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Chapter 2: Problem 70

What is the far point of a person whose eyes have a relaxed power of \(50.5 \mathrm{D} ?\)

Short Answer

Expert verified
The far point of a person with a relaxed eye power of \(50.5 \mathrm{D}\) is 0.0198 meters or 19.8 millimeters away from their eyes.

Step by step solution

01

Find the focal length of the eye using the power given

The power (P) of a lens is the inverse of its focal length (f). Therefore, we can write the formula as: \[f = \frac{1}{P}\] Given, the power of the lens (eye) is \(50.5 \mathrm{D}\), we can find the focal length using the above formula: \[f = \frac{1}{50.5}\]
02

Calculate the focal length

Calculate the focal length by plugging the value of power into the formula: \[f = \frac{1}{50.5} = 0.0198 \mathrm{m}\] The focal length of the eye is 0.0198 meters or 19.8 millimeters.
03

Use the lens formula to find the far point

The lens formula is given by: \[\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\] Where: \(f\) = focal length of the lens (eye) \(d_o\) = object distance \(d_i\) = image distance For the far point, the object distance, \(d_o\) is considered to be at infinity (\(d_o → ∞\)). This means that at the far point, the image formed will be at the focal point (which is also the farthest point where a person can see clearly).
04

Calculate the far point

As the object distance (\(d_o\)) approaches infinity in the lens formula, the equation becomes: \[\frac{1}{f} = 0 + \frac{1}{d_i}\] Therefore, at the far point: \[d_i = f\] Hence, the far point of the person is equal to the focal length of their eyes when relaxed: \[d_i = f = 0.0198 \mathrm{m}\] Thus, the far point of the person is 0.0198 meters or 19.8 millimeters away from their eyes.

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Most popular questions from this chapter

A boy has a near point of 50 \(\mathrm{cm}\) and a far point of \(500 \mathrm{cm} .\) Will a \(-4.00 \mathrm{D}\) lens correct his far point to infinity?

An object of height \(3.0 \mathrm{cm}\) is placed \(5.0 \mathrm{cm}\) in front of a converging lens of focal length \(20 \mathrm{cm}\) and observed from the other side. Where and how large is the image?

How far from the lens must the film in a camera be, if the lens has a 35.0 -mm focal length and is being used to photograph a flower \(75.0 \mathrm{cm}\) away? Explicitly show how you follow the steps in the Problem-Solving Strategy: Lenses.

Suppose a 200 mm-focal length telephoto lens is being used to photograph mountains \(10.0 \mathrm{km}\) away. (a) Where is the image? (b) What is the height of the image of a \(1000 \mathrm{m}\) high cliff on one of the mountains?

Use a ruler and a protractor to draw rays to find images in the following cases. (a) A point object located on the axis of a concave mirror located at a point within the focal length from the vertex. (b) A point object located on the axis of a concave mirror located at a point farther than the focal length from the vertex. (c) A point object located on the axis of a convex mirror located at a point within the focal length from the vertex. (d) A point object located on the axis of a convex mirror located at a point farther than the focal length from the vertex. (e) Repeat (a)-(d) for a point object off the axis.
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