In Young's double slit experiment, a fine beam of coherent monochromatic light of wavelength $$\lambda = 600\,\text{nm}$$ is incident on identical slits $$S_1$$ and $$S_2$$ at separation $$d$$. The intensity at the central maximum formed at $$O$$ is $$I_{\max}$$ and the angular fringe width is $$\beta = 0.1^\circ$$. When a thin transparent film is placed in front of the slit $$S_2$$, the intensity at $$O$$ changes. It is found that the smallest thickness of the film, for which the intensity at $$O$$ becomes half the maximum intensity $$\frac{I_{\max}}{2}$$, is $$250\,\text{nm}$$. Neglecting the absorption of light by the film, the zero order fringe earlier at $$O$$ now forms at $$O'$$ where $$OO' = 0.5\,\text{mm}$$. Choose correct option or options.