final-equation-sheets - Some Equations for Exam 1 tan = sin...

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Some Equations for Exam 1 tan θ = sin θ/ cos θ ; sin 2 θ + cos 2 θ =1 . sin 30 / 2; cos 30 = 3 / 2; tan 30 / 3. sin 60 = 3 / 2; cos 60 / 2; tan 60 = 3. Some constants: c =3 × 10 8 m/s; e . 602 × 10 - 19 C; ± 0 =8 . 854 × 10 - 12 C 2 / N · m 2 ; 1 / (4 π± 0 )=9 . 0 × 10 9 N · m 2 / C 2 . For light in vacuum: = c . For light in matter: v = c/n . Law of Re±ection: θ = θ ± ; Law of Refraction: n 1 sin θ 1 = n 2 sin θ 2 The Mirror Equation: 1 p + 1 i = 2 r = 1 f . ( p is object distance, i is image distance, f focal length. We often used p for object distance in class). The Spherical Refracting Surface Equation: n 1 p + n 2 i = n 2 - n 1 r . For a thin lens: 1 p + 1 i = 1 f , and 1 f =( n - 1) ± 1 r 1 - 1 r 2 ² . f> 0 converging lens, f< 0 diverging lens. The lateral magni²cation is m = - i p For a double slit, the conditions for maxima/minima are (with m =0 , ± 1 , ± 2 ,... ): d sin θ = (max) d sin θ m + 1 2 ) λ (min) Single-Slit Diffraction: minima when a sin θ = , m = ± 1 , ± 2 . Rayleigh’s criterion for a circular aperture: θ R . 22 λ D . Equations for thin ²lm in air or ²lm coating on larger index objects (here m , 1 , 2 ): 1. maximum when 2 dn m + 1 2 ) λ (thin ²lm in air) 2. minimum when 2 dn = (thin ²lm in air) 3. minimum when 2 dn film m + 1 2 ) λ (thin ²lm on larger n substrate). Magnitude of electric ²eld of a point charge: E = 1 4 0 q r 2 ; of an in²nite line charge: E = λ 2 0 r . Force on a point charge: F = q E . Electric potential for a point charge: V = 1 4 0 q r .
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final-equation-sheets - Some Equations for Exam 1 tan = sin...

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