A farsighted person can read printing as close as 25.0 cm when she wears contacts that have a fo

step 1 From the thin lens equation I can write 1 by f is equal to 1 by d0 that is object distance plus

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

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

Key Concepts

Magnifying Glass

A magnifying glass is a simple converging lens used to produce an enlarged, virtual image of an object. It works by bending light rays to create a larger, more detailed view of objects that are otherwise too small to be seen clearly. The effectiveness of a magnifying glass, measured in terms of angular magnification, depends on its focal length and the observer’s near point, making it a fundamental example of how lenses can aid in vision improvement.

Corrective Lenses

Corrective lenses are used to adjust the way light enters the eye, compensating for imperfections such as farsightedness or nearsightedness. They modify the effective near or far point of the eye, enabling clearer vision at distances that would otherwise be problematic. In the context of magnification, understanding how a corrective lens changes the effective near point is critical when calculating the angular magnification for an individual whose unaided vision deviates from the norm.

Near Point

The near point is the closest distance at which the eye can focus on an object clearly. For a normal eye, this distance is typically taken as 25.0 centimeters. However, persons with refractive errors (such as farsightedness) may have a near point that is farther away, which can affect how they see small objects without corrective measures. Knowledge of the near point is essential when determining the effectiveness and design parameters of optical aids.

Angular Magnification

Angular magnification refers to the factor by which an optical instrument increases the apparent angular size of an object. Essentially, it compares the angle subtended by the image (as seen through the instrument) to the angle subtended by the object when viewed with the naked eye at a standard viewing distance. Understanding how this magnification is calculated (for example, using formulas like M = 1 + D/f when the image is formed at the near point) is crucial in the design and analysis of optical devices such as magnifying glasses.

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