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The intensity of light in a diffraction pattern of a single slit is described by the equation
where ϕ = (πa sin θ)/λ. The central maximum is at ϕ = 0, and the side maxima are approximately at
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Chapter 37 Solutions
Physics for Scientists and Engineers
- 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.arrow_forwardThe structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.085 nm are used?arrow_forwardProblem 4: Consider light that has its third minimum at an angle of 21.2° when it falls on a single slit of width 3.95 µm. Randomized Variables 0 = 21.2° w = 3.95 μm Find the wavelength of the light in nanometers. 2 || = sin() cos() cotan() asin() atan() acotan() cosh() tanh() O Degrees tan() acos() sinh() cotanh() Radians π () 7 8 9 E ^^^ 4 5 6 3 1 2 0 + VO BACKSPACE * DEL HOME END CLEARarrow_forward
- Problem 7: Consider light falling on a single slit, of width 1.05 μm, that produces its first minimum at an angle of 33.6°.Randomized Variables θ = 33.6°w = 1.05 μm Calculate the wavelength of the light in nanometers.arrow_forwardYou measure three segments of the distance between a diffraction slit an the screen on which the pattern forms: x1 = (14.7 ± 0.1) cm, x2 = (9.9 ± 0.3) cm, and x3 = (17.2 ± 0.3) cm. What is the uncertainty of the total distance x1 + x2 + x3?arrow_forwardAn electric current through an unknown gas produces several distinct wavelengths of visible light. Consider the first order maxima for the wavelengths 403 nm, 428 nm, 511 nm, and 682 nm of this unknown spectrum, when projected with a diffraction grating of 5,000 lines per centimeter.Randomized Variablesλ1 = 403 nmλ2 = 428 nmλ3 = 511 nmλ4 = 682 nm Part (a) What would the angle (in degrees) be for the 403 nm line? Part (b) What would the angle (in degrees) be for the 428 nm line? Part (c) What would the angle (in degrees) be for the 511 nm line? Part (d) What would the angle (in degrees) be for the 682 nm line? Part (e) Using this grating, what would be the angle (in degrees) of the second-order maximum of the 403 nm line?arrow_forward
- Problem 1: In a double slit experiment the first minimum for 415 nm violet light is at an angle of 42°. Randomized Variables 2 = 415 nm e = 42 ° Find the distance between the two slits in micrometers. d= 8 9 5 6 sin() cos() tan() 7 HOME cotan() asin() acos() E A 4 atan() acotan() sinh() 1 2 3 cosh() tanh() cotanh() END O Degrees O Radians Vol BACKSPACE DEL CLEAR +arrow_forwardFind the angular radius of the tenth bright fringe in a Michelson interfer- ometer when the central-path difference (2d) is (a) 1.50 mm and (b) 1.5 cm. The orange light of a krypton arc is 6057.8 ˚Aand that the interferometer is adjusted in each case so that the first bright fringe forms a maximum at the center of the pattern. Ans: (a) 4.885◦ , (b) 1.542◦arrow_forwardThe diffraction grating is a way of separating or dispersing light of different wavelengths, producing a spectrum of light. The grating interferes light constructively in particular directions: dsinθm=mλdsinθm=mλ For a particular angle, we calculate the wavelength. The grating constant (or line density) is 500 lines per mm -- every millimeter has 500 lines scratched onto it, equally spaced. The quantity d is the distance between the lines, and λ is the light wavelength. In the previous problem, calculate y2, where one of the second-order spots appears on the meter stick. Either that, or show that y2 can't be determined.arrow_forward
- The diffraction grating is a way of separating or dispersing light of different wavelengths, producing a spectrum of light. The grating interferes light constructively in particular directions: dsinθm=mλdsinθm=mλ For a particular angle, we calculate the wavelength. The grating constant (or line density) is 500 lines per mm -- every millimeter has 500 lines scratched onto it, equally spaced. The quantity d is the distance between the lines, and λ is the light wavelength. A meter stick shows the spots, and ym is position on the meter stick of the mth-order light beam. (Negative order is the same as positive order.) Calculate the light wavelength, λ in nm, given this information: The grating constant is 500 lines/mm. L = 31.5 cm y1 = 56.9 cm y-1 = 40.8 cm y0 isn't specified because of computer issues. (It's the average of y1 and y-1.)arrow_forwardThe figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of a Its) Hepre T thickness t and refractive index u is put in front of one of the slits, the a(μµ − 1) - central maximum gets shifted by a distance equal to n fringe widths. If the wavelength of light used is λ, t will be 2nDλ (a) (b) 2Dλ a(μ-1) (c) Dλ a(µ − 1) - D (d) Screen nDλ a(μµ - 1)arrow_forward632.8 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 21.0°, what is the spacing between adjacent grooves in the grating? (In this problem, assume that the light is incident normally on the grating.) μm A helium-neon laser (1 =arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
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