120
The apparent lengths with the naked eye, and with the lens, are therefore, as 1120 and 18, or as 8 and 120, of which numbers the latter being fifteen times the former, the object is said to be magnified in length fifteen times.
In order to generalize this, let c be the nearest distance for correct vision,
and let | k=OA, | the distance of the eye from the lens, |
∆=AQ, | ||
F=AF; | ||
δ=Aq. |
Then since δ=∆FF−∆, the linear magnitudes of the object and image are as ∆:δ, that is, as F−∆:F.
The angular magnitudes, that is, the angles subtended by the object and image at O, are as F−∆∆+k:Fδ+k, but the fairer way of stating the matter is to compare the angular magnitudes of the object at the distance c and the image at the distance δ+k: these are as
F−∆c:Fδ+k,
and the magnifying power of the lens is
Fδ+k·cF−∆.
This of course is increased by diminishing k. If we make this =0 by placing the eye close to the lens, the magnifying power becomes
Fδ·cF−∆, which is equal to c∆,
and is inversely as the distance AQ, which may consequently be diminished with advantage, as long as Aq is left greater than c.