A point P on the interference screen in a Young’s double-slit set-up is situated such that the straight line joining P to the mid-point of the two slits makes an angle 30° with the normal to the plane of the slits. The slit separation is 0.25 mm and the experiment uses monochromatic light of wavelength 500 nm.
a) Find the path difference between the two waves reaching P.
b) Will the point P appear bright or dark? Justify your answer.
c) If the point is bright, determine the order m (m ≥ 0) of that bright fringe; if it is dark, determine the value of m for which that dark fringe occurs.