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 16.0 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 9.30 mm, and that the focal length of the eyepiece is 4.50 mm. Also assuming that the user has arranged the microscope such that the object being viewed is at a distance of 9.87 mm relative to the objective and that the eyepiece is at a distance of 165.3 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

We find the image formed by the refraction of the first lens

: (1/do1) + (1/di1) = 1/f1

Assuming that the focal length of the objective is 9.30 mm

1/9.3 =1/160 +1/di1

di1=9.87mm

This image is the object for the second lens. Because it is beyond the second lens, it is a virtual object for the second lens and has a negative object distance:

d02=16.53-9.87

=6.66

1/6.66 +1/di2=1/4.5

di2=13.875mm

Thus the final image is real, 13.875 mm beyond second lens

The total magnification is the product of the magnifications for the two lenses:

.m = m1m2 = (

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