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What If? Suppose light strikes a single slit of width a at an angle β 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
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Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics
- Table P35.80 presents data gathered by students performing a double-slit experiment. The distance between the slits is 0.0700 mm, and the distance to the screen is 2.50 m. The intensity of the central maximum is 6.50 106 W/m2. What is the intensity at y = 0.500 cm? TABLE P35.80arrow_forwardIn the double-slit arrangement of Figure P36.13, d = 0.150 mm, L = 140 cm, = 643 nm. and y = 1.80 cm. (a) What is the path difference for the rays from the two slits arriving at P? (b) Express this path difference in terms of . (c) Does P correspond to a maximum, a minimum, or an intermediate condition? Give evidence for your answer. Figure P36.13arrow_forwardA beam of 580-nm light passes through two closely spaced glass plates at close to normal incidence as shown in Figure P27.23. For what minimum nonzero value of the plate separation d is the transmitted light bright?arrow_forward
- 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?arrow_forwardFigure P36.53 shows two thin glass plates separated by a wire with a square cross section of side length w, forming an air wedge between the plates. What is the edge length w of the wire if 42 dark fringes are observed from above when 589-nm light strikes the wedge at normal incidence? FIGURE P36.53arrow_forwardIn 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 P36.10arrow_forward
- A monochromatic beam of light of wavelength 500 nm illuminates a double slit having a slit separation of 2.00 105 m. What is the angle of the second-order bright fringe? (a) 0.050 0 rad (b) 0.025 0 rad (c) 0.100 rad (d) 0.250 rad (e) 0.010 0 radarrow_forwardInterference fringes are produced using Lloyds mirror and a source S of wavelength = 606 nm as shown in Figure P36.41. Fringes separated by y = 1.20 mm are formed on a screen a distance L = 2.00 m from the source. Find the vertical distance h of the source above the reflecting surface. Figure P36.41arrow_forwardIn Figure P37.18, let L = 120 cm and d = 0.250 cm. 0T he slits are illuminated with coherent 600-nm light. (Calculate the distance y from the central maximum for which the average intensity on the screen is 75.0% of the maximum.arrow_forward
- Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at λ2 and an intensity maximum is observed at λ1, where λ1 > λ2. (a) Assuming no intensity minima are observed between λ1 and λ2, find an expression for the integer m in Equations 27.13 and 27.14 in terms of the wavelengths λ1 and λ2. (b) Assuming n = 1.40, λ1 = 500 nm, and λ2 = 370 nm, determine the best estimate for the thickness of the film.arrow_forwardDiffraction occurs for all types of waves, including sound waves. High-frequency sound from a distant source with wavelength 9.00 cm passes through a slit 12.0 cm wide. A microphone is placed 8.00 m directly in front of the center of the slit, corresponding to point O in Fig. The microphone is then moved in a direction perpendicular to the line from the center of the slit to point O. At what distances from O will the intensity detected by the microphone be zero?arrow_forward= 35. Figure P36.35 shows a radio-wave transmitter and a receiver separated by a distance d 50.0 m and both a distance h = 35.0 m above the ground. The receiver can receive sig- nals both directly from the transmitter and indirectly from signals that reflect from the ground. Assume the ground is level between the transmitter and receiver and a 180° phase shift occurs upon reflection. Determine the longest wave- lengths that interfere (a) constructively and (b) destructively. h Transmitter d Receiver Figure P36.35 Problems 35 and 36.arrow_forward
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