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Ch 34: Geometric Optics
Chapter 34, Problem 34

BIO A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. (a) Is she nearsighted or farsighted?

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Identify the condition described: The person can see clearly up close but has difficulty focusing on objects that are farther away than 75.0 cm.
Understand the terms: Nearsightedness (myopia) is when a person can see objects clearly when they are close but has difficulty seeing objects that are far away. Farsightedness (hyperopia) is when a person can see distant objects clearly but has difficulty seeing objects that are close.
Compare the symptoms with the definitions: Since the person can see clearly up close but not at a distance, this aligns with the symptoms of nearsightedness.
Conclude the type of vision problem: Based on the symptoms and comparison, the person is nearsighted.
Understand the correction method: Contact lenses or glasses with concave lenses are typically used to correct nearsightedness by diverging the light rays before they enter the eye, helping to focus the image correctly on the retina.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nearsightedness (Myopia)

Nearsightedness, or myopia, is a common vision condition where distant objects appear blurry while close objects can be seen clearly. This occurs when the eyeball is too long or the cornea has too much curvature, causing light rays to focus in front of the retina instead of directly on it. Individuals with myopia often require corrective lenses to adjust the focal point, allowing them to see distant objects more clearly.

Farsightedness (Hyperopia)

Farsightedness, or hyperopia, is a condition where nearby objects are difficult to see clearly, while distant objects may be seen more clearly. This happens when the eyeball is too short or the cornea is too flat, causing light rays to focus behind the retina. People with hyperopia may struggle with tasks that require close vision, such as reading, and often need corrective lenses to bring the focal point forward.

Corrective Lenses

Corrective lenses are optical devices designed to improve vision by altering the way light enters the eye. For nearsighted individuals, concave lenses are used to diverge light rays, allowing them to focus on the retina. Conversely, convex lenses are used for farsightedness to converge light rays, helping to focus images on the retina. Contact lenses, like those mentioned in the question, provide a convenient alternative to glasses, directly correcting the vision without the bulk of frames.
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Ray Diagrams for Diverging Lenses