Question

An angular magnification (magnifying power) of `30 X` is desired using an objective of focal length `1.25 cm` and an eye piece of focal length `5 cm`. How will you set up the compound microscope ?

Answer 1

In normal adjustment, image is formed at least distance of distinct vision, `d = 25 cm`
Angular magnification of eye piece `= (1 +(d)/(f_e)) = (1 + (25)/(5)) = 6`
As total magnification is `30`, magnification of objective lens,
`m = (30)/(6)=5 :. m = (v_0)/(-u_0) = 5` or `v_0 = -5 u_0`
As `(1)/(v_0)-(1)/(u_0)=(1)/(f_0) :. (1)/(- 5 u_0) - (1)/(u_0)=(1)/(1.25)`
`- (6)/(5 u_0) = (1)/(1.25)`
`u_0 = (-6 xx 1.25)/(25) = -1.5 cm`
i.e., object should be held at `1.5 cm` in front of obejctive lens.
As `v_0 = - 5 u_0 :. v_0 = -5 (-1.5) = 7.5 cm`
From `(1)/(u_e) = (1)/(v_e)-(1)/(f_e)=(1)/(-25) - (1)/(5) = -(6)/(25)`
`u_e = (-25)/(6) = -4.17 cm`
`:.` Separation between the objective lens and eye piece `= |u_e|+|v_0| = 4.17 + 7.5 = 11.67 cm`.