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. 11.67 cm
B. 12 cm
C. 12.75 cm
D. 13 cm

Answer

A

Explanation

For objective lens, `(1)/(f_(o))=(1)/(v_(o))-(1)/(u_(o))`
Using proper sign convention,
`(1)/(+2.5)=(1)/(v_(o))-(1)/((-3.75))rArr v_(o)=7.5 cm`
For eye lens, `(1)/(f_(e ))=(1)/(v_(e ))-(1)/(u_(e ))`
`(1)/(+5)=(1)/((-25))-(1)/(u_(e )) rArr u_(e )=-4.16 cm`
or `" " |u_(e )|=4.16 cm`
`therefore` Distance between the lens `= 7.5+4.16=11.67 cm`