Question:
Estimate the distance for which ray optics is a good approximation for an aperture of 4 mm and wavelength 400 nm.
Solution:
Fresnel's distance $\left(Z_{F}\right)$ is the distance which is used in ray optics for a good approximation. Following is the relation,
$Z_{F}=\frac{a^{2}}{\lambda}$
Where,
Aperture width, a = 4 mm = 4 × 10-3 m
Wavelength of light, $\lambda=400 \mathrm{~nm}=400 \times 10^{-9} \mathrm{~m}$
$Z_{F}=\frac{\left(4 \times 10^{-3}\right)^{2}}{400 \times 10^{-9}}=40 \mathrm{~m}$
Therefore, 40m is the distance for which the ray optics is a good approximation.