# Microscope objective and eyepiece focal lengths

## Homework Statement

A microscope has a 13.0 x eyepiece and a 57.0 x objective lens 20.0 cm apart. Calculate the focal length of each lens. Where the object must be for a normal relaxed eye to see it in focus?

## Homework Equations

M=m(objective)*m(eyepiece)=f(objective)/f(eyepiece)

length=f(objective)+f(eyepiece)

with a relaxed eye m(eyepiece)=N/f(eyepiece) where N=near point (25 cm for normal naked human vision)

M≈(N*l)/[f(eyepiece)*f(objective)]

m(objective)=[l-f(eyepiece)]/do where do=distance of the object from the objective and l=length (distance between lenses)

## The Attempt at a Solution

We had a similar problem where you could use f(objective)=length-f(eyepiece) to get M(tot)=[length-f(eyepiece)]/f(eyepiece) to determine the focal length of the eyepiece, but that does not work on this problem for some reason. All of the other equations I know of involving either focal length contain unknown variables and I can't find a way to get rid of those unknowns.

Also, I'm a little lost conceptually on the ideas of near points and relaxed vision. The problems we have had so far dealing with those concepts I have gotten lucky on but it would be nice to visualize and understand what I'm plugging in and why when I'm dealing with a "relaxed eye" situation.

Thanks for the help.