A compound microscope uses an objective lens of focal length `4 cm` and eye lens of focal length `10 cm`. An object is placed at `6 cm` from the objective lens. Calculate magnifying power of compound microscope if final image is formed at the near point. Also, calculate length of the tube of compound microscope.

Explanation

First we shall find the image distance for nth objective `(v_(0))`.
`(1)/(f_(0))=(1)/(v_(0))-(1)/(u_(0))`
`f_(0)=4cm, u_(0)=-6"cm"`
`Rightarrow v_(0)=12"cm"`
(ii) Magnification of the microscope is,
`m=m_(0)m_(e)=(v_(0))/(u_(0))(1+(D)/(f_(e)))`
`" "=((12)/(-6))(1+(25)/(10))`
The length of the microscope is `v_(0)+u,u=|u_(e)|` is the object distance for the eyepiece. And `u_(e)`can the found using.
`Rightarrow (1)/(f_(0))=(1)/(D)-(1)/(u_(e))`
Hence, `u=|u_(e)|=7.14cm`
Length of the micropcope `v_(0)+u=19.14cm`
`L=(mf_(0)f_(e))/(D)=(7xx4xx10)/(25)=11.2cm`