Angular Magnification of Microscope

AI Thread Summary
The discussion revolves around calculating the angular magnification of a microscope with an objective power of +100D and an eyepiece power of +50D, separated by 18 cm. The user has determined the object distance to be -1.07 cm but is struggling to calculate the angular magnification, which is known to be 204.6x. They have attempted to use Gauss's Law and diagrammed the lenses but are unsure how to incorporate the 4D accommodation into their calculations. A suggestion is made to analyze an off-axis ray through the lenses to determine the exit angle for magnification. The conversation highlights the complexities of optical calculations in microscopy.
LeeLoo
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Homework Statement

Hey, I'm having trouble with this question on microscopes.

A microscope is made up of an objective of power +100D and an eyepiece of power +50D, the two lenses being separated by 18cm. How far in front of the objective must an object be placed if the image of the object formed by the microscope is viewed by an emmetrope exercising 4D of accommodation? Assume the observer's eye is close to the eyepiece. What will be the angular magnification in this case?

I worked out the object distance to be -1.07cm but I can't figure out how to get the angular magnification (the answer is 204.6x).


Relevant equations

Gauss Law


The attempt at a solution

I drew a diagram with the two lenses and labelled the distance between them (18mm). Then I worked backwards by treating the final image distance as 1/-8 as the person has to accommodate by 8D and from there I found the object distance for lens 2 which is the image distance for lens 1. Then I found the initial object distance. So now I'm stuck on the angular magnification. Can someone please show me the working out?

Thanks! :)
 
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I'm not sure what role the 4D accomodation plays, but couldn't you take a slightly off-axis ray passing through the center of the 100D lens, and calculate at what angle it exits the 50D lens?
 

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