(a) At what distance should the lens be held from the card sheet in Exercise 9.22 in order to view the squares distinctly with the maximum possible magnifying power? (b) What is the magnification in this case? (c) Is the magnification equal to the magnifying power in this case? Explain.
The lens should be held at a distance of approximately 6.62 cm (or 225/34 cm) from the card sheet.
The magnification in this case is 34/9 or approximately 3.78.
Yes, the magnification is equal to the magnifying power in this case. When the image is formed at the least distance of distinct vision (near point), both magnification (m = v/u) and magnifying power (MP = 1 + D/f) yield the same value.
Explanation
This question builds on Exercise 9.22 where a converging lens of focal length 9 cm is used. For maximum magnifying power, the image must be formed at the near point (25 cm). Using the lens formula and calculating magnification shows that under these specific conditions, linear magnification equals angular magnification.