Question

Consider the interference pattern produced by two parallel slits of width a and separation d, in which d=3a. The slits are illuminated by normally incident light of wavelength λ.

Consider the interference pattern produced by two parallel slits of width a and separation d, in which d = 3a. The slits are illuminated by normally incident light of wavelength λ

Answer 1

(a) the condition for central maxima for diffraction grating is, d sin theta = m lambda here, m is the order of the fringe, d is the separation of the slits next four maxima of interference pattern (m = 1, 2, 3, 4) respectively sin theta_1 = lambda/d, sin theta_2 = 2 lambda/d, sin theta_3 = 3 lambda/d & sin theta_4 = 4 lambda/d (b) expression for intensity corresponding each interference pattern is, I = I_0[sin(bet/2)/beta/2]^2 here, beta = 2 pi/lambda a sin theta (here d = 3 a) = 2 pi/lambda (d/3 sin theta intensity for next four maxima a of interference pattern respectively, 1) bet_1/2 = 2 pi/2 lambda(d/30 sin theta_1 = 2 pi/2 lambda(d/3)(lambda/d) = pi/3 I_1 = I_0[sin(pi/3)/pi/3]^2 almostequalto 0.684I_0 2) Beta_2/2 = 2 pi/2 lambda (d/3) sin theta_2 = 2 pi/2 lambda(d/3) (2 lambda/d) = 2 pi/3 I_2 = I_0[sin(2 pi/3)/2 pi/3]^2 almostequalto 0.17I_0 3) beta-3/2 = 2 pi/2 lambda(d/3) sin theta_3 = 2 pi/2 lambda(d/3)(3 lambda/d) = pi