How Far Should a Magnifying Glass Be Held for Maximum Angular Magnification?

[A_lilah]

Homework Statement

If you have normal vision and are properly using a magnifying glass with a refractive power of 12.5 diopters, how far should you hold it from the object to achieve maximum angular magnification?

Homework Equations

1 diopter = 1/focal length = m^-1
M=angular magnification
Mmax = [(Near Point)/f] +1
Near point for someone with normal vision = 25cm

The Attempt at a Solution

First I use 12.5 diopters to figure out the focal length:

1/12.5 = .08m = 8cm
Then I plugged this into the equation for Mmax for someone with normal vision:
[25cm / 8cm] + 1 = 4.125 = Mmax

I don't know how to use any of this to find the maximum distance the object should be held at though. The prof already posted the answers-this should be 6.67 cm- I'm just trying to practice before an exam and learn how to do this, so any help/tips would be great. Thanks!

 

[Nax13]

Maybe you can use this:

M = (f-v)/f

4.125 = 8-v/8

v = 25cm

I am not so sure abt the answer. Another formula that you might find useful is M = f/(f+u)