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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 P_{1}.

(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 P_{1} would remain zero or not. If not, will P_{1} become the location of a maximum constructive interference (bright) fringe? In each case, explain your reasoning.

(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.

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