A compound micrscope consists of an objective lens of focal length 1.0 cm and an eyepiece lens of focal length 5.0 cm separated by 12.2 cm At what distance from the objective lens should an object be placed to focus it properly so that the final image is formed at the least distance of clear vision (25cm)? b. calculate the angular magnificationn in this case.

Answer

`2.50`

Explanation

Here, `D=25cm, f_(0)=2.0cm, f_(e)= 6.25cm`

For the eyepiece:
`(1)/(f_(e)) = (1)/(v_(e)) -(1)/(u_(e)), (1)/(u_(e))= (1)/(v_(e))- (1)/(f_(e)) = (1)/(-25) - (1)/(6.25) (" as " u_(e)= -D= -25)`
`(1)/(u_(e))= - (1)/(5) or u_(e)= - 5cm`
or As `v_(0) +|u_(e)|=L= 15cm, v_(0) = 15-|u_(e)\=15-5= 10cm`
For the objective.
`(1)/(f_(0))= (1)/(v_(0)) - (1)/(u_(0))`
or `(1)/(2)= (1)/(10) - (1)/(u_(0))`
or `(1)/(u_(0))= (1)/(10) -(1)/(2)= -(4)/(10)`
or `u_(0)= -2.5cm`
Thus, the object should be placed at a distance 2.50 cm in front of the objective.