In a compound microscope, the focal length of the objective and the eye lens are `2.5 cm` and `5 cm` respectively. An object is placed at `3.75cm` before the objective and image is formed at the least distance of distinct vision, then the distance between two lenses will be `( i.e.` length of the microscope tube )

Options

A. `11.67cm`
B. `12.67cm`
C. `13.00 cm`
D. `12.00 cm`

Answer

A

Explanation

`L_(D)=V_(o)=u_(e)` and for objective lens `(1)/(f_(o))=(1)/(v_(o))-(1)/(u_(o))`
Putting the values with proper sign convention.
`(1)/(+2.5)=(1)/(v_(o))-(1)/((-3.75))impliesv_(o)=7.5cm`
For eye lens `(1)/(f_(e))=(1)/(v_(e))-(1)/(u_(e))`
`rArr (1)/(+5)=(1)/((-25))-(1)/(u_(e))impliesu_(e)=-4.16cm`
`=|u_(e)|=4.16cm`
Hence `L_(D)=7.5+4.16=1.67 cm`