Chapter 27 ---------- 3). The angle of bright fringes in 2-slit experiment is given by the formula 27.1: sin(theta_m) = m*lambda/d m=0,1,2,3... sin(theta_1) = 1*630*10^(-9)m/5.3*10^(-5)m = 1.2*10^(-2) => theta_1 = 0.68 degrees sin(theta_2) = 2*630*10^(-9)m/5.3*10^(-5)m = 2.4*10^(-2) => theta_2 = 1.36 degrees sin(theta_3) = 3*630*10^(-9)m/5.3*10^(-5)m = 3.6*10^(-2) => theta_3 = 2.04 degrees 21). The angle of dark fringes for sigle slit diffraction (equation 27.4) sin(theta) = m * lambda / W m=0,1,2,3... where n -- order of the dark fringe, lambda -- wavelength and W -- the width of the slit. For the slit width W = 1.8*10^(-4)m sin(theta_1) = 1 * 675*10^(-9)m/1.8*10^(-4)m = 0.00375 theta_1 = 0.215 degrees For a slit that is 100 times smaller sin(theta_1) = 1 * 675*10^(-9)m/1.8*10^(-6)m = 0.375 theta_1 = 22 degrees 34). Resolving power is given by formula 27.6 theta = 1.22 * lambda/D, where D is the diameter of aperture. theta = 1.22 * 550*10^(-9) m/2.4 m = 2.79*10^(-7) The distance between the asteroids is equal to theta*distance_from_earth = 2.79*10^(-7) * 2*10^(10) m = = 5591 m ~ 5.5 km