A farsighted person has a near point that is 67.0 cm from...

Name: Problem 115, Chapter 26: Physics
Uploaded: 2020-05-08T22:15:38-08:00
Duration: 2 min
Channel: Adnan Gill
Description: A farsighted person has a near point that is 67.0 cm from her eyes. She wears eyeglasses that are designed to enable her to read a newspaper held at a distance of 25.0 cm from her eyes. Find the focal length of the eyeglasses, assuming that they are worn (a) 2.2 cm from the eyes and (b) 3.3 cm from the eyes.

A farsighted person has a near point that is 67.0 cm from her eyes. She wears eyeglasses that are designed to enable her to read a newspaper held at a distance of 25.0 cm from her eyes. Find the focal length of the eyeglasses, assuming that they are worn (a) 2.2 cm from the eyes and (b) 3.3 cm from the eyes.

Key Concepts

Farsightedness

Farsightedness, or hyperopia, is a vision condition in which the eye naturally focuses images of distant objects better than those that are near. Individuals with hyperopia have a near point that is farther away from the eye than normal, necessitating corrective measures to allow clear vision up close.

Near Point

The near point is the minimum distance at which the eye can focus an object sharply. In individuals with vision conditions like farsightedness, the near point is abnormally far, and corrective lenses are employed to shift the apparent position of the object so it falls within the comfortable focusing range of the eye.

Corrective Lenses

Corrective lenses for farsightedness are typically converging (convex) lenses that bend light rays to reduce the effective viewing distance of near objects. By forming a virtual image of the object at the patient's near point, these lenses allow the eye to focus correctly without strain.

Thin Lens Equation

The thin lens equation, 1/f = 1/v - 1/u, is a fundamental principle in geometric optics that relates the focal length of a lens to the object distance (u) and the image distance (v). This equation is essential for calculating the specifications of corrective lenses by determining the necessary focal length to achieve the desired image position.

Object and Image Distance Considerations

In practical applications of the thin lens equation, especially for corrective eyewear, it is important to account for the positions of the lenses relative to the eye. The distances from the lens to the object and the virtual image (which is usually formed at the person's near point) must be adjusted based on the lens-to-eye separation for accurate calculations.

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