Explain that for a greater distance, the spreading due to diffraction dominates over due to ray optics.

Explanation

An aperture of size .a. illuminated by a parallel beam sends diffracted light into an angle `theta` , then angular width
`theta~~(lamda)/(a)`
In travelling a distance z, the diffracted beam acquires a width `=ztheta`
`=(zlamda)/(a)` due to diffraction
The value of z the spreading due to diffraction is equal to the size of a of the aperture.
`:.a=(zlamda)/(a)`
`:.z=(a^(2))/(lamda)`
This quantity is called the Fresnel distance `z_(F)`.
`:z_(F)=(a^(2))/(lamda)`
This equation shows that for distances much smaller than `z_(F)` the spreading due to diffraction is smaller compared to the size of the beam (That means moving in a straight line). Hence, spreading due to diffraction dominates over that due to ray optics and it shows that ray optics is valid in the limit of wavelength tending to zero.