Re: [Phys-L] lens magnification

[John Denker <jsd@av8n.com>]

On 05/17/2013 12:20 PM, Anthony Lapinski wrote:
> Magnifying glasses (biconvex lenses) are sold with a power rating (3x,
> 4x, etc.). How is this determined?

I just now fixed the wikipedia article to get this right.
  http://en.wikipedia.org/wiki/Magnifying_glass

By longstanding convention, the so-called "magnification" is 
      (0.25 m) Φ + 1                      [1]
where Φ is the actual optical power (typically measured in diopters).
Example, a so-called "2x" lens has Φ = 4 diopters.

Any sane person would use Φ directly.  For example, eyeglass prescriptions 
are written in diopters.

In expression [1], the factor of (0.25 m) represents an assumption about 
the "typical" near point of the *unaided* eye, i.e. how close you could 
bring an object to the eye and still focus on it.  The true near point 
varies tremendously from person to person.

Also, the true angular magnification depends very much on details of how
the lens is used, so expression [1] must be considered arbitrary, several
times over.  It is, however, the answer to the question that was asked.