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

Explanation

(i) Fresnel's distance is the distance upto which ray optics is obeyed and beyond which ray optics is not obeyed but, wave optics becomes significant.
(ii) From the diffraction equation for first minimum,
` sin theta =lamda/a, theta = lamda/a`
(iii) From the definition of Fresnel's distance,
` sin 2 theta = a/z , 2 theta =a/z`
(iv) Equating the above two equation gives,
` lamda/a = (a)/(2z)`
After rearranging, we get Fresnel's distance z as
` z = (a^2)/(2 lamda)`