A man cannot see closer than 1m from the eyes clearly. What is the power of the corrective lensused?

1. Break Down the Problem

To find the power of the corrective lens for a man who cannot see objects closer than 1 meter clearly, we need to determine the focal length of the lens required to correct his vision.

2. Relevant Concepts

The power $P$ of a lens is given by the formula: $P = \frac{1}{f}$ where $P$ is in diopters (D) and $f$ is the focal length in meters (m). Since the man can see clearly at a distance of 1 meter, the lens must create a virtual image at this distance.

3. Analysis and Detail

For a man who cannot see closer than $d = 1 m$, the correct focal length $f$ would be negative, as corrective lenses for hyperopia (farsightedness) are concave lenses: $f = -1 \text{ m}$

Using the power formula: $P = \frac{1}{f} = \frac{1}{-1} = -1 \text{ D}$

4. Verify and Summarize

The calculations have been verified, and the power of the corrective lens required for the man to see objects closer than 1 meter is indeed $-1$ diopter.

Final Answer

The power of the corrective lens used is $-1$ D.