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 ?

Explanation

Assume that microscope is in such a position that the final image is formed at 25 cm (at least distance of distinct vision).
Angular magnification of the eyepiece (magnifying power of the eyepiece)
`m_(e)=(1+(D)/(f_(e)))`
`=1+(25)/(5)=6`
Total magnification, `M=30`
Magnification of the objective is
`|m_(o)|=(M)/(m_(e))=(30)/(6)=5`
`"Also, "m_(o)=(v_(o))/(u_(o))=-5`
`rArr" "v_(o)=-5u_(o)`
`therefore" For the objective lens, "`
`-(1)/(5u_(o))-(1)/(u_(o))=(1)/(1.25)`
`rArr" "u_(o)=-1.5m`
`therefore" "v_(o)=5xx1.5=7.5cm`
This implies that the object should be placed at 1.5 cm from the objective lens, which in turn forms the image at a distance of 7.5 cm behind the objective lens.
For the eyepiece,
`v_(e)=-25cm`
Using,
`(1)/(v_(e))-(1)/(u_(e))=(1)/(f_(e))`
`(1)/(-25)-(1)/(u_(e))=(1)/(5)`
`rArr" "u_(e)=-(25)/(6)=-4.17cm`
The separation between the objective and eyepiece should be
`L=|v_(o)|+|u_(e)|=7.5+4.17=11.67cm`