While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the XY-plane containing two small holes that act as two coherent point sources (S₁, S₂) emitting light of wavelength 600 mm. The student mistakenly placed the screen parallel to the XZ-plane (for z > 0) at a distance D = 3 m from the mid-point of S₁S₂, as shown schematically in the figure. The distance between the source d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S₁S₂.


Which of the following is(are) true of the intensity pattern on the screen?

A light source, width emits two wavelengths $$\lambda$$₁ = 400 nm and $$\lambda$$₂ = 600 nm, is used in a Young's double-slit experiment. If recorded fringe widths for $$\lambda$$₁ and $$\lambda$$₂ are $$\beta$$₁ and $$\beta$$₂ and the number of fringes for them within a distance y on one side of the central maximum are m₁ and m₂, respectively, then