Concept explainers
(a) By differentiating Equation 4.4, show that the higher-order maxima of the single-slit diffraction pattern occur at values of
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
University Physics Volume 3
Additional Science Textbook Solutions
College Physics
Lecture- Tutorials for Introductory Astronomy
University Physics with Modern Physics (14th Edition)
Physics: Principles with Applications
Sears And Zemansky's University Physics With Modern Physics
Essential University Physics: Volume 2 (3rd Edition)
- A 475 nm wavelength spectral line is actually a doublet, 0.0043 nm separation. (a) What is the smallest number of lines that a diffraction network needs to have to separate this doublet in the 2nd order spectrum? (b) If this network is 10 cm long, in what direction will the line be observed in this spectrum? What will be the angular separation between the two components?arrow_forwardIf we treat a double slit experiment as a point-like source where distances from the slits are measured by r₁ and r2 respectively, a plane wave from each slit would Ae-i where ;=kr; -wt+do and 01 - 02= take the form ₁ Ae-i1 and 2: = = k(r₁ r₂). 1. Solve for the probability density ₁+ 22 in terms of A, k, r₁ and r2. -arrow_forwardIf the wavelength l of the Xrays is too large relative to the spacing of planes in the crystal, no Bragg diffraction will be seen because sin u would be larger than 1 in the Bragg equation, even for n 5 1. Calculate the longest wavelength of Xrays that can give Bragg diffraction from a set of planes separated by 4.20 Å.arrow_forward
- 1.30. Suppose that a thin piece of glass were placed in front of the lower slit in a double-slit apparatus so that the amplitude for a photon of wavelength λ to reach that slit differs in phase by 180° with the amplitude to reach the top slit. (a) Describe in detail the interference pattern on the screen. At what angles will there be bright fringes? (b) What is the minimum thickness of glass required, assuming the index of refraction for the glass is n?arrow_forwardQ1/ A/ Consider a resonator consisting of two concave spherical mirrors both with radius of curvature 4 m and separated by a distance of 1 m. Calculate the minimum beam diameter of the TEMy mode at the resonator center and on the mirrors when the laser oscillation is Art laser wavelength 2=514.5 nm. Then, Find if this cavity is stable or not. B/ One of the mirrors in A is replaced by a concave mirror of 1.5m radius of curvature, calculate the position of minimum beam radius. Then calculate the beam waist and radius of curvature at 150 cm from M1.arrow_forwardIn young's double slit experiment, the fringe width obtained by using monochromatic light of wavelength 6000 Å is 2 mm. If the whole apparatus is immersed in water of R. I. 1.33, then the change in fringe width will bearrow_forward
- Problem 5: Prove that the coherence distance of the laser emission is d = 4 and find its valued if the emission line exposure is 450 MHzarrow_forward) Consider a crystal consisting of m + 1 lattice planes of spacing d, of total thickness t = md, being set for diffraction as depicted in Fig. 2. At the incidence angle ӨB, Braggs law is satisfied. Explain the phenomenon through which the angles Ө1 and Ө2 are the limiting angles at which the diffracted intensity falls to zero.arrow_forwardThe analysis of any two-point source interference pattern and a successful determination of wavelength demands an ability to sort through the measured information and equating the values with the symbols in Young's equation. Apply your understanding by interpreting the following statements and identifying the values of y, d, m and L. Finally, perform some conversions of the given information such that all information share the same unit. Consecutive bright bands on an interference pattern are 3.5 cm apart when the slide containing the slits is 10.0 m from the screen. The slit separation distance is 0.050 mm. y= ________ d=________ m=_______ L=________arrow_forward
- A thin crystalline layer has to be characterized in terms of lattice constant (roughly 0.56 nm, twice the atom’s distance). You try to apply the technique of x-ray diffraction based on the Kß-line of 42Mo (ignore any screening effects). At which diffraction angle(s) can we expect a signal?arrow_forwardConsider the interference pattern produced by two parallel slits of width a and separation d, in which d = 3a. The slits are illuminated by normally incident light of wavelength λ. (a) First we ignore diffraction effects due to the slit width. At what angles θ from the central maximum will the next four maxima in the two-slit interference pattern occur? Your answer will be in terms of d and λ. (b) Now we include the effects of diffraction. If the intensity at θ = 0° is I0, what is the intensity at each of the angles in part (a)? (c) Which double-slit interference maxima are missing in the pattern?arrow_forwardLight of wavelength 633 nm is incident on a pair of identical stits of width 0.15 mm and center-to-center separation of 1.5 mm. The diffraction pattern is observed on a screen at distance 4 m. Calculate the spacing between consecutive zeros of intensity (in mm to 2 d.p.); and calculate how many peaks in total (on both sides) have intensity above 20 percent of the on-axis peak. (Hint: note sinc 2.0 = 0.454) The spacing of zeros is 1.69 mm, and the total number of peaks with at least 20 percent of central intensity isarrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON