A microscope consists of an objective of focal length 1.9 cm and eyepiece of focal length 5 cm. The two lenses are kept at a distance of 10.5 cm. If the image is to be formed at the least distance of distinct vision, the distance at which the object is to be placed before the objective is (least distance of distinct vision is 25 cm)

Options

A. 6.2 cm
B. 2.7 cm
C. 21.0 cm
D. 4.17 cm

Answer

B

Explanation

`f_(o)=1.9 cm, f_(e)=5 cm `
`L=v_(o)+u_(e)=10.5cm`
`v_(o)= +D = 25 cm`
From lens formula
`(1)/(v_(e)) - (1)/(mu_(e))= (1)/ (f_(e)) rArr (1)/(-25) = (1)/ (u_(e))+(1)/(5)`
`(-6)/(25)= (1)/(u_(e)) rArr |mu_(e)|= (25)/(6) cm `
`L = v_(o) + |u_(e)| = (21)/(2)cm`
`|u_(e)|=(25)/(6) cm `
`v_(o)=(21)/(2) -(25)/(6)`
`v_(o)=(76)/(12)=(19)/(3) cm `
`v_(o)= +(19/3) cm `
From lens formula,
`(1)/(u_(o))=(1)/(v_(o))-(1)/(f_(o)) rArr u_(o)= (f_(o)v_(o))/(f_(o)-v_(o))`
`u_(o) = (19/3 xx 19/10)/(19/10 -19/3) = (19/30)/((-7)/(30)) = (19)/(-7) = -2.71 cm `
`u_(o) = 2.7cm `