For what distance is ray optics a good approximation when the aperture is $3\; mm$ wide and the wavelength is $500\; nm$?

(18 M) The Fresnel distance $(z_{F})$ is the distance for which ray optics is a good approximation. It is given by the formula $z_{F} = \frac{a^{2}}{\lambda}$,where $a$ is the aperture width and $\lambda$ is the wavelength.
Given: $a = 3\; mm = 3 \times 10^{-3}\; m$ and $\lambda = 500\; nm = 5 \times 10^{-7}\; m$.
Substituting the values:
$z_{F} = \frac{(3 \times 10^{-3})^{2}}{5 \times 10^{-7}}$
$z_{F} = \frac{9 \times 10^{-6}}{5 \times 10^{-7}}$
$z_{F} = 1.8 \times 10^{1} = 18\; m$.
Thus,ray optics is a good approximation for distances up to $18\; m$.