Two flat glass plates of length \(L\) lie on a lab bench, touching at one end and separated at the opposite end by a thin hair of diameter \(d\) to form an air wedge. Monochromatic light of wavelength \(\lambda\) shines perpendicularly onto the top plate, producing an interference pattern with a constant spacing \(\Delta x\) between adjacent dark fringes. Which of the following expressions correctly gives the diameter \(d\) of the hair?