A person has normal for point (infinity) and normal near point (25 cm). He intends to read a book using a magnifying glass of `f = 5 cm`. What is the
(i) Closest and
(ii) farthest distance at which he can read the book through the magnifying glass.

Answer

`-4.17 cm ; -5 cm`

Explanation

Here, `f = 5 cm`
Let `u` be the minimum distance at which he can read the book through the magnifying glass. The image must be formed at `25 cm` in front of the eye. Therefore, `v = -25 cm`.
From `(1)/(f)=(1)/(v)-(1)/(u)`
`(1)/(u)=(1)/(v)-(1)/(f)=( f - v)/(v f)`
`u = (vf)/(f - v) = (25 xx 5)/(5 - (-25)) = - (125)/(30)`
`= - 4.17 cm`
Again, let `u'` be the farthest distance at which he can read the book through the magnifying glass. In that case, image be formed at inifinity,
i.e., `v = oo`
From `u' = (vf)/(f - v) = (f)/(f//v - 1) =(5)/(5//oo - 1) = 5 cm`
`u' = -5 cm` (using sign convention).