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Chapter 2: Problem 66

Unless otherwise stated, the lens-to-retina distance is 2.00 Calculate the power of the eye when viewing an object \(3.00 \mathrm{m}\) away.

Short Answer

Expert verified
The power of the eye when viewing an object 3.00 meters away is approximately \(49.67\,\text{D}\) (diopters).

Step by step solution

01

Convert distances to meters if necessary

In this case, the lens-to-retina distance is given in cm. Convert it to meters: \(v = 2.00\,\text{cm} = 0.02\,\text{m}\) Note that the object distance of 3.00 m is already in meters.
02

Use the lens formula to find the focal length

Plug in the given values for the image distance \(v = 0.02\) m and the object distance \(u = 3.00\) m into the lens formula: \(\frac{1}{f} = \frac{1}{0.02\,\text{m}} - \frac{1}{3.00\,\text{m}}\)
03

Solve for the focal length

First, find the common denominator for the fractions: \(\frac{1}{f} = \frac{1}{0.02\,\text{m}} \cdot\frac{3.00}{3.00} - \frac{1}{3.00\,\text{m}}\cdot\frac{0.02}{0.02}\) Now subtract the fractions: \(\frac{1}{f} = \frac{3.00 - 0.02}{0.02 \times 3.00}\) \(\frac{1}{f} = \frac{2.98}{0.06}\) Now, divide to find the reciprocal of the focal length: \(\frac{1}{f} \approx 49.67\) Finally, find the focal length by taking the reciprocal of the result: \(f \approx \frac{1}{49.67} \approx 0.0201\,\text{m}\)
04

Calculate the Power of the eye

Use the formula for the power of a lens and the calculated focal length: \(P = \frac{1}{f} \approx \frac{1}{0.0201\,\text{m}}\) \(P \approx 49.67\,\text{D}\) The power of the eye when viewing an object 3.00 meters away is approximately 49.67 diopters.

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Most popular questions from this chapter

Under what circumstances will an image be located at the focal point of a spherical lens or mirror?

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