A transmission grating is used with light incident normal to its plane. The width of each slit is one-third the spacing between slits. By considering single-slit diffraction, show that the third-order (j = 3) multislit diffraction maxima are missing from the diffraction pattern of the grating.
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- In a Young's double-slit experiment, a set of parallel slits with a separation of 0.108 mm is illuminated by light having a wavelength of 584 nm and the interference pattern observed on a screen 3.50 m from the slits. (a) What is the difference in path lengths from the two slits to the location of a third order bright fringe on the screen? answer in ?m (b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern? answer in ?mAn experiment is setup to measure the diameter of the sphere in the diagram using sizing measurements based on interference. A thin piece of glass slab is placed one side of a highly reflective substrate. A yellow light created by Sodium wavelength = 589.3nm having a normally incident. Fringes can be observed on the glass from the interference. With a gap between the two bright fringes is measured to be g = 0.118mm, with an overall length for the setup to be L = 20mm. The setup will be placed in air having n = 1. What is the diameter of the sphere? WFringes in the Thomas Young experiment are produced using sodium light of wavelength 613 nm and two slits which are 1.1 mm apart. If the fringes are formed on a screen 0.9 m away from the slits, how far is the third order bright fringe from the middle of the screen? Give your answer in millimeters (mm).
- The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See figure (b).) (a) Does the intensity drop to one-half the maximum value when sin²α = a²/2? (b) Is a = 1.39 rad (about 80°) a solution to the transcendental equation of (a)? (c) Is the FWHM AÐ = 2sin¹(0.442 A/a), where a is the slit width? Calculate the FWHM of the central maximum for slit width (d) 1.17 A, (e) 5.03 A, and (f) 11.7 A. 20 20 Relative intensity 15 10 0.8 0.6 a=2 0.4 0.2 5 05 8 (degrees) (a) 10 15 20 20 Relative intensity 1.0 0.8 0.6 -A0- 0.4 0.2 a= 52 20 15 10 5 0 5 10 15 20 (degrees) (b)There is a circular slit with its radius a = 0.1mm. The distance between the slit plane and detector plane is given by R=1m. Roughly estimate the requirement of the wavelength of incident light for Fraunhofer diffraction with appropriate justification.In a Young’s double-slit experiment, two parallel slits with a slit separation of 0.100 mm are illuminated by light of wavelength 589 nm, and the interference pattern is observed on a screen located 4.00 m from the slits. (a) What is the difference in path lengths from each of the slits to the location ofthe center of a third-order bright fringe on the screen? (b) What is the difference in path lengths from the two slits to the location of the center of the third dark fringe away from the center of the pattern?