths from the two slits to the location of a fifth order bright fringe on the screen? ?m(b) What is the difference in path lengths from the two slits to the location of the fifth dark fringe on the screen, away from the center of the pattern? ?marrow_forwardAn investigator finds a fiber at a crime scene that he wishes to use as evidence against a suspect. He gives the fiber to a technician to test the properties of the fiber. To measure the diameter of the fiber, the technician places it between two flat glass plates at their ends as in the figure below. When the plates, of length 15.8 cm, are illuminated from above with light of wavelength 670 nm, she observes bright interference bands separated by 0.595 mm. What is the diameter of the fiber? ?marrow_forwardA laser beam is incident on two slits with separation d = 0.026 mm. A screen is placed L = 3.2 m from the slits. The wavelength of the laser light is λ = 5750 Å. θ1 and θ2 are the angles to the first and second bright fringes above the center of the screen. Part (a) Express sin(θ1) in terms of d and λ. Part (b) Express sin(θ2) in terms of d and λ. Part (c) Express the distance between the two bright fringes on the screen, y, in terms of θ1, θ2 and L. Part (d) Solve for the numerical value of y in meters.arrow_forward
- In a Young's double-slit experiment, two parallel slits with a slit separation of 0.185 mm are illuminated by light of wavelength 563 nm, and the interference pattern is observed on a screen located 4.05 m from the slits. (a) What is the difference in path lengths from each of the slits to the location of the center of a fifth-order bright fringe on the screen? µm(b) What is the difference in path lengths from the two slits to the location of the center of the fifth dark fringe away from the center of the pattern? µmarrow_forwardIn a location where the speed of sound is 353 m/s, a 2,000 Hz sound wave impinges on two slits 30 cm apart. (a) At what angle is the first-order maximum located? °(b) If the sound wave is replaced by 2.50 cm microwaves, what slit separation gives the same angle for the first-order maximum? cm(c) If the slit separation is 1.00 ?m, what frequency of light gives the same first-order maximum angle? Hzarrow_forwardConsider a source of light with wavelength ? = 530 nm that shines on two identical narrow slits. The slits are separated by a distance a = 30 ?m. An interference pattern is observed on a screen located a distance L away from the slits. On the screen, the location of the second dark spot to the left of the central bright spot is found to be y = 1.2 cm from the central bright spot. Let this particular position on the screen be referred to as P1.A. Light from both slits travels to the point P1. How much further does the light from one slit travel compared to the light from the other slit?distance = __________ nmB. The path difference in part A is equal to a·sin? where the angle ? is the separation between the central bright spot and the second dark spot. What is this angle ??? = _______ °C. Using the angle ? and the location y of the second dark spot on the screen, determine the distance L between the slits and the screen.L = _______ marrow_forward
- In a Young’s double-slit experiment, light of wavelength 500 nm illuminates two slits that are separated by 1 mm. What is the separation distance between the central maximum (m = 0) and the 3rd order maximum (m = 3) on a screen 5.0 m from the slits? A. 0.10 cm. B. 0.25 cm. C. 0.50 cm. D. 0.75 cm. E 1.0 cm.arrow_forwardLight of wavelength λ = 430 nm and intensity I(0) = 210 W/m^2 is incident upon two narrow slits that are separated by a distance d = 36 μm. Part (a) Write an equation for the cosine of half of the phase difference Φ between the waves passing through the two slits in terms of the intensity of the central maximum I(0) and the resulting intensity I. cos(Φ/2) = Part (b) What is the smallest phase angle, Φ in radians, for which the resulting intensity of the light will be I = 110 W/m^2? Φ =arrow_forwardIn a Young's double-slit experiment, a set of parallel slits with a separation of 0.118 mm is illuminated by light having a wavelength of 565 nm and the interference pattern observed on a screen 3.50 m from the slits. (a) What is the difference in path lengths from the two slits to the location of a fourth order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the fourth dark fringe on the screen, away from the center of the pattern?arrow_forward
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