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 ≥ (a^{2}/λ)

Here, (a^{2}/λ) is called Fresnel distance.

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