A microscope is made up of two convergent lenses, the objective lens and the eye

Question

A microscope is made up of two convergent lenses, the objective lens and the eyepiece lens. The objective is usually placed close to the object being viewed projecting a real enlarged image at the end of the microscope's 15.0 cm tube. The eyepiece acts as a magnifier, projecting a virtual enlarged image of the objective's image. Assuming that the focal length of the objective is 10.40 mm, and that the focal length of the eyepiece is 4.90 mm. Also assuming that the user has arranged the microscope such that the object being viewed is at a distance of 10.17 mm relative to the objective and that the eyepiece is at a distance of 157.9 mm from the objective.

a) Find in mm the final image distance (di), relative to the eyepiece, for a two lens microscope setup.

b) Find the overall magnification of a two lens system in this microscope setup.

Explanation / Answer

The image produced by objective lens will act like an object for eye-piece

fo= 10.40 mm

u = -10.17 mm

1/ fo= 1/ Vo-1/u

Vo= - 46 cm apprx ( objective will produce virtyual and enlarged image)

The object ditance for eyepeiec = 15 + 46 = 60.98 cm apprx or 609.8 mm apprx

using lens equation

1/.fe= 1/ Ve- 1/ Ue

1/ 4.90 = 1/  Ve - ( - 1/ 609.8)

Ve= 4.94 mm apprx ---final image distance relative to the eyepiece,

b)total magnification = m1m2

m1= (v/u) = (4.523)

m2( v/u) = ( 4.94/ -609.8) =

final mafgniufication= 0.03

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