The far point of a nearsighted person is 6.0 m from her...

Name: Problem 81, Chapter 26: Physics
Uploaded: 2020-05-02T22:47:06-08:00
Duration: 2 min 19 s
Channel: Adnan Gill
Description: The far point of a nearsighted person is 6.0 m from her eyes, and she wears contacts that enable her to see distant objects clearly. A tree is 18.0 m away and 2.0 m high. (a) When she looks through the contacts at the tree, what is its image distance? (b) How high is the image formed by the contacts?

The far point of a nearsighted person is 6.0 m from her eyes, and she wears contacts that enable her to see distant objects clearly. A tree is 18.0 m away and 2.0 m high. (a) When she looks through the contacts at the tree, what is its image distance? (b) How high is the image formed by the contacts?

Key Concepts

Thin Lens Equation

This fundamental relation in geometrical optics, typically written as 1/f = 1/v + 1/u (with appropriate sign conventions), connects the focal length of a lens with the object distance and the image distance. It enables one to determine where an image will form (whether real or virtual) and is central to solving problems involving lenses, including corrective lenses for vision.

Virtual Image Formation

In many optical systems, including corrective lenses for nearsighted individuals, lenses form images that appear to be located at positions from which no light actually emanates. These virtual images, produced by diverging (concave) lenses when the object is beyond the person’s far point, allow the eye to comfortably focus by making the object appear to be at a distance it can see clearly.

Magnification

Magnification is the ratio of the image height to the object height and, in the context of lens systems, is also given by the ratio of the image distance to the object distance (m = v/u) when sign conventions are properly observed. This concept helps in determining the size of the image produced by a lens, which is especially relevant when assessing how an object’s dimensions are perceived after correction.

Myopia Correction and Far Point

Myopia (nearsightedness) is a condition in which the eye cannot focus on distant objects because its far point is too close. Corrective lenses, such as contact lenses, are designed to adjust the effective image distance, so that objects located farther away are brought into focus at the wearer’s far point. Understanding the far point is crucial in designing lenses that produce images at distances where the eye can focus comfortably.

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