Manufacturers of wire (and other objects of small dimension) sometimes use a laser to continually monitor the thickness of theproduct. The wire intercepts the laser beam, producing a diffraction pattern like that of a single slit of the same width as the wirediameter (the figure below). Suppose a helium-neon laser, of wavelength 632.8 nm, illuminates a wire, and the diffraction patternappears on a screen at distance L = 2.75 m. If the desired wire diameter is 1.44 mm, what is the observed distance between thetwo 11-th-order minima (one on each side of the central maximum)?Wire-makingmachineWireHe-NelaserUnitsNumber

Given data:Wavelength helium – neon laser = 632.8 nm = 632.8 x 10-9 mDistance between the slit and…

Answered: Manufacturers of wire (and other…

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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Consider the single-slit diffraction pattern for =600 nm, D=0.025 mm , and x=2.0 m. Find the intensity in terms of Io at =0.5 , 1.0°, 1.5°, 3.0°, and 10.0°.
Coherent light rays of wavelength strike a pair of slits separated by distance d at an angle 1, with respect to the normal to the plane containing the slits as shown in Figure P27.14. The rays leaving the slits make an angle 2 with respect to the normal, and an interference maximum is formed by those rays on a screen that is a great distance from the slits. Show that the angle 2 is given by 2=sin1(sin1md) where m is an integer.
Two slits each of width 1800 nm and separated by the center-to-center distance of 1200 nm are illuminated by plane waves from a krypton ion laser-emitting at wavelength 461.9 nm. Find the number of interference peaks in the central diffraction peak.
Consider a single-slit diffraction pattern for =589 nm, projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?
The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.085 nm are used?
As a single crystal is rotated in an x-ray spectrometer (Fig. 3.22a), many parallel planes of atoms besides AA and BB produce strong diffracted beams. Two such planes are shown in Figure P3.38. (a) Determine geometrically the interplanar spacings d1 and d2 in terms of d0. (b) Find the angles (with respect to the surface plane AA) of the n = 1, 2, and 3 intensity maxima from planes with spacing d1. Let = 0.626 and d0 = 4.00 . Note that a given crystal structure (for example, cubic) has interplanar spacings with characteristic ratios, which produce characteristic diffraction patterns. In this way, measurement of the angular position of diffracted x-rays may be used to infer the crystal structure. Figure P3.38 Atomic planes in a cubic lattice.
An apparatus is formed by a laser, a single slit of width a and a shield at distance L onto which the diffraction pattern is projected. It is verified that the central maximum has width W. Some processes (listed below) are performed. Present as an answer the sum of the numbers of the processes that result in a central maximum with 2W width1- Doubles the wavelength2- Double the laser power4- Fold the bulkhead distance8 - Halve the wavelength16 - Double the slit width32- Decrease by half the distance from the bulkhead64 - Decrease the slit width by half128 - Making the light pass through a material with a refractive index equal to 2 before reaching the slit256 - Sink the entire apparatus in a liquid with a refractive index equal to 2512 - Cut laser power in half
A He-Ne gas laser which produces monochromatic light of a known wavelength ? =6.35 ? 10^−7 ? is used to calibrate a reflection grating in a spectroscope. The first-orderdiffraction line is found at an angle of 22 degrees to the incident beam. How many lines per meter are there on the grating?
Monochromatic laser light flows through a small slit in a thin aluminum plate and generates a diffraction pattern on a screen 0.620 m from the slit in a huge vacuum chamber. When the aluminum plate is heated to 20.0C, the width of the diffraction pattern's center maximum is 2.75 mm. When the temperature of the plate is increased to 520.0C, what is the change in the breadth of the center maximum? When the temperature is raised, does the breadth of the center diffraction maximum rise or decrease?
Young's experiment uses a laser with a wavelength λ = 632.8 nm, a slit separation of 0.5 mm and an observation distance of 40 cm. What is the separation of the stripes if the experiment is performed in (a) air (n = 1,0003), (b) a carbon dioxide environment (n = 1,0005), and (c) in water (n = 1,333)?
Consider a double-slit diffraction experiment with slits of width 0.260 mm. Monochromatic light of wavelength 435 nm is used. If the value of the parameter for a point that is an angular distance of 0.0120 rad from the center of the central diffraction peak is 31.76 rad, what must be the slit separation (in mm)?
A He-Ne gas laser which produces monochromatic light of a known wavelength ? =6.35 ? 10^−7 m is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 22 degrees to the incident beam. How many lines per meter are there on the grating?

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