Question

We are given Young's double-slit set-up, however, instead of two point sources issuing "in-phase" sine waves at the source points, the sine waves are "out of phase". Specifically, the sources are "out of phase" by a quarter wavelength. Assume temporarily for convenience that the waves have wavelength "2π". The specifications provided thus far allow that the two wave trains arriving at "a point" on a distant screen corresponding to a "path length difference" of "Δx" be represented by "sin(x)" and "cos(x+Δx)".

A) Sum these two waves and provide the expression for the aggregate amplitude.

B) Dark spots on the screen are spots of no light (i.e., vanishing 'amplitude'). Find all mathematically possible values of "Δx" (as potentially distinct from "physically plausible" ones) corresponding to the dark spots. Be certain to list the sequence of values suitably.

C) If the separation of the two point sources is "d" and the spot corresponding to "Δx " (pld) on the screen is at an angle "θ" relative to the sources-to-screen forward direction, express "Δx " in terms "θ" and "d".

D) If the light sources are of wavelength "λ" instead now, and if "d" = "10λ", determine in degrees the two angular positions on the screen of two dark spots! On physical grounds is there a limit here on the number of dark spots? Explain/comment

Answer 1

4 2너 Cc)

d) : (nt Thìn th4care lu wung,咋.hhr dark fob h fl lo 10 5.7s。