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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
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- A 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_forwardIn 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_forward
- 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 P36.10arrow_forwardA 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_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
- Interference 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_forwardBoth 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_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
- Light of wavelength 470 nm passes through a double slit, yielding a diffraction pattern whose graph of intensity I versus angular position e is shown in the figure. Calculate (a) the slit width and (b) the slit separation. If Im = 7.1 mW/cm2 what are the intensities of the (c) m 1 and (d) m = 2 interference fringes? 9. e (degrees) Units (a) Number 4496 Units (b) Number 1.798e4 nm UnitsmW/m^2 (c) Number 5.75e4 UnitsmW/m^2 (d) Number | 1.15e5 Intensity (mW/cm²)arrow_forward35. Figure P36.35 shows a radio-wave transmitter and a receiver separated by a distance d - 50.0 m and both a distance A - 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. Transmitter Recriver Figure P36.35 Problems 35 and 36.arrow_forwardA red He-Ne laser and a green Kr-Ar laser shine through a double slit, where the spacing between the slits is 50.0 um. The red laser has a wavelength of 632.8 nm while the green laser has a wavelength of 514.5 nm. The distance between the central bright spot and the first red fringe is 3.1 cm. The small angle approximation can be assumed in this question. Recall u = 10-6 n = 2 n = 1 n = 1 Central bright spot Part A What is the distance between the screen and the double slit? Hνα ΑΣφ D = m Submit Request Answer Part B How far (in centimeters) from each side of the first red fringe is a green fringe located? (Find r1 and rz on the screen illustrated above) ? T1, r2 = cm Submit Request Answerarrow_forward
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