[UPSC CSE 2011] Interference (Q200, 10M)

When a thin film of a transparent material is put behind one of the slits in Young's double-slit interference experiment, the zero-order fringe moves to the position previously occupied by the fourth-order bright fringe. The index of refraction of the film is n=1.2 and the wavelength of light, \lambda=5000\,\mathring{\mathrm{A}}. Determine the thickness of the film.