How is the working of a telescope different from that of a microscope ? The focal lengths of the objective and eyepiece 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 anangular magnificatio of 30 in normal adjustment.

Explanation

Working differences `:`
1. Objective of a telescope forms the image of a vey far off object at, or within, the focus of its eyepiece. The microscope does the same for a small object kept just beyond the focus of its objective.
2. The final image formed by a telescope is magnified relative to its size as seen by the unaided eye while the final image formed by a microscope is magnified relative to its absolute size.
3. The objective of a telescope has large focal length & large aperture while the corresponding for a microscope have very small values.
Given `:` `f_(0) = 1.25cm`
`f_(e ) = 5 cm`
Angular magnification m = 30
Now, `m = m_(e ) xx m_(0)`
In normal adjustment , angular magnifucation of eyepiece
`m_(e ) = ( d // f_(e )) = ( 25)/( 5) = 5 `
Hence, `m_(0) = 6`
But `m_(0) = ( v_(0))/( u_(0))rArr =-6 = ( v_(0))/( u_(0))`
`v_(0) = - 6 u_(0)`
Applying lens equation to the objective lens `:`
`(1)/( f_(0)) = ( 1)/( v_(0)) - ( 1)/( u_(0))`
`(1)/( 1.25) = ( 1)/( - 6u_(0)) - ( 1)/( u_(0))`
`(1)/( 1.25) = ( - 1- 6)/( 6u_(0))`
`6 u_(0) = 1.25 xx ( - 7)`
`u_(0) = ( - 12.5 xx 7 )/( 6) cm`
`= 1.46 cm`