The focal lengths of objective and eye piece of a microscope are `1.25 cm and 5 cm` respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of `30` in normal adjustment.

Explanation

Here, `f_(0) = 1.25 cm, f_(e) = 5 cm, mu_(0) = ?`,
`m = 30`
In normal adjustment, magnification produced
by the eye piece,
`m_(e) = (d)/(f_(e)) = (25)/(5) = 5`
As `m = m_(0) xx m_(e) :. m_(0) = (m)/(m_(e)) = (30)/(5) = 6`
As real image is formed by objective lens,
therefore, `m_(0) = (v_(0))/(u_(0)) = -6, v_(0) = -6 u_(0)`
From `(1)/(v_(0)) - (1)/(u_(0)) = (1)/(f_(0))`
`(1)/(-6 u_(0)) - (1)/(u_(0)) = (1)/(1.25) or = u_(0) = (- 7 xx 1.25)/(6)`
`= - 1.46 cm`
`:.` Object must be held `1.46 cm` in front of objective lens.