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Chapter 2: Problem 78

The normal power for distant vision is 50.0 D. A young woman with normal distant vision has a \(10.0 \%\) ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?

Short Answer

Expert verified
The closest object that the young woman can clearly see is at 18.2 cm away from her.

Step by step solution

01

Understanding the problem

First, understand the problem and terms. The normal power of distant vision is 50.0 D, which means the ability of the eye to see far objects clearly. The woman has a 10.0% ability to increase her power for closer objects. So, in order to find the nearest distance where she can see clearly, the total power needs to be found.
02

Calculating the Power increase due to accommodation

Next, calculate the increase in power due to accommodation. Since it is given that the woman can accommodate 10.0%, this means the increase is 0.10 * 50.0 D = 5.0 D.
03

Finding the total power

Now, add the normal power and the accommodative power to get the total power of the eye. This is calculated as 50.0 D + 5.0 D = 55.0 D.
04

Calculation of the nearest distance the woman can see clearly

Finally, calculate the nearest distance the woman can see clearly by using the definition of power in terms of distance. Since power is defined as 1/distance, and we know the power is 55.0 D, the nearest distance is calculated as 1/55.0 D = 0.0182 m, which is 18.2 cm when converted to centimeters.

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