3. Light with wavelength A is projected through a double slit system. As multiples of the wavelength, the slit separation is d = 40 and the slit width is a = 5.0X. What is the intensity at the angle 0 = 6.0° as a fraction of the intensity at 0 = 0°? (Answer 26%)

3. Light with wavelength A is projected through a double slit system. As multiples of the wavelength, the slit separation is d = 40 and the slit width is a = 5.0X. What is the intensity at the angle 0 = 6.0° as a fraction of the intensity at 0 = 0°? (Answer 26%)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter35: Diffraction And Interference

Section: Chapter Questions

Problem 81PQ: Table P35.80 presents data gathered by students performing a double-slit experiment. The distance...

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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 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.
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
A Fraunhofer diffraction pattern is produced on a screen located 1.00 m from a single slit. If a light source of wavelength 5.00 107 m is used and the distance from the center of the central bright fringe to the first dark fringe is 5.00 103 m, what is the slit width? (a) 0.010 0 mm (b) 0.100 mm (c) 0.200 mm (d) 1.00 mm (e) 0.005 00 mm
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 P35.80
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?
A horizontal laser beam of wavelength 632.8 nm has a circular cross section 2.00 nun in diameter. A rectangular aperture is to lie placed in the center of the beam so that when the light falls perpendicularly on a wall 4.50 m away, the central maximum fills a rectangle 110 mm wide and 6.00 mm high. The dimensions are measured between the minima bracketing the central maximum. Find the required (a) width and (b) height of the aperture. (c) Is the longer dimension of the central bright patch in the diffraction pattern horizontal or vertical? (d) Is the longer dimension of the aperture horizontal or vertical? (e) Explain the relationship between these two rectangles, using a diagram.
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,
Consider the double-slit arrangement shown in Figure P37.60, where the slit separation is d and the distance from the slit to the screen is L. A sheet of transparent plastic having an index of refraction n and thickness t is placed over the upper slit. As a result, the central maximum of the interference pattern moves upward a distance y Find y.
(a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7.50 m. At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?
A spacer is cut from a playing card of thickness 2.90 104 m and used to separate one end of two rectangular, optically flat. 3.00-cm long glass plates with n = 1.55, as in Figure P24.24. Laser light at 594 nm shine straight down on the top plate. The plates have a length of 3.00 cm. (a) Count the number of phase reversals for the interfering waves. (b) Calculate the separation between dark interference Kinds observed on the lop plate.
Two closely spaced wavelengths of light are incident on a diffraction grating. (a) Starting with Equation 37.7, show that the angular dispersion of the grating is given by dd=mdcos (b) A square grating 2.00 cm on each side containing 8 000 equally spaced slits is used to analyze the spectrum of mercury. Two closely spaced lines emitted by this element have wavelengths of 579.065 nm and 576.959 nm. What is the angular separation of these two wavelengths in the second-order spectrum?