Statement - I :Diffraction determines the limitations of the concept of light rays.
Statement - II :A beam of width α starts to spread out due to diffraction after it has travelled a distance $\left(2{\mathrm{\alpha }}^2/\mathrm{\lambda }\right)$

Diffraction us defined as the bending of light around the corners of the obstacle or aperture into the region Of geometrical shadow if the obstacle. Diffraction occurs with all waves, including sound waves, water waves and electromagnetic waves. A beam of width α travels a distance of $\frac{{\mathrm{\alpha }}^2}{\mathrm{\lambda }}$ , called the Fresnel distance before it starts to spread out due to diffraction.

hence second statement is wrong.