Interference: Calculate the angle between propagation directions of two waves to obtain an interference pattern of two monochromatic plane waves at 530 nm (green light) with period of interference L = 1 mm

Interference: Calculate the angle between propagation directions of two waves to obtain an interference pattern of two monochromatic plane waves at 530 nm (green light) with period of interference L = 1 mm

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter36: Wave Optics

Section: Chapter Questions

Problem 31AP: Two coherent waves, coming from sources at different locations, move along the x axis. Their wave...

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Concept explainers

Diffraction of light

In physics, the term diffraction is defined as the bending of light around the corners of the obstacle. As a light ray passes by an aperture, it bends around the edges or through slits, it spreads out through a narrow opening. The diffracted light will produce fringes of bright and dark or colored bands which are labeled as a diffraction pattern.

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1. Interference: Calculate the angle between propagation directions of two waves to obtain an
interference pattern of two monochromatic plane waves at 530 nm (green light) with period of
interference L = 1 mm

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Two coherent waves, coming from sources at different locations, move along the x axis. Their wave functions are E1=860sin[2x1650924t+6] and E2=860sin[2x2650924t+8] where E1 and E2 are in volts per meter, x1 and x2 are in nanometers, and t is in picoseconds. When the two waves are superposed, determine the relationship between x1, and x2 that produces constructive interference.
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.
Consider a wave passing through a single slit. What happens to the width of the central maximum of its diffraction pattern as the slit is made hall' as wide? (a) It becomes one-half as wide. (b) It becomes one-half as wide. (c) Its width does not change. (d) It becomes twice as wide. (e) It becomes four limes as wide.
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 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.)
Two narrow, parallel slits separated by 0.850 mm are illuminated by 600-nm light, and the viewing screen is 2.80 in away from the slits. (a) What is the phase difference between the two interfering waves on a screen at a point 2.50 mm from the central bright fringe? (b) What is the ratio of the intensity at this point to the intensity at the center of a bright fringe?
In Figure 37.7, show mathematically how many interference maxima are enclosed by the central diffraction maximum in the pattern. Notice that the diagram is generated by using 650-nm light to illuminate two 3.0-m slits separated by 18 m. Figure 37.7 The combined effects of two-slit and single-slit interference. This pattern is produced when 650-nm light waves pass through two 3.0-m slits that are 18 m apart.
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.