The separation between the eye piece of focal length `0.3 m` and objective of focal length `0.4 m` of a microscope is `0.2 m`. The eye piece and objective are to be interchanged such that the angular magnification of the instrument remains the same. What is the new separation between the lenses ?

Explanation

For relaxed eye i.e., normal setting of microscope, final image is formed at inifinity
`m = -(v_0)/(u_0)((d)/(f_e))` …(i)
If object lies close to focus of objective lens, `u_0 ~~ f_0 and v_0 = (L - f_e)`, where `L` is distance between the two lenses.
:. From (i), `m = (-(L - f_e)d)/(f_0 f_e)` ...(ii)
Let `L'` be the new distance betwen the two lenses when objective and eye lens are interchanged.
`:. m' = (-(L' - f_0)d)/(f_e f_0)` ...(iii)
As `m' = m`, therefore, from (ii) and (iii),
`L' = f_0 = L - f_e`
or `l' = L - f_e+ f_0 = 0.2 - 0.3 + 0.4 = 0.3 m`.