Light exhibits both wave-like and particle-like properties. One important consequence of its wave nature is diffraction — a phenomenon in which light bends slightly and spreads when it passes around the edges of an object or through a small aperture.

In Fraunhofer diffraction, both the source and the screen are at an infinite distance from the obstacle. As a result, the incident wavefront is plane. Fraunhofer diffraction is a specific type of diffraction that occurs when parallel light waves usually from a very distant source — pass through a narrow slit or diffracting object. The resulting pattern is observed on a screen at a far distance from the aperture, or at the focal plane of a converging lens. This far-field condition for a well-defined and stable diffraction pattern.

Let a parallel beam of monochromatic light of wavelength λ be incident normally upon a narrow slit AB of width d. After passing through the slit, the light gets diffracted and spreads out as shown in Fig. 1. If a converging lens L is placed in the path of the diffracted beam, a real image of the diffraction pattern is formed on the screen SS′ at its focal plane.

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Path Difference and Phase Difference

The path difference between rays from opposite edges of the slit is:

BD = AB sinθ = d sinθ     …(1)

The corresponding phase difference is:

ϕ = (2π / λ) · d sinθ     …(2)

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Resultant Amplitude

Consider the width AB of the slit divided into n equal parts. Each part acts as an elementary source. The amplitude of vibration at point P₀ due to the wave from each part is the same (a), and the phase difference between waves from any two consecutive parts is:

ϕ' = (1/n) · (2π / λ) d sinθ

The resultant amplitude at P₀ is:

A = a · sin(nϕ'/2) / sin(ϕ'/2)     …(3)

Letting α = πd sinθ / λ, the intensity at any point in the diffraction pattern is:

I = I₀ · (sinα / α)²     …(4)

where I₀ is the intensity at the central maximum (θ = 0).

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Condition for Maxima (Approximation)

θ = 0°   (central maximum)

d sinθ ≈ (k + ½)λ   for k = 0, 1, 2, 3, …     …(5)

Symbol	Description
d	Width of slit
θ	Angle of diffraction
k	Order of maximum (k = 0, 1, 2, 3, …)
λ	Wavelength of light

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Condition for Minima

d sinθ = kλ   for k = 1, 2, 3, …     …(6)

Symbol	Description
d	Width of slit
θ	Angle of diffraction (θ > 0°)
k	Order of minimum (k = 1, 2, 3, …)
λ	Wavelength of light

The half-angular width of the central maximum is:

Δθ = arcsin(λ / d) ≈ λ / d   (for small angles)     …(7)

The intensity of the first secondary maximum is approximately 4.7% of the central maximum, occurring near α = 3π/2.