A double slit separated by 0.0576 mm is placed 1.35 m from a screen. (a) If yellow light of wavelength 589 nm strikes the double slit, what is the separation between the zeroth-order and first-order maxima on the screen? cm (b) If blue light of wavelength 411 nm strikes the double slit, what is the separation between the second-order and fourth-order maxima? cm

A double slit separated by 0.0576 mm is placed 1.35 m from a screen. (a) If yellow light of wavelength 589 nm strikes the double slit, what is the separation between the zeroth-order and first-order maxima on the screen? cm (b) If blue light of wavelength 411 nm strikes the double slit, what is the separation between the second-order and fourth-order maxima? cm

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 68PQ

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Similar questions

A beam of monochromatic green light is diffracted by a slit of width 0.550 mm. The diffraction pattern forms on a wall 2.06 m beyond the slit. The distance between the positions of zero intensity on both sides of the central bright fringe is 4.10 mm. Calculate the wavelength of the light.
A monochromatic light of unknown wavelength is incident on a slit of width 20 m. A diffraction pattern is seen at a screen 2.5 m away where the central maximum is spread over a distance of 10.0 cm. Find the wavelength.
A diffraction pattern is produced on a screen 1.40 m from a single slit, using monochromatic light of wavelength 5.00 102 nm. The distance from the center of the central maximum to the first-order maximum is 3.00 mm. Calculate the slit width. Hint: Assume that the first-order maximum is halfway between the first- and second-order minima.
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)
An effect analogous to two-slit interference can occur with sound waves, instead of light. In an open field, two speakers placed 1.30 m apart are powered by a single-function generator producing sine waves at 1200-Hz frequency. A student walks along a line 12.5 m away and parallel to the line between the speakers. She hears an alternating pattern of loud and quiet, due to constructive and destructive interference. What is (a) the wavelength of this sound and (b) the distance between the central maximum and the first maximum (loud) position along this line?
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
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 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 slits are separated by 0.180 mm. An interference pattern is formed on a screen 80.0 cm away by 656.3-nm light. Calculate the fraction of the maximum intensity a distance y = 0.600 cm away from the central maximum.
Red light (wavelength 632.8 nm in air) from a Helium-Neon laser is incident on a single slit of width 0.05 mm. The entire apparatus is immersed in water of refractive index 1.333. Determine the angular width of the central peak.
A monochromatic beam of light of wavelength .500 nm illuminates a double slit having a slit separation of 2.00 10-5 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 rad
A wide beam of laser light with a wavelength of 632.8 nm is directed through several narrow parallel slits, separated by 1.20 mm, and falls on a sheet of photographic film 1.40 m away. The exposure time is chosen so that the film stays unexposed everywhere except at the central region of each bright fringe. (a) Find the distance between these interference maxima. The film is printed as a transparency; it is opaque everywhere except at the exposed lines. Next, the same beam of laser light is directed through the transparency and allowed to fall on a screen 1.40 m beyond. (b) Argue that several narrow, parallel, bright regions, separated by 1.20 mm, appear on the screen as real images of the original slits. (A similar train of thought, at a soccer game, led Dennis Gabor to invent holography.)