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Chapter 33: Problem 87

You visit your eye doctor and discover that you require lenses having a diopter value of -8.4 . Are you nearsighted or farsighted? With uncorrected vision, how far away from your eyes must you hold a book to read clearly?

Short Answer

Expert verified
Answer: A person with a diopter value of -8.4 is nearsighted. To read a book clearly without correction, they should hold it approximately 11.9 centimeters away from their eyes.

Step by step solution

01

Determine if the person is nearsighted or farsighted

A diopter is a unit of measurement for the optical power of a lens. A positive diopter value indicates farsightedness (difficulty in seeing things close-up), while a negative diopter value indicates nearsightedness (difficulty in seeing things far away). Since the given diopter value is -8.4, the person is nearsighted.
02

Calculate the focal length

To determine the comfortable reading distance for the person, we will use the formula for the focal length (f) of a lens: f = 1 / D where D is the diopter value. In this case, D = -8.4, so: f = 1 / (-8.4) = -0.119 meters, or -11.9 centimeters Since the focal length is negative, it indicates that the focal point is on the same side of the lens as the object being viewed. This is a characteristic of a diverging lens, which is used to correct nearsightedness.
03

Determine the distance to hold the book

The comfortable reading distance is determined by the focal point of the uncorrected vision. As the focal length is -11.9 centimeters, the person must hold the book at approximately 11.9 centimeters away from their eyes to read it clearly without correction.

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Most popular questions from this chapter

Two converging lenses with focal lengths \(5.00 \mathrm{~cm}\) and \(10.0 \mathrm{~cm}\), respectively, are placed \(30.0 \mathrm{~cm}\) apart. An object of height \(h=5.00 \mathrm{~cm}\) is placed \(10.0 \mathrm{~cm}\) to the left of the \(5.00-\mathrm{cm}\) lens. What will be the position and height of the final image produced by this lens system?

The distance from the lens (actually a combination of the cornea and the crystalline lens) to the retina at the back of the eye is \(2.0 \mathrm{~cm}\). If light is to focus on the retina, a) what is the focal length of the lens when viewing a distant object? b) what is the focal length of the lens when viewing an object \(25 \mathrm{~cm}\) away from the front of the eye?

Mirrors for astronomical instruments are invariably first-surface mirrors: The reflective coating is applied on the surface exposed to the incoming light. Household mirrors, on the other hand, are second-surface mirrors: The coating is applied to the back of the glass or plastic material of the mirror. (You can tell the difference by bringing the tip of an object close to the surface of the mirror. Object and image will nearly touch with a first-surface mirror; a gap will remain between them with a second-surface mirror.) Explain the reasons for these design differences.

A refracting telescope has the objective lens of focal length \(10.0 \mathrm{~m}\). Assume it is used with an eyepiece of focal length \(2.00 \mathrm{~cm}\). What is the magnification of this telescope?

The radius of curvature for the outer part of the cornea is \(8.0 \mathrm{~mm}\), the inner portion is relatively flat. If the index of refraction of the cornea and the aqueous humor is 1.34: a) Find the power of the cornea. b) If the combination of the lens and the cornea has a power of \(50 .\) diopter, find the power of the lens (assume the two are touching).
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