Illustrates one approach to solving problems such as this...

Illustrates one approach to solving problems such as this one. A farsighted person has a near point that is $67.0 \mathrm{~cm}$ from her eyes. She wears eyeglasses that are designed to enable her to read a newspaper held at a distance of $25.0 \mathrm{~cm}$ from her eyes. Find the focal length of the eyeglasses, assuming that they are worn (a) $2.2 \mathrm{~cm}$ from the eyes and (b) $3.3 \mathrm{~cm}$ from the eyes.

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Key Concepts

Thin Lens Equation

The thin lens equation relates the object distance, image distance, and focal length of a lens. It is central to determining the necessary focal length of corrective lenses that form images at the desired locations, such as adjusting the virtual near point for a farsighted person.

Virtual Image Formation

In corrective optics, a lens may form a virtual image, which is an image that cannot be projected on a screen but can be seen by the eye. For farsighted individuals, the eyeglasses are designed to form a virtual image of an object held at a closer distance, typically at the wearer’s natural near point, to enable comfortable reading.

Corrective Lenses in Prescriptive Optics

Corrective lenses are used to compensate for imperfections in vision, such as the extended near point in farsighted individuals. The design of such lenses involves calculating the focal length needed to adjust the effective near point to a more desirable reading distance.

Optical Sign Conventions

Proper application of sign conventions in optics is crucial when using the lens formula. Accurate modeling using these conventions allows for correct determination of object and image distances, especially when dealing with virtual images and the distances between the lens and the eye.

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