A compound microscope has tube length 300 mm and an objective of focal length 7.5 mm and an eyepiece of certain focal length. When eyepiece is replaced by another lens of focal length 20 mm, the magnifying power of compound microscope is increased by 100. The focal length of previous eyepiece is

Options

A. 10mm
B. 15mm
C. 22mm
D. 25mm

Answer

D

Explanation

`m=(L)/(f_(0))(1+(D)/(fe))," "m'=(L)/(f_(0))(1+(D)/(fe'))`
`implies m'-m=(DL)/(f_(0))(1)/(fe')-(1)/(fe) implies 100=(250xx300)/(7.5)((1)/(20)-(1)/(fe))`
`implies (1)/(fe)=(1)/(20)-(1)/(100)=(1)/(25) implies fe=25mm`.