Particle size determination: An undergraduate lab in Mie scattering

A technique for determining the size of microscopic spherical particles using light scattering is presented as an undergraduate physics lab. Scatterer size is determined from angular scattering distribution measurements of laser light scattered from a dilute suspension of latex spheres with diameters of $4.99±0.05$ and $6.038±0.045 μm.$ Previous experiments of this type used approximate theoretical corrections and required the construction of specialized sample cells to minimize complicating effects. As a significant improvement to these, we generate angular scattering distributions from Mie theory and, using an accurate numerical procedure, correct these distributions for Snell’s law and foreshortening effects. Scatterer size is then determined using a fast, robust fitting algorithm to compare these corrected angular scattering distributions to measured angular scattering distributions. We fit the scatter from a solution of 6.04-μm-diam spheres to spheres of $5.95±0.11 μm$ diameter, and that from a solution of 4.99-μm spheres to $4.85±0.15 μm.$ Additionally, scattering data for a 2:1 mixture of spheres of diameters 4.99 and 6.04 μm are taken, and after numerical adjustment for Snell’s law and foreshortening effects, good agreement with theory is obtained.