Question

1. At what distance should the lens be held from the card sheet in order to view the squares distinctly with the maximum possible magnifying power?
2. What is the magnification in this case?
3. Is the magnification equal to the magnifying power in this case? Explain.

Answer 1

(a) For maximum magnifying power, the image should be at least a distance of distinct vision, i.e., 25 cm.

`1/"v" - 1/"u" = 1/"f"`

`1/(-25) - 1/"u" = 1/9`

`-1/"u" = 1/9 + 1/25`

`-1/"u" = 34/225`

u = `-225/34` 

∴ u = −6.62 cm

(b) Linear magnification in the situation of maximum magnifying power.

m = `"v"/"u"`

= `(-25)/(-225/34)`

= 3.77

(c) Maximum magnifying power in the same situation,

m = `"D"/"u"_"min"` or `(1 + "D"/"f"_"e")`

m_max = `25/(225/34)` or `(1 + 25/10)`

m_max = 3.77

So, it can be observed that in the situation when the image is at least a distance of distinct vision, the angular magnification and linear magnification have similar values.