Final answer:
A projected reduced Snellen chart viewed through a 0.1 mm pinhole aperture is most accurate for near-sightedness and astigmatism. The pinhole aperture helps to reduce the effects of refractive errors by allowing only central light rays to enter the eye.
Step-by-step explanation:
The question relates to the accuracy of a projected reduced Snellen chart when viewed through a 0.1 mm diameter aerial pinhole aperture in various eye conditions. Using a pinhole aperture can help to improve visual acuity temporarily by increasing depth of field and reducing the effects of refractive errors, such as near-sightedness (myopia) or far-sightedness (hyperopia), and astigmatism. The pinhole works by allowing only the central rays to enter the eye, which are the least affected by refractive errors. Therefore, viewing a Snellen chart through a pinhole is most accurate with the conditions of near-sightedness (myopia) and astigmatism, as it helps to marginalize the effect of the refractive errors on the visual acuity to some extent.
It's important to note that pinhole testing does not improve vision in conditions such as cataracts or glaucoma, since these are not primarily caused by refractive errors. Cataracts cloud the lens, and glaucoma damages the optic nerve; neither would benefit as much from the pinhole effect, which targets refractive issues. So, the best answer to the student's question would be option b) Far-sightedness (FS) and Astigmatism (AST), considering that far-sightedness could be interpreted as a type of refractive error that can be alleviated by the pinhole test.