Q.Estimate the distance for which ray optics is good approximation for an aperture of $4\ \text{mm}$ and wavelength $400\ \text{nm}$.

Ray optics remains a good approximation only up to the Fresnel distance, the distance over which a beam passing through a given aperture stays narrow before diffraction s …

Step 1: The Fresnel distance formula

For a beam of wavelength $\lambda$ passing through an aperture (or slit) of size $a$, diffraction causes the beam to spread out significantly only after it has travelled the Fresnel distance:

For $z \ll z_F$, the beam travels essentially as a ray (negligible spreading); ray optics is a good approximation up to about this distance.

Step 2: Substitute the given values …