Q.What is Fresnel's distance? Obtain the equation for Fresnel's distance.

Fresnel's distance $z$ is the distance, measured from a diffracting aperture, up to which the rectilinear (straight-line ray) propagation of light remains a good approximation, and beyond which diffraction spreading becomes significant enough that ray optics is no longer valid. It is found from the first-minimum diffraction angle $\theta=\lambda/a$ for a slit (or aperture) of width $a$: the TN textbook defines Fresnel's distance via the FULL angular spread of the central maximum, $2\theta$, equated to the angular width $a/z$ the aperture itself subtends by simple ray-optics geometry at distance $z$: $2\theta=a/z$, i.e. $2\lambda/a=a/z$, giving $z=\dfrac{ …