Susan is quite nearsighted; without her glasses, her far...

Susan is quite nearsighted; without her glasses, her far point is $35 \mathrm{cm}$ and her near point is $15 \mathrm{cm}$. Her glasses allow her to view distant objects with her eye relaxed. With her glasses on, what is the closest object on which she can focus?

Key Concepts

Virtual Image

A virtual image is one that cannot be projected onto a screen because it is formed by the apparent divergence of rays rather than their actual convergence. In the context of corrective lenses, the lens creates a virtual image of an object at a distance that lies within the eye's focusing range, allowing the eye to view distant objects clearly even if its natural far point is closer.

Corrective Lenses

Corrective lenses are used to adjust the path of light entering the eye, ensuring that the final retinal image falls within the eye’s range of clear focus. For a myopic person, a diverging (negative) lens is used to form a virtual image of distant objects at the far point of the uncorrected eye, thereby allowing clear distance vision. They also affect how near objects are perceived.

Thin Lens Equation

The thin lens equation (1/f = 1/do + 1/di) provides the fundamental relationship between the focal length of a lens, the object distance, and the image distance. It is a critical tool in geometrical optics for determining how corrective lenses form images at the proper locations so that the eye’s optical limitations, such as its near and far points, are properly accommodated.

Far Point

The far point is the maximum distance at which the eye can see objects clearly when it is relaxed (no accommodation). In myopia (nearsightedness), this point is at a finite distance rather than at infinity, which means that objects beyond this distance are blurred. Corrective lenses are used to adjust the image so that even distant objects appear to be located within the clear vision range.

Near Point

The near point is the minimum distance at which the eye can focus on an object clearly. It represents the closest distance at which the eye's lens can adjust its focal power without strain. In vision correction, the near point defines the limit on how close an object can be before the image becomes too divergent for the eye to focus comfortably.

Please give Ace some feedback