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Ch 34: Geometric Optics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 34: Geometric OpticsProblem 53a
Chapter 33, Problem 53a

Where is the near point of an eye for which a contact lens with a power of +2.75 diopters is prescribed?

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Understand the problem: The power of a lens (in diopters) is related to its focal length (in meters) by the formula: P=1f. Here, the power of the contact lens is given as +2.75 diopters, and we need to find the focal length of the lens, which corresponds to the near point of the eye.
Rearrange the formula to solve for the focal length: f=1P. Substitute the given power of the lens, P=2.75, into the equation.
Perform the calculation to find the focal length: f=12.75. This will give the focal length in meters.
Interpret the result: The focal length of the lens represents the distance at which the lens focuses light. Since the lens is correcting for the near point of the eye, this focal length corresponds to the near point distance of the eye with the contact lens in place.
Convert the focal length to centimeters if needed (1 meter = 100 centimeters) for a more practical representation of the near point distance.

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Key Concepts

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

Power of a Lens

The power of a lens, measured in diopters, is the reciprocal of its focal length in meters. A positive power indicates a converging lens, which is used to correct hyperopia (farsightedness). In this case, a contact lens with a power of +2.75 diopters means it has a focal length of approximately 0.364 meters, or 36.4 centimeters.
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Near Point

The near point of the eye is the closest distance at which an object can be seen clearly without strain. For a normal eye, this distance is typically around 25 centimeters. However, for individuals with vision impairments, such as hyperopia, the near point can be farther away, necessitating corrective lenses to bring it closer.
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Lens Formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens, expressed as 1/f = 1/v - 1/u. This formula is essential for determining how a lens affects the position of the image formed by an object. In the context of contact lenses, it helps calculate the effective near point when a lens is used.
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Related Practice
Textbook Question

Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 45.0 cm from his eyes instead of the usual 25.0 cm. Is this person nearsighted or farsighted?

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Textbook Question

Repeat Exercise 34.41 using the same lenses except for the following changes: The second lens is a diverging lens having a focal length of magnitude 60.0 cm.

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Textbook Question

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. Is she nearsighted or farsighted?

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Textbook Question

Zoom Lens. Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. (a) For a distant object, where is the of the converging lens? (c) Where is the final image? Compare your answer to Fig. 34.43a.

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Textbook Question

You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. If the dimensions of the picture on a 35 mm color slide are 24 mm ✖ 36 mm, what is the minimum size of the projector screen required to accommodate the image?

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Textbook Question

BIO Ordinary Glasses. Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their power in diopters?

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