Fresnel vs Fraunhofer Diffraction: Difference Explained

Diffraction is the bending and spreading of waves when they pass through a narrow opening or around an obstacle. It is divided into two classes based on distances: Fresnel diffraction and Fraunhofer diffraction. The difference is whether the source and screen are close to the aperture or effectively at infinity.

Understanding these classes matters because they determine which formulas and experiments are used. Fresnel diffraction explains complicated patterns near an edge, while Fraunhofer diffraction gives simple patterns for slits and gratings used in spectrometers. Both prove that light does not always travel in perfectly straight lines.

Key Concepts

In Fresnel diffraction, source or screen or both are at finite distance from the aperture, and the incident wavefront is spherical or cylindrical. The pattern changes with distance and is harder to calculate. In Fraunhofer diffraction, source and screen are at infinity, achieved in practice with lenses, and the incident wavefront is plane. The pattern is the Fourier transform of the aperture and stays in the focal plane.

• Fresnel number is large when distance is small.
• Fraunhofer needs collimated beam and lens focusing.
• Single slit Fraunhofer minima follow a simple rule.

Formulas

For Fraunhofer single slit of width a, minima satisfy a sin theta equals m lambda, where m equals plus minus 1, 2 and so on, theta is diffraction angle, lambda wavelength. Central maximum width on a screen at focal length f is 2 lambda f divided by a. No such simple formula covers all Fresnel cases; Fresnel zones and integrals are used. Assumptions: monochromatic plane wave, slit width comparable to lambda. Fresnel diffraction becomes Fraunhofer when distances are much larger than a squared divided by lambda.

Worked Example

Light of wavelength 600 nm falls on a single slit of width 0.12 mm. A lens of focal length 50 cm forms the Fraunhofer pattern. Find the width of central maximum.

Convert: lambda equals 6.0 times 10 to power minus 7 m, a equals 0.12 mm equals 1.2 times 10 to power minus 4 m, f equals 0.50 m.

Width equals 2 lambda f divided by a equals 2 multiplied by 6.0 times 10 to power minus 7 multiplied by 0.50 divided by 1.2 times 10 to power minus 4.

Numerator equals 6.0 times 10 to power minus 7. Divide by 1.2 times 10 to power minus 4 gives 5.0 times 10 to power minus 3 m equals 5 mm. The central bright band is 5 mm wide.

Common Misconceptions

• Diffraction and interference are totally unrelated: Wrong. Diffraction pattern is interference of wavelets from different parts of same aperture.
• Fraunhofer pattern needs source really at infinity: Wrong. A convex lens brings parallel rays to its focal plane, making infinity effectively accessible in the lab.
• Fresnel diffraction is just blurred Fraunhofer: Wrong. It is a different regime with curved wavefronts and distance-dependent patterns like Poisson spot.

Real-World Applications

Fraunhofer diffraction by a grating is the basis of spectrometers that analyse starlight and chemical composition. X-ray diffraction uses similar geometry to reveal crystal structures. Fresnel diffraction models are used in designing Fresnel lenses, zone plates and near-field microscopy. Laser beam shaping and barcode readers account for diffraction limits.

Remember: finite distances give Fresnel diffraction; plane wavefronts and lens focusing give Fraunhofer diffraction with simple slit formula a sin theta equals m lambda. Distance and wavefront curvature decide the class.