• Tags: Fresnel-distance, ray-optics, validity
• Difficulty: Advanced

The Fresnel distance Z_F = $a^{2}$/λ is the distance beyond which diffraction effects dominate over ray optics for a beam of width a. For distances much less than Z_F, light travels in straight lines (ray optics is valid). For distances comparable to or greater than Z_F, diffraction spreading becomes significant. For visible light (λ ~ 500 nm) and a beam of width 1 mm: Z_F = (10^{-3})^{2}/($5 \times 10^{-7}$) = 2 m. This means for distances less than about 2 m, a 1 mm beam travels essentially as a straight line. For laser beams, the small beam width makes Z_F small, requiring beam expanders for long-distance propagation.$