Concept explainers
Assume Figure 38.1 was photographed with red light of a single wavelength λ0. The light passed through a single slit of width a and traveled distance L to the screen where the photograph was made. Consider the width of the central bright fringe, measured between the centers of the dark fringes on both sides of it. Rank from largest to smallest the widths of the central fringe in the following situations and note any cases of equality. (a) The experiment is performed as photographed. (b) The experiment is performed with light whose frequency is increased by 50%. (c) The experiment is performed with
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Chapter 38 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- In a double split experiment, the slits were cut 1.9 cm apart and the screens are placed 8.81 m apart. What is the wavelength of the light that produceds a fourth order fringe on the screen 3.7 cm from the central fringe? Put answer in μm.arrow_forwardA "diffraction" grating is made up of slits of width 310nm with a 930nm separation between centers. The grating is illuminated by monochromatic plane waves, λ=615nm, with the angle of incidence zero. (a) How many diffraction (or interference if you prefer that nomenclature) maxima are there? (b) Find the width of the spectral lines observed in the first order if the grating has 1120 slitsarrow_forwardA diffraction grating is made up of slits of width 300 nm with separation 900 nm. The grating is illuminated by monochromatic plane waves of wavelength l = 600 nm at normal incidence. (a) How many maxima are there in the full diffraction pattern? (b)What is the angular width of a spectral line observed in the first order if the grating has 1000 slits?arrow_forward
- 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)arrow_forwarda beam of white light is shined at normal incidence onto the outside of a soap bubble (index of soap solution = 1.340). An observer looking at the bubble, opposite to the direction of the beam, notices that green light (Lambda = 555.0 nm) is particularly bright in the reflected spectrum. What is the second thinnest wall thickness of the bubble?arrow_forwardA beam of light with wavelength of 1.00 µm and M2 = 20 is incident on an aperture of 1.5 mm diameter. a) Calculate the divergence angle of the beam in degrees (give the cone full-angle). b) Calculate the diameter of the beam at a distance of 10.00 m away from the aperture in the propagation direction in units of cm. c) It is given that the longitudinal (temporal) coherence length is 70 times the transverse (spatial) coherence length. Calculate the wavelength linewidth of the light in units of pm.aarrow_forward
- Ex. 9: In Young's experiment interference bands are produced on the screen placed at 1.5 m from the two slits separated by a distance of 0.15 mm and illuminated by a light O of wavelength 4500 A, find (1) the fringe width and (2) the change in fringe width if screen is brought towards the slit by 50 cm.arrow_forwardThe interplanar distance of (101) plane of ZnO crystal is 0.45 nm. If the first-order diffraction maximum is observed at an incidence angle of 36.2°, what is the wavelength of the X-ray scattering from this crystal? And estimate the crystallite size of the ZnO nanomaterial if FWHM of (101) plane is 2.51° (degree to radian Degree x T/180) and k = 0.9.arrow_forwardA 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_forward
- In a modified Young's double slit experiment, a monochromatic uniform and parallel beam of light of wavelength 6000 A and intensity (10/) Wm2 is incident normally on two apertures A and B of radii 0.001 m and 0.002 m respectively. A perfectly transparent film of thickness 2000 A and refractive index 1.5 for the wavelength of 6000A is placed in front of aperture A (see figure). Calculate the power (in W) received at the focal spot F of the lens. The lens is symmetrically placed with respect to the apertures. Assume that 10% of the power received by each aperture goes in the original direction and is brought to the focal spot.arrow_forwardIn a double slit experiment, the distance between the slits is 0.2 mm and the distance to the screen is 100 cm. What is the phase difference (in degrees) between the waves from the two slits arriving at a point 5 mm from the central maximum when the wavelength is 400 nm? (Convert your result so the angle is between 0 and 360°.)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_forward
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