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 The distance for which ray optics is a good approximation is given by the Fresnel's distance.
aperture, a = 4 mm = 4
×10^(-3) m
wavelength, \lambda = 400nm = 400×10^(-9) m

Z_F= \frac{a^2}{ \lambda} = \frac{(4 \times 10^{-3})^2}{400 \times 10^{-9}} =\frac{16 \times 10^{-6}}{4 \times 10^{-7}}=\boxed{40m}