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Changing interference

Consider a plane wave of monochromatic green light, λ = 500 nm, that is incident normally upon two identical narrow slits (the widths of the individual slits are much less than λ). The slits are separated by a distance a= 30 μm. An interference pattern is observed on a screen located a distance L away from the slits. On the screen, the location nearest the central maximum where the intensity is zero (i.e., the first dark fringe) is found to be 1.5 cm from this central point. Let this particular position on the screen be referred to as P1.

(a) Calculate the distance, L, to the screen. Show all work.

(b) In each of the parts below, one change has been made to the problem above (in each case, all parameters not explicitly mentioned have the value or characteristics stated above). For each case, explain briefly whether the light intensity at location P1 would remain zero or not. If not, will P1 become the location of a maximum constructive interference (bright) fringe? In each case, explain your reasoning.

(1) One of the two slits is made slightly narrower, so that the amount of light passing through it is less than that through the other.
(2) The wavelength is doubled so that λ = 1000 nm.
(3) The two slits are replaced by a single slit whose width is exactly 60 μm.