Lista Difração - Física 3 D

UNIDADE III - DIBRAÇÃO\n1) λ = 4.41.10⁻⁹ m d = 2m\n a1) tg α = 1.5m θ = 0.43°\n 200cm\n d = dsenα = 2.44.10⁻⁹\n d = d(1.48.10⁻⁹ m) = 0.11.10⁻³ m = 0.11mm\n2) λ = 6.33.10⁻⁹ m θ = 4°\n d = d.1.633.10⁻⁹ = 6.04.10⁻⁵\n sen 0.6 = 60.4μm\n3) λ = 0.35.10⁻⁷ m λ = 550.10⁻⁹\n dsen(8.75.10⁴) = 4.550.10⁻⁹\n a) d = 2.5cm\n tg α = 0.35.10⁻⁷ = 2.875.10⁹\n b) sen α = 1.550.10⁹ = 2.82.10⁻⁴ rad\n 25.10⁷\n4) λ = 590.10⁻⁹ m d = 0.4.10⁻³\n a) p = paralelo, refletindo no foco = 70cm\n b) sen α = 1.590.10⁻⁹ => θ = 0.1475.10⁻³ rad\n tg(4.75.10⁻³) = x\n 0.7 x = 1.03mm\n5) f = 3000Hz v = 343m/s\n 343 = 3000.λ\n 0.114m = λ\n 27/05/18\n6) λ = 632.8.10⁻⁹ m D = 2.6m d = 1.37.10⁻³ m Δn = 80\n x = sen θ = 0.632.8.10⁻⁹\n 1.37.10⁻³\n tg 0.26 = x\n 26 x = 0.01m 2x = 0.024m = 24mm\n7) d = 0.1.10⁻³ m λ = 589.10⁻⁹ m θ = 30°\n Δφ/d = ΔΦ entre a onda da tapa e da ponta media\n Δφ = 2π (0.38.10⁻³ sen π) = 266.69 rad\n x = 160.°\n8) λ = 538.10⁻⁹ m d = 0.025.10⁻³ m\n D = 3.5m\n a) tg α = 11.10⁻²\n D = 3.5m\n b) Ø = 2π Δ L = 2π (0.025.10⁻³ sen(θ) = 0.18°\n 538.10⁻⁹ 538.10⁻⁹\n x = 0.917 y = 0.458\n 28/05/18\n9) D = 1.4m λ = 550.10⁻⁹ m a) sen α = 550.10⁻⁹ 122\n d = 5.10⁻³\n b) α = 1.34.10⁻⁴ rad\n = 1.4μm\n x = 1.4\n L max = x\n10) a) tg α = x\n (1.22.500.10⁻⁸) 8.10⁻⁸ = x\n x = 10.736.10³ Km\n y = 0.4m D = 8.10⁻³ 500.10⁻⁹ = 10.5km\n 5.1\n11) λ = 0.41.10⁻³ m d = 4.10⁻³ m\n y = 5.10⁻²\n 5.10⁻² = 1.22.0.41.10⁻³ d\n x = 4.10⁻³\n x = 1639.3Km\n12) λ = 7.6.10⁻² m queremos sen(θ) = 122°\n d = 2.3m\n x = 6.2.10³ m\n y = 1.22 + 1.6.10⁻²\n y = 2.3\n y = 52.68m\n 28/05/18\n13)\n\td=0.6m\n\ta)\n\t\t1450=\u03bb.2.10^3\n\t\tf=2.5.10^3 Hz\n\t\t\u03bb=0.058m\n\t\tsen\u03b8=1.222.0.0582 \u03b8=6.77\u00b0\n\t\t60.10^2\n\tb)\n\t\t1450=\u03bb.10^3\n\t\tsen.122.145 \n\t\tx=1.45\n\t\t60.10^2\n\t\tno existe\n14)\n\t\tapresemos entre (sen\u03b8-m\u03b8)\n\t\t\t\to\na\u00b0min a\u00b0max\n\t\t\t\tsen\u03b8=2.\u03bb\n\t\t\tyo \tyo)\n\t\t\to\n\t\t\t\t\u00bf\n\t\t\t\t\tno también\n\t\t\t\ts\n\t\tte}\n\n15)\n\ta)\n\t\tsen\u03b8=m\u03bb\n\t\t30.m\u03b8sen=1.550.10^s\n\t\t\u03bb=550.10^-9\n\t\td=0.15.10^-3\n\tb)\n\tT=Im/sinal3 (sen\u03b8)2\n\t\tt\u03b1=0.15.10^-3\n\t\ti=0.18\n\t\tm=5\n\t\tt=\u03b2=\\3.15.10^-9\n\t\tdsen\u03b2=9.42 rad - rad\n\t\t550.10^-9\n\t\tbt0=\u03f0=0.11\n\t\tm=6.+n-0.11=1.288 rad\n\t\t4.0+centros\n 12/06/18\n\n21) \\( \\lambda_0 = 656,3 \\cdot 10^{-9} \\) m = 656,3 \\cdot 10^{-9} N.l\n\\( \\Delta \\lambda = 0,18 \\cdot 10^{-9} \\) m\nm = 1\nN = 3646 nanómetros\n\n22) \\( \\Delta \\lambda = 9 \\cdot 10^{-12} \\)\n\\( \\lambda = 415,4982 \\cdot 10^{-9} \\)\na) \\( 2N = 415,4982 \\cdot 10^{-9} \\)\nm = 2\n\\( 9 \\cdot 10^{-12} \\)\nN = 23082\n\nb) \\( d = 4 \\cdot 10^{-2} - 1,73 \\cdot 10^{-6} m = w \\)\n23082\n\\( d_{seno} = m \\) \n\\( seno = 0,4795 = 0.5 rad = 28.65° \\)\n\n23) \\( N_s = 40,000 \\)\na) \\( D = m \\)\n\\( \\omega = 76 \\cdot 10^{-3} \\)\n\\( 1.9 \\cdot 10^{-6} \\)\n\\( \\lambda = 589 \\cdot 10^{-9} m \\)\nm = 1 \\Longrightarrow 1.9 \\cdot 10^{-6} seno = 1,529 \\cdot 10^{-9} m\nm = 3 \\Longrightarrow = 0.3 rad\n\\( d = 1.9 \\cdot 10^{-6} \\)\nm = 2 \\Longrightarrow \\( \\theta = 0.60 rad \\)\nm = 3 \\Longrightarrow \\( \\theta = 1.0 rad \\)\n\n\\( D_{1} = 1 \\)\n\\( \\omega = 1.9 \\cdot 10^{-6} cos 0.31 \\)\n= 0.554 rad/um\n\\( D_{2} = 2 \\)\n\\( 1.9 \\cdot 10^{-6} cos 0.66 \\) = 1.34 rad/um\n\\( D_{3} = 3 \\)\n\\( 1.9 \\cdot 10^{-6} cos 1.2 \\) = 4.24 rad/um\nb) \\( R = m.N \\)\nm = 1 \\Longrightarrow 1,40.000 = 40.000\nm = 2 \\Longrightarrow 2.40.000 = 280.000\nm = 3 \\Longrightarrow 3.40.000 = 120.000\n\n 13/06/18\n\n24) \\( d = 30 \\cdot 10^{-12} \\) m\n\\( 2.0 \\cdot 3.10^{-9} seno = 1.30 \\cdot 10^{-12} \\)\nd = 0.3 \\cdot 10^{-9} m\n\\( seno = 0.05 \\) rad = 2,86°\n\n25) \\( \\lambda ? \\)\n\\( 2.39,2 \\cdot 10^{-2} \\cdot seno 30° = D_{1} \\)\nd = 39,8 \\cdot 10^{-2} m = \\lambda\nm = 1\n\n26) \\( \\theta = 45° \\)\n\\( 2D_{d} = m \\)\n\\( \\lambda_{1} = 85 \\cdot 10^{-12} \\)\n\\( \\lambda \\Longrightarrow m = 4.09 \\)\n3.4 estos\n\\( \\lambda_{2} = 140 \\cdot 10^{-12} \\)\nm = 2 \\Longrightarrow m = 2.77\n\\( d = 2.75 \\cdot 10^{-12} = 41.\\lambda \\)\nm = 4 \\Longrightarrow \\lambda = 37.93 pm\n\nm = 3 \\Longrightarrow 2.275 \\cdot 10^{-12} = 3\n\\( \\lambda = 123,64 pm \\)\n