Multiple Rainbows from Single Drops of Water and Other Liquids

The scattering of light by spherical drops and the theory of rainbows are reviewed in detail to predict the angular positions of rainbows from single drops. The angular positions of the first 13 rainbows of water, observed from a drop suspended in a student spectrometer, were compared to these theoretical positions. Since the rainbows were dependent on the refractive index, the positions shifted with drops of other fluids having other refractive indices. Light corn syrup yielded 11 rainbows, including the 17th-order one. The light emerging from the drops was white except for the multicolors of the rainbows and the faint blue of the rays that had been nearly tangentially incident to the drops. With a hand-held polarized filter, all of the observed rainbows appeared to be polarized parallel to the plane of incidence. Using the 6328-A˚ light from a student He-Ne laser, one of the interference patterns composing all natural rainbows was created and photographed. The angular positions of the principal maxima of this pattern differed from the theoretical rainbow positions predicted by geometrical optics by amounts dependent on the drop radius

Multiple Rainbows from Single Drops of Water and Other Liquids

The scattering of light by spherical drops and the theory of rainbows are reviewed in detail to predict the angular positions of rainbows from single drops. The angular positions of the first 13 rainbows of water, observed from a drop suspended in a student spectrometer, were compared to these theoretical positions. Since the rainbows were dependent on the refractive index, the positions shifted with drops of other fluids having other refractive indices. Light corn syrup yielded 11 rainbows, including the 17th-order one. The light emerging from the drops was white except for the multicolors of the rainbows and the faint blue of the rays that had been nearly tangentially incident to the drops. With a hand-held polarized filter, all of the observed rainbows appeared to be polarized parallel to the plane of incidence. Using the 6328-A˚ light from a student He-Ne laser, one of the interference patterns composing all natural rainbows was created and photographed. The angular positions of the principal maxima of this pattern differed from the theoretical rainbow positions predicted by geometrical optics by amounts dependent on the drop radius

Karate Strikes

Analysis of a forward karate punch is made as an example of collision mechanics. The energy lost to deformation of an opponent is evaluated, and the deformation is shown to be maximized if contact is made when the fist has the greatest speed. In karate fighting the maximum deformation is obtained by focusing a punch to terminate several centimeters inside an opponent’s body. The average impact force is calculated and compared with that neeeded to break a human bone by stressing it beyond its ultimate bending stress value. Similar breaking forces needed for bricks and wooden boards are also computed. A brief description of breaking demonstrations for the physics classroom is made

Using Refraction Caustics to Monitor Evaporation of Liquid Drop Lenses

Irregularities in the perimeter of a water droplet adhering to a vertical pane of glass cause perturbations in the curvature of the droplet surface. When laser light passes through such a droplet, the perturbations produce a far field refraction caustic, which is a section of the caustic known as the parabolic umbilic in the catastrophe theory classification. As the water evaporates and the droplet surface curvature changes, the section of the parabolic umbilic caustic on the viewing screen also changes. We determine the evolution of curvature of the droplet surface by observing the evolution of the far field caustic and the locations on the droplet responsible for the various features of the caustic