As shown in the figure, a beam of monochromatic light of wavelength ? is incident on two slits S₁ and S₂ separated by a distance d. Derive an expression in terms of ?, L, d, and m for the distance y_m from the center to the m-th brightest fringe of the interference pattern observed on a screen at a distance L, if L >> y_m.

If the fringes are separated by 2 mm and illuminated by a helium-neon laser of wavelength 612 nm, calculate the spacing of the fringes observed on a screen at 4 m.

Screen