A compound microscope is used to enlarge an object kept at a distance 0.03m from its objective which consists of several convex lenses in contact and has focal length 0.02m. If a lens offocal length 0.1m is removed from the objective, find out the distance by which the eyepiece of the microscope must be moved to refocus the image?

Options

A. 2.5 cm
B. 6 cm
C. 15 cm
D. 9 cm

Answer

D

Explanation

Initially `v_(o) = (u_(o)f_(o))/(u_(o) - f_(o)) = (3xx 2)/(3-2 ) = 6 cm `
Now,
`(1)/(f_(eq)) = (1)/(f_(1)) + (1)/(f_(2)) + (1)/(f_(3)) +…. = (1)/(f_(1)) + (1)/(f._(eq))`
`[ (1)/(f._(eq)) = (1)/(f_(2)) + (1)/(f_(3)) + …. ] `
If one lens is removed then
`(1)/(f_(eq)) = (1)/(f_(eq)) - (1)/(f_(1)) = (1)/(2) - (1)/(10 ) rArr f._(eq) = 2.5 `cm
Finally
`therefore " " v_(o) = (u_(o) f_(eq))/(u_(o) - f_(eq)) = (3 xx 2.5 )/(3 -2.5) = 15` cm
For refocusing the image, eye piece must be moved by
15 − 6 = 9cm .