Question

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

Answer 1

1. Fresnel’s distance is the distance up to which the ray optics is valid in terms of rectilinear propagation of light.
2. Fresnel’s distance is the distance up to which ray optics is obeyed and beyond which ray optics is not obeyed but, wave optics becomes significant.
3. From the diffraction equation for first minimum,
   sin θ = `lamda/"a"`;
   θ = `lambda/"a"`
4. From the definition of Fresnel’s distance,
   sin 2θ = `"a"/"z"`
   2θ = `"a"/"z"`
   
5. Equating the above two equation gives,
   `lambda/"a" = "a"/(2"z")`
6. Equating the above two equation gives,
   z = `"a"^2/(2lambda)`