Why is magnifying glass magnification M = 1 + (N/f) for a strained eye?

[RaulTheUCSCSlug]

Homework Statement

This is not really a homework problem but I wanted to figure out how to derive the equation for a strained eye
which is $$ M= (N/f) $$ where N is the object distance from the normal near point, and f is the focal length of a magnifying glass. But then, this is for a relaxed eye, why is it $$ M= (1+(N/g))$$ for a strained eye?

Homework Equations

I know that the equation for angular magnification is $$M=(θ'/θ)$$ and I also know that this is for when you use a simple magnifying lens.

(I tried inserting Greek letters using latex but doesn't seem to work? I wrote /theta, isn't that how you do it?)

The Attempt at a Solution

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I know that for a strained eye, is like when you squint the eye, which would reduce the light rays that enter your eye, but how does that change the focal point, and how does that lead to a plus one in magnification?

 

[haruspex]

I'm not at all sure what you mean by a strained eye in this context. Squinting will change depth of field, but will not directly change the focal point. It might exert some pressure on the eyeball, distorting it. Indeed, 'straining' might mean exerting such pressure, whether by squinting or otherwise.
You start off saying M=N/f is for a strained eye, but then say that's for a relaxed eye and switch to the other equation for strained.
What is g here?
Can you post any links as references for these equations?

For controls in LaTeX, including Greek letters, use backslash.

 

[andrevdh]

See HyperPhysics - Simple Magnifier.
Please ask if you do not understand what is written on the HyperPhysics web page.
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html