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. 12cm
C. 12.75cm
D. 13cm

Answer

A

Explanation

For object a lens, `(1)/(f_(o))=(1)/(v_(o))=(1)/(u)`
Using proper sign convention, `(1)/(+2.5)=(1)/(v_(o))-(1)/(-3.75) Rightarrow v_(u)=7.5cm`
For eye lens, `(1)/(f_(e))=(1)/(v_(e))-(1)/(u_(e))`
`(1)/(+5)=(1)/(-25) -(1)/(u_(e)) Rightarrow mu_(e)=-4.16cm`
or, `|u_(e)|=4.16cm`
`therefore` Distance between the two lens=7.5+4.16=11.67cm