What is Fresnel distance? derive an expression for it.

Fresnel distance: It is the minimum distance that a beam of light has to travel before its deviation from straight line path. 

Derivation:

From the theory of diffraction of light for a single slit, the angle of diffraction for central maxima is 

sinθ ≈ θ = λ/a 

After travelling distance x, the half angular width of beam would become (xλ/a).

This beam width will be more than width of slit(a).

So, (xλ/a) ≥ a

=> x ≥  (a2/λ)

Here, (a2/λ) is called Fresnel distance.

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In optics and radio com munications (indeed, in any situation involving the radiation of waves, which includes electrodynamics, acoustics, and gravitational radiation), a Fresnel zone, named for physicist Augustin -Jean Fresnel, is one of a (theoretically infinite) number of concentric ellipsoidswhich define volumes in the radiation pattern of a (usually) circular aperture. Fresnel zones result from diffraction by the circular aperture. [1]

The cross section of the first (innermost) Fresnel zone is circular. Subsequent Fresnel zones are annular (doughnut-shaped) in cross section, and concentricwith the first.

 

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