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An optometrist prescribes contact lenses that have a focal length of \(55.0 \mathrm{~cm}\). (a) Are the lenses converging or diverging, and (b) is the person who wears them nearsighted or farsighted? (c) Where is the unaided near point of the person located, if the lenses are designed so that objects no closer than \(35.0 \mathrm{~cm}\) can be seen clearly?

Short Answer

Expert verified
(a) Converging lenses. (b) Farsighted. (c) Unaided near point: 96.3 cm.

Step by step solution

01

Determine Type of Lens

The focal length (\(f\)) of the lens is given as \(55.0\, \mathrm{cm}\). A positive focal length indicates a converging lens, while a negative focal length indicates a diverging lens. Since the focal length is positive, the lenses are converging.
02

Identify Vision Problem

Converging lenses are used to correct for farsightedness, also known as hyperopia. Farsighted individuals have difficulty seeing nearby objects because their near point is farther than normal. Therefore, since the prescribed lenses are converging, the person who wears them is farsighted.
03

Calculate Unaided Near Point

Given: The lens is designed so that objects at least \(35.0\, \mathrm{cm}\) away can be seen clearly. This is the effective near point with correction, meaning:\(\frac{1}{v} = \frac{1}{u} + \frac{1}{f}\). With \(v = 35.0\, \mathrm{cm}\) and \(f = 55.0\, \mathrm{cm}\), calculate \(u\) .\(\frac{1}{u} = \frac{1}{v} - \frac{1}{f} = \frac{1}{35.0\, \mathrm{cm}} - \frac{1}{55.0\, \mathrm{cm}}\). Evaluating this gives \(u = 96.3\, \mathrm{cm}\). So, the unaided near point of the person is located \(96.3\, \mathrm{cm}\) away.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converging Lens
A converging lens, often referred to as a convex lens, is designed to bring parallel rays of light to a single point of focus. This lens is identified by its characteristic shape, usually thicker in the middle and thinner at the edges.

The major function of a converging lens is to focus light, and it is characterized by a positive focal length. When light passes through a converging lens, it bends towards the optical axis, causing the light rays to meet at a point called the focus.

Converging lenses are used in a variety of applications such as cameras, eyeglasses, and microscopes. In the context of vision correction, these lenses help people see objects at a closer range by making objects appear sharper and in focus.
  • Positive focal length indicates a converging lens
  • Thicker in the center, thinner at the edges
  • Brings light rays to a focal point
Farsightedness
Farsightedness, or hyperopia, is a common vision condition where distant objects can be seen more clearly than nearby ones. This happens because the eye focuses images behind the retina instead of directly on it.

People with farsightedness struggle to see objects that are close, leading to eye strain and difficulties with tasks such as reading or using a smartphone.
A common symptom is having to hold reading materials at an arm's length to see them clearly.

Converging lenses are used as corrective lenses for those with this condition. They help bend light more effectively so it focuses on the retina, allowing for clearer vision at closer distances.
  • Difficulty seeing nearby objects
  • Images focus behind the retina
  • Corrected with converging lenses
Optometry
Optometry is the field of healthcare concerned with eye health and vision care. Optometrists are trained professionals who evaluate vision, prescribe corrective lenses, and diagnose various eye conditions.

During an eye examination, an optometrist assesses visual acuity and determines how the eye focuses and works together. They often prescribe lenses, like the converging lenses in this exercise, to correct vision problems such as farsightedness.

Optometrists play a crucial role in maintaining eye health through regular checkups and providing guidance on eye care practices.
  • Evaluation of vision health
  • Prescription of corrective lenses
  • Diagnosis of eye conditions
Unaided Near Point
The unaided near point refers to the closest distance at which the eye can clearly see an object without the use of corrective lenses. This varies from person to person and changes with age as the eye's lens loses flexibility.

In healthy young adults, the unaided near point is typically around 25 cm. However, for individuals with vision issues such as farsightedness, the near point may be further away.

In the exercise, the individual's unaided near point was calculated to be approximately 96.3 cm. This means that without their corrective lenses, objects need to be placed at least this distance away to be seen clearly.
  • Closest clear viewable distance without lenses
  • Varies due to age and vision health
  • Farther in farsighted individuals

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Most popular questions from this chapter

Two systems are formed from a converging lens and a diverging lens, as shown in parts \(a\) and \(b\) of the drawing. (The point labeled \(" F_{\text {converging }}^{\prime \prime}\) is the focal point of the converging lens.) An object is placed inside the focal point of lens 1 . Without doing any calculations, determine for each system whether the final image lies to the left or to the right of lens \(2 .\) Provide a reason for each answer. The focal lengths of the converging and diverging lenses are \(15.00\) and \(-20.0\) \(\mathrm{cm}\), respectively. The distance between the lenses is \(50.0 \mathrm{~cm}\), and an object is placed \(10.00 \mathrm{~cm}\) to the left of lens \(1 .\) Determine the final image distance for each system, measured with respect to lens 2. Check to be sure your answers are consistent with your answers to the Concept Question.

Amber \((n=1.546)\) is a transparent brown-yellow fossil resin. An insect, trapped and preserved within the amber, appears to be \(2.5 \mathrm{~cm}\) beneath the surface when viewed directly from above. How far below the surface is the insect actually located?

To focus a camera on objects at different distances, the converging lens is moved toward or away from the film, so a sharp im age always falls on the film. A camera with a telephoto lens \((f=200.0 \mathrm{~mm})\) is to be focused on an object located first at a distance of \(3.5 \mathrm{~m}\) and then at \(50.0 \mathrm{~m}\). Over what distance must the lens be movable?

The contacts worn by a farsighted person allow her to see objects clearly that are as close as \(25.0 \mathrm{~cm}\), even though her uncorrected near point is \(79.0 \mathrm{~cm}\) from her eyes. When she is looking at a poster, the contacts form an image of the poster at a distance of \(217 \mathrm{~cm}\) from her eyes. (a) How far away is the poster actually located? (b) If the poster is \(0.350 \mathrm{~m}\) tall, how tall is the image formed by the contacts?

An object is placed to the left of a lens, and a real image is formed to the right of the lens. The image is inverted relative to the object and is onehalf the size of the object. (a) What kind of lens, converging or diverging, is used to produce this image? (b) How is the height \(h_{\mathrm{i}}\) of the image related to the height \(h_{0}\) of the object? Don't forget to take into account the fact that the image is inverted relative to the object. (c) What is the ratio \(d_{i} / d_{0}\) of the image distance to the object distance? For the situation described in the Concept Questions, the distance between the object and the image is \(90.0 \mathrm{~cm}\). (a) How far from the lens is the object? (b) What is the focal length of the lens?

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