Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 36, Problem 42PQ
To determine
The expression for resolving power of this diffraction grating for the first order maxima of two similar
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A. An x-ray beam with wavelength 0.130 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 62.0∘. What is the spacing d between the planes of the crystal? Express your answer in nanometers to three significant figures.
B.Find the angle θ2 at which you will find a second maximum. Express your answer in degrees to three significant figures.
A laser beam with wavelength λ = 675 nm hits a grating with n = 4750 grooves per centimeter.
A. Calculate the grating spacing, d, in centimeters.
B. Find the sin of the angle, θ2, at which the 2nd order maximum will be observed, in terms of d and λ.
C. Calculate the numerical value of θ2 in degrees.
Problem 2
For wavelengths in the visible spectrum, the index of refraction of a cer-
tain type of crown glass can be approximated by the relation n(A) = 1.5255 +
(4825 nm²)/x?.
a. Find the index of refraction of this glass for 400 nm light, 500 nm light,
and 700 nm light.
b. Find the phase velocity, in this glass, for a pulse with frequency com-
ponents centered around 500 nm.
Chapter 36 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 36.2 - Prob. 36.1CECh. 36.3 - Prob. 36.2CECh. 36.4 - Prob. 36.3CECh. 36.5 - Prob. 36.4CECh. 36.5 - Prob. 36.5CECh. 36 - Many circular apertures are adjustable, such as...Ch. 36 - Many of the images we regularly look at are...Ch. 36 - The hydrogen line at 1420.4 MHz corresponds to the...Ch. 36 - Prob. 4PQCh. 36 - Estimate the diffraction-limited resolution of the...
Ch. 36 - Prob. 6PQCh. 36 - Prob. 7PQCh. 36 - Prob. 8PQCh. 36 - Prob. 9PQCh. 36 - Prob. 10PQCh. 36 - Prob. 11PQCh. 36 - Prob. 12PQCh. 36 - Prob. 13PQCh. 36 - Prob. 14PQCh. 36 - Prob. 15PQCh. 36 - Prob. 16PQCh. 36 - Prob. 17PQCh. 36 - Prob. 18PQCh. 36 - Prob. 19PQCh. 36 - Prob. 20PQCh. 36 - Prob. 21PQCh. 36 - Prob. 22PQCh. 36 - Prob. 23PQCh. 36 - Prob. 24PQCh. 36 - Light of wavelength 566 nm is incident on a...Ch. 36 - Prob. 26PQCh. 36 - Prob. 27PQCh. 36 - Prob. 28PQCh. 36 - Prob. 29PQCh. 36 - Prob. 30PQCh. 36 - A light source emits a mixture of wavelengths from...Ch. 36 - Prob. 32PQCh. 36 - Prob. 33PQCh. 36 - Prob. 34PQCh. 36 - Prob. 35PQCh. 36 - Prob. 36PQCh. 36 - Prob. 37PQCh. 36 - Prob. 38PQCh. 36 - Prob. 39PQCh. 36 - Prob. 40PQCh. 36 - Prob. 41PQCh. 36 - Prob. 42PQCh. 36 - Prob. 43PQCh. 36 - Prob. 44PQCh. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - Prob. 47PQCh. 36 - Prob. 48PQCh. 36 - Problems 49 and 50 are paired. C Optical flats are...Ch. 36 - Optical flats are flat pieces of glass used to...Ch. 36 - Prob. 51PQCh. 36 - Prob. 52PQCh. 36 - Figure P36.53 shows two thin glass plates...Ch. 36 - Viewed from above, a thin film of motor oil with...Ch. 36 - Newtons rings, discovered by Isaac Newton, are an...Ch. 36 - Prob. 56PQCh. 36 - What is the radius of the beam of an argon laser...Ch. 36 - Prob. 58PQCh. 36 - A diffraction grating with 428 rulings per...Ch. 36 - How many rulings must a diffraction grating have...Ch. 36 - Prob. 61PQCh. 36 - White light is incident on a diffraction grating...Ch. 36 - X-rays incident on a crystal with planes of atoms...Ch. 36 - Prob. 64PQCh. 36 - Prob. 65PQCh. 36 - Prob. 66PQCh. 36 - The fringe width b is defined as the distance...Ch. 36 - The fringe width is defined as the distance...Ch. 36 - Prob. 69PQ
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- White light is incident on a diffraction grating that has 2.85 103 rulings per centimeter, producing first-order maxima at 6.55, 8.75, and 11.2. a. What are the wavelengths responsible for these three first-order maxima? b. At which angles do these wavelengths produce second-order maxima?arrow_forward(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 m. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.arrow_forward(a) Show that a 30,000 line per centimeter grating will not produce a maximum for visible light. (b) What is the longest wavelength for which it does produce a first-order maximum? (c) What is the greatest number of line per centimeter a diffraction grating can have and produce a complete second-order spectrum for visible light?arrow_forward
- How many rulings must a diffraction grating have if it is just to resolve the sodium doublet (589.592 nm and 588.995 nm) in the second-order spectrum?arrow_forwardMonochromatic light of wavelength 530 nm passes through a horizontal single slit of width 1.5 m in an opaque plate. A screen of dimensions 2.0m2.0m is 1.2 m away from the slit. (a) Which way is the diffraction pattern spread out on the screen? (b) What are the angles of the minima with respect to the center? (c) What are the angles of the maxima? (d) How wide is the central bright fringe on the screen? (e) How wide is the next bright fringe on the screen?arrow_forwardRed light of wavelength of 700 nm falls on a double slit separated by 400 nm. (a) At what angle is the first-order maximum in the diffraction pattern? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?arrow_forward
- (a) What is the minimum angular spread of a 633-nm wavelength He-Ne laser beam that is originally 1.00 mm in diameter? (b) If this laser is aimed at a mountain cliff 15.0 km away, how big will the illuminated spot be? (c) How big a spot would be illuminated on the moon, neglecting atmospheric effects? (This might be done to hit a corner reflector to measure the round-trip time and, hence, distance.)arrow_forward(a) The dwarf planet Pluto and its moon, Charon, are separated by 19,600 km. Neglecting atmospheric effects, should the 5.08-m-diameter Palomar Mountain telescope be able to resolve these bodies when they are 4.50109 km from Earth? Assume an average wavelength of 550 nm. (b) In actuality, it is just barely possible to discern that Pluto and Charon are separate bodies using a ground-based telescope. What are the reasons for this?arrow_forwardTo save money on making military aircraft invisible to radar, an inventor decides to coat them with a nonreflective material having an index of refraction of 1.20, which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers. (a) What thickness should the coating be to inhibit the reflection of 4.00-cm wavelength radar? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?arrow_forward
- What is the radius of the beam of an argon laser with wavelength 454.6 nm when viewed 50.0 km away from the laser if the lasers aperture has a radius of 3.00 mm?arrow_forwardA diffraction grating with 2000 lines per centimeter is used to measure the wavelengths emitted by a hydrogen gas discharge tube. (a) At what angles will you find the maxima of the two first-order blue lines of wavelengths 410 and 434 nm? (b) The maxima of two other first-order lines are found at 1=0.097 rad and 2=0.132 rad . What are the wavelengths of these lines?arrow_forwardProblem 2. A) A Michelson interferometer uses light of wavelength 500 nm. The irradiance of the beam exiting the laser is IL. What are the possible differences in the lengths of the arms of the interferometer when the irradiance at the detector is IL/3? B) Young's Double slit experiment is performed with HeNe laser wavelength 632.8 nm. The screen is 2 m from the slits and the slit separation is 0.2 mm. Find the distance of the 3th bright fringe from the center of the interference pattern on the screen (call the central bright fringe the "Oth" fringe).arrow_forward
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