Draw a ray diagram to show the working of a compound microscope . Deduce an expression for the total magnification when the final is formed at the near point .
In a compound microscope, an object is place at a distance of 1.5cm from the objective of focal length 1.25cm. If the eye piece has a focal length of 5cm and the final image is formed at the near point, estimate the magnifying power of the microscope.

Explanation

Labelled Ray Diagram `:`

Expression for total magnification `:`
Magnification due to the objective ,
`m_(0) = ( h.)/( h ) = ( L)/( f_(0))`
Magnification `m_(e )`, due to eyepiece , ( when the final image is formed at the near point )
`m_(e ) = ( 1+ ( D)/( f_(e )))`
Total magnification,
`m= m_(0) m_(e ) = ( L)/( f_(0)) ( 1+ (D )/( f_(e)))`
Estimation of magnifying power `:`
Given `:` `u_(0) = - 1.5 cm, f_(0) = 1.25 cm`,
we have
`(1)/( f_(0)) = ( 1)/( v_(0)) - ( 1)/( u _(0))`
`(1)/(1.25) = ( 1)/( v_(0)) - ( 1)/( - 1.5) rArr v_(0) = 7.5 cm`
`m= (v_(0))/( u_(0)) ( 1 + ( D)/( f_(e)))`
`= ( 7.5 )/( - 1.5 ) ( 1+ ( 25)/( 5)) rArr m = - 30`