To solve this problem, we need to understand the concept of lenses and specifically how corrective lenses (glasses) work. Corrective lenses have a specific power measured in diopters (D), which is the reciprocal of the focal length in meters.
The man's glasses have a power of \(3D\). This means the focal length of the glasses is calculated as follows:
\(f = \frac{1}{P} = \frac{1}{3}\,m = 0.33\,m\) or \(33\,cm\)
When the glasses are on, the image is formed at the least distance of distinct vision, which is \(25\,cm\) (because that's where he can see the newspaper clearly with glasses). Without glasses, the man must rely on his unaided eye's ability to focus, known as the near point.
The lens formula relates object distance (u), image distance (v), and the focal length (f):
\(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\)
With glasses, the object appears at the least distance of distinct vision, so \(v = -25\,cm = -0.25\,m\). Note that we use negative since the image is formed on the same side as the object for concave lenses.
Substituting the given values:
\(\frac{1}{0.33} = \frac{1}{-0.25} - \frac{1}{u}\)
Solve for \(u\):
\(\frac{1}{-u} = \frac{1}{0.33} + \frac{1}{0.25}\)
\(\frac{1}{-u} = 3 + (-4) = -1\)
\(u = -1\)
The result shows that without glasses, the man would require the newspaper to be at \(-1\,m\) to see it clearly. This negative value indicates a virtual position which is typically associated with far-sightedness.
Thus, if he takes off his glasses, he would need the newspaper to be \(-1\,m\) away to see it clearly. Therefore, the correct answer is: