Required informationA laser has a wavelength of 530 nm. A grating and a lens are used to split the beam into three parallel beams spaced 1.85cm apart.What is the minimal value of the slit spacing so that the grating produces three and only three beams?µm Required informationA laser has a wavelength of 530 nm. A grating and a lens are used to split the beam into three parallel beams spaced 1.85cm apart.What is the maximal value of the slit spacing so that the grating produces three and only three beams?µm

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Required information A laser has a wavelength of 530 nm. A grating and a lens are used to split the beam into three parallel beams spaced 1.85 cm apart. What is the minimal value of the slit spacing so that the grating produces three and only three beams?

Required information A laser has a wavelength of 530 nm. A grating and a lens are used to split the beam into three parallel beams spaced 1.85 cm apart. What is the minimal value of the slit spacing so that the grating produces three and only three beams?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 72P: X-rays of wavelength 0.103 nm reflects off a crystal and a second-order maximum is recorded at a...

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Youngs double-slit experiment underlies the instrument landing system used to guide aircraft to safe landings at some airports when the visibility is poor. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her plane with a runway as suggested in Figure P27.2. Two radio antennas (the black dots in the figure) are positioned adjacent to the runway, separated by d = 40.0 m. The antennas broadcast unmodulated coherent radio waves at 30.0 MHz. The red lines in Figure P27.2 represent paths along which maxima in the interference pattern of the radio waves exist. (a) Find the wavelength of the waves. The pilot locks onto the strong signal radiated along an interference maximum and steers the plane to keep the received signal strong. If she has found the central maximum, the plane will have precisely the correct heading to land when it reaches the runway as exhibited by plane A. (b) What If? Suppose the plane is flying along the first side maximum instead as is the case for plane B. How far to the side of the runway centerline will the plane be when it is 2.00 km from the antennas, measured along its direction of travel? (c) It is possible to tell the pilot that she is on the wrong maximum by sending out two signals from each antenna and equipping the aircraft with a two-channel receiver. The ratio of the two frequencies must not be the ratio of small integers (such as 34). Explain how this two-frequency system would work and why it would not necessarily work if the frequencies were related by an integer ratio.
Youngs double-slit experiment underlies the instrument landing system used to guide aircraft to sale landings at some airports when the visibility is pool. Although real systems are more complicated than the example described here, they operate on the same principles. A pilot is trying to align her plane with a runway as suggested in Figure P37.22. Two radio antennas (the black dots in the figure) are positioned adjacent to the runway, separated by d = 40.0 m. The antennas broadcast unmodulated coherent radio waves at .10.0 MHz. The red lines in Figure P37.22 represent paths along which maxima in the interference pattern of the radio waves exist. (a) Find the wavelength of the waves. The pilot locks onto the strong signal radiated along an interference maximum and steers the plane to keep the received signal strong. If she has found the central maximum, the plane will have precisely the correct heading to land when it reaches the runway as exhibited by plane A. (b) What If? Suppose the plane is living along the first side maximum instead as is the case for plane B. How far to the side of the runway centerline will the plane be when it is 2.00 km from the antennas, measured along its direction of travel? (c) It is possible to tell the pilot that she is on the wrong maximum by sending out two signals from each antenna and equipping the aircraft with a two-channel receiver. The ratio of the two frequencies must not be the ratio of small integers (such as 34). Explain how this two-frequency system would work and why it would not necessarily work if the frequencies were related by an integer ratio.
if the distance between the slits is doubled in Youngs experiment, what happens to the width of the central maximum? (a) The width is doubled. (b) The width is unchanged. (c) The width is halved.
X-rays of wavelength 0.103 nm reflects off a crystal and a second-order maximum is recorded at a Bragg angle of 25.5°. What is the spacing between the scattering planes in this crystal?
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.
Integrated Concepts (a) During laser vision correction, at brief burst at 193 nm ultraviolet light is projected onto the cornea of the patient. It makes a spot 1.00 mm in diameter and deposits 0.500 mJ of energy. Calculate the depth of the layer ablated, assuming the corneal tissue has the same properties as water and is initially at 34.0°C. The tissue’s temperature is increased to 100°C and evaporated without further temperature increase. (b) Does your answer imply that the shape of the cornea can be ?nely controlled?
X-rays incident on a crystal with planes of atoms located 0.378 nm apart produce a diffraction pattern in which a first-order maximum is observed at an angle of 14.2. a. What is the wavelength of the X-rays incident on the crystal? b. How many orders are visible in the diffraction pattern?
Radio telescopes are telescopes used for the detection of radio emission from space. Because radio waves have much longer wavelengths than visible light, the diameter of a radio telescope must be very large to provide good resolution. For example, the radio telescope in Penticton, BC in Canada, has a diameter of 26 m and can be operated at frequencies as high as 6.6 GHz. (a) What is the wavelength corresponding to this frequency? (b) What is the angular separation of two radio sources that can be resolved by this telescope? (c) Compare the telescope’s resolution with the angular size of the moon.
Light from the He-Ne laser of wavelength 633 nm passes through a circular aperture. It is observed on a screen 2.00 m behind the aperture. The width of the central maximum is 3.40 cm what is the diameter of the hole? A. 45.4 micro meters B. 90.9 micro meters C. 3.40 centi meters D. 74.5 micro meters E. 633 nano meters
4. Why do longitudinal modes occur in a laser beam? A HeNe laser (n = 1) has a cavity length of 60cm and an output wavelength of 632.8 nm. Find the mode spacing.
X-rays of wavelength 0.200 nm are reflected from a certain crystal, and the first-order maximum occurs at an angle of 15.2°. What value does this give for the interplanar spacing of the crystal? nm
Question 8 In TEM, we can obtain a diffraction pattern of a thin sample through the use of objective apertures that act as a barrier for incoming electron radiation in the microscope column. Due to the small angle that the beam makes as it transmits through the crystal planes of TEM samples, the Bragg condition can be modified to: nd = 2d0B If electrons with wavelength (3.60x10^-12) m travel down and transmit through a thin Cu film sample with a lattice parameter of (4.8500x10^-10) m and the distance R between the transmitted and first order (111) spot is (6.872x10^-3) m, what is the camera length in meters? Express your answer in scientific notation of the form X.YZ x 10^n. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10