Question

B. Using complex variables to simplify interference problems This question concerns a set up from Physics 123 (optics) in which light with wavelength λ and angular frequency w 2nc/λ passes through a grating with 5 narrow slits a distance a apart. (See also Boas p.79.) Recall that one sees an interference pattern when the light hits a screen after passing through the grating. In particular, assuming the screen to be distant from the grating, the am plitude of the electric field in the wave at an angle θ from the directio n of the incoming light is given by summing the contributions from each of the slits: Here, the "phase shift" is a sin θ
Can someone do question ii), please? Please do not copy others' answers online. They are incorrect!

Answer 1

Given that angular frequency omega = 2 pi C/lambda find E (theta, t) = E_0 ln [sigma^4_n = 0 e^i (omega t - n delta)] (1) Given E (theta, t) = E_0 [sin omega t + sin (omega t - delta) + sin (omega t - 2 delta) + sin (omega t - 3 delta) + sin (omega t - 4 delta) (2) from the above equation (1) E (theta, t) = E_0 ln [e^i (omega t) + e^i (omega t - delta) + e^i (omega t - 2 delta) + e^i (omega t - 4 delta)] = E_0 ln [cos omega t + i sin omega t + cos (omega t - delta) + i sin (omega t - delta) + i sin (omega t - delta) + cos (omega t - 2 delta) + isin (omega t - 2 delta) + cos (omega t - 3 delta) + i sin (omega t - 3 delta)