C Suppose that the lens in a particular eye has a focal...

C Suppose that the lens in a particular eye has a focal length that can vary between $1.85 \mathrm{cm}$ and $2.00 \mathrm{cm},$ but the distance from the lens to the retina is only $1.90 \mathrm{cm}$. (a) Is this eye nearsighted or farsighted? Explain. (b) What range of distances can the eye see clearly without corrective lenses?

Key Concepts

Near and Far Points

The near point and far point refer to the closest and farthest distances, respectively, at which the eye can focus an image sharply on the retina. These limits are determined by the eye's capacity to change its focal length through accommodation. An eye with a reduced range of accommodation may have a near point that is farther away than normal, indicating difficulty in focusing on nearby objects, which is a characteristic of farsightedness.

Accommodation

Accommodation is the process by which the eye changes its optical power to focus on objects at varying distances. This is achieved by altering the shape of the lens, thereby changing its focal length to ensure that images are properly focused on the retina. In the context of vision defects, a limited range of accommodation can lead to difficulties in focusing on near or distant objects, which are symptoms of farsightedness (hyperopia) and nearsightedness (myopia) respectively.

Lens Equation

The lens equation, given by 1/f = 1/u + 1/v, relates the focal length (f) of a lens to the object distance (u) and the image distance (v). This essential relationship in geometrical optics allows us to determine where an image will form for a given lens setting. Understanding and applying the lens equation is crucial when analyzing how variations in the eye’s lens focal length affect where the image is focused on the retina.

Nearsightedness vs Farsightedness

Nearsightedness (myopia) and farsightedness (hyperopia) are common refractive errors that occur when the eye's focusing ability is misaligned with the position of the retina. In myopia, a person can see near objects clearly but has difficulty with distant objects because images are focused in front of the retina. In contrast, hyperopia (farsightedness) occurs when near objects are blurred because the images are formed behind the retina, typically due to an eye that is too short or a lens that is not sufficiently converging.

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