Fortunately for most people who wear glasses, it is not essential that the examining practitioner understand all of the optical details involved before writing down the final prescription. After a reasonable amount of experience, the average refractionist finds that the technique of retinoscopy becomes almost a matter of habit, and the basic concepts underlying his procedures may soon be forgotten. Indeed, the advisability of teaching more than the descriptive aspect of optics to future oculists has recently been debated.1 Nevertheless, it is generally agreed that a certain minimum of familiarity with the fundamental mathematical relationships is to be recommended, at least for the beginning student of refraction.
The geometrical properties associated with spherical lenses are universally included in courses for such students, but cylindrical lenses are often not as well described, even though a major percentage of the population has some degree of astigmatism requiring cylindrical correcting lenses. The
ASKOVITZ SI. The Circle of Least Confusion on Sturm's Conoid of Astigmatism. AMA Arch Ophthalmol. 1956;56(5):691-697. doi:10.1001/archopht.1956.00930040699007