A laser with wavelength λ=632nm illuminates a double–slit arrangement in which every rectangular slit has width a=0.15mm and the center-to-center separation of the slits is d=0.90mm. A flat viewing screen is placed L=2.0m downstream of the slits so that an interference–diffraction pattern forms on the screen.
(a) Show that the interference orders m that are absent from the pattern satisfy a simple proportional relationship between m and an integer n associated with diffraction minima. Express m explicitly in terms of a, d, and n. State any assumptions made.
(b) Using the numerical values above, calculate the first three positive interference orders that are missing from the pattern.
(c) Determine the linear distance on the screen between the central maximum and the first missing bright fringe. Give your answer to an appropriate number of significant figures.
(d) Suppose the experimenter doubles the slit width while leaving every other parameter unchanged. Qualitatively describe how this modification affects (i) the set of missing interference orders and (ii) the overall brightness contrast of the surviving fringes inside the central diffraction envelope.