The Keyhole Limit: Magnifier Power, the Shrinking Window, and the Strongest Lens That Still Lets a Sentence Be Read

A hand magnifier trades the two things a reader wants against each other: stronger lenses enlarge print more but show less of the page at once. This paper computes that trade-off for a stated geometric model of a 50 mm diameter simple magnifier and a stated word footprint of 12 mm, and finds where fluency breaks. Magnification rises linearly with power, from 1.0 times at +4 D to 6.0 times at +24 D, while the visible field falls in inverse proportion, from 50.0 mm to 8.3 mm. Against a stated fluency criterion of about four words in view, the strongest usable general-purpose magnifier in this size is +4 D; stronger lenses remain right for spotting prices and labels but force word-by-word reading of text. The dispensing rule is to prescribe the weakest power that makes print legible, never the strongest the wearer can decipher a single word through. This study is simulated, not measured.