At age forty, a man requires contact lenses (f=65.0 cm) to read a book held 25.0 cm from his eye

step 1 So in order to solve part A, first thing we need to find is the near point at H40. So that's the

At age forty, a man requires contact lenses (f=65.0 cm) to...

At age forty, a man requires contact lenses $(f=65.0 \mathrm{cm})$ to read a book held $25.0 \mathrm{cm}$ from his eyes. At age forty-five, while wearing these contacts he must now hold a book $29.0 \mathrm{cm}$ from his eyes. (a) By what distance has his near point changed? (b) What focal-length lenses does he require at age forty-five to read a book at $25.0 \mathrm{cm} ?$

Key Concepts

Near Point

The near point is the closest distance at which the eye can focus on an object clearly. In the context of vision and optics, it is a critical measure that indicates the eye's ability to accommodate for near vision, and changes in the near point are significant in diagnosing and correcting vision problems.

Presbyopia

Presbyopia is an age-related condition where the eye’s lens loses its flexibility, resulting in difficulty focusing on nearby objects. This condition shifts the near point further from the eye, which is why individuals, as they age, often require corrective lenses to read comfortably at normal reading distances.

Corrective Lenses

Corrective lenses, often in the form of converging (or convex) lenses, are used to adjust the focal point of incoming light so that the eyes can focus images on the retina. In the case of presbyopia, these lenses effectively move the object’s virtual image closer to the eye, compensating for the increased near point and allowing for clearer vision at standard reading distances.

Lens Formula

The lens formula, given by 1/f = 1/v - 1/u, relates the focal length (f) of a lens to the object distance (u) and the image distance (v). This relationship is fundamental in designing and understanding corrective lenses, as it allows for precise adjustments to ensure objects are focused at the desired positions for improved clarity.

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