A farsighted person can read printing as close as 25.0 cm...

Name: Problem 89, Chapter 26: Physics
Uploaded: 2020-05-04T17:27:32-08:00
Duration: 2 min 37 s
Channel: Adnan Gill
Description: A farsighted person can read printing as close as 25.0 cm when she wears contacts that have a focal length of 45.4 cm. One day, she forgets her contacts and uses a magnifying glass, as in Figure 26.39b. Its maximum angular magnification is 7.50 for a young person with a normal near point of 25.0 cm. What is the maximum angular magnification that the magnifying glass can provide for her?

A farsighted person can read printing as close as 25.0 cm when she wears contacts that have a focal length of 45.4 cm. One day, she forgets her contacts and uses a magnifying glass, as in Figure 26.39b. Its maximum angular magnification is 7.50 for a young person with a normal near point of 25.0 cm. What is the maximum angular magnification that the magnifying glass can provide for her?

Key Concepts

Angular Magnification

Angular magnification refers to the factor by which an optical instrument increases the angular size of an object relative to the size seen by the unaided eye. It is a key concept in optics, as it quantifies how much larger an image appears when viewed through devices like magnifying glasses by comparing the angle subtended by the image at the eye to the angle subtended by the object when observed at a standard distance.

Near Point

The near point is the closest distance at which the eye can focus on an object clearly. In human vision, particularly for reading or detailed work, this distance is crucial for defining comfortable and effective viewing. The near point is used as a standard reference in calculating angular magnification and ensuring that optical instruments are optimized for clear vision.

Magnifying Glass

A magnifying glass is a simple convex lens used to produce an enlarged, virtual image of an object. By positioning the object within the focal length of the lens, the magnifying glass allows the viewer to see details that are not easily visible with the naked eye. Its performance is largely determined by its focal length and design parameters that control the apparent increase in angular size.

Corrective Lenses

Corrective lenses are designed to compensate for deficiencies in the eye's ability to focus light, as seen in conditions such as farsightedness (hyperopia). They adjust the effective focal point and the near point, allowing individuals to see objects clearly at a standard reading distance. In the study of optical magnification, corrective lenses play an important role in defining the baseline performance of visual aids and determining how additional optical devices, like magnifying glasses, further enhance vision.

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