Diopters, reading glasses and stacking lens powers
What the diopter number on reading glasses means, how strengths translate to focal length, and why stacked lenses simply add up.
Reading the strength on a pair of glasses
Off-the-shelf reading glasses are labelled with a power such as +1.50 or +2.50, and that number is diopters. A higher diopter value is a stronger converging lens with a shorter focal length, which pulls a comfortable reading distance in closer. Feeding +2.00 into the power-to-focal-length mode returns a 0.5 m focal length, a useful sense of the distance the lens is optimised for. The plus sign marks a converging lens, the normal case for reading help.
From diopters to a focal length you can picture
Because power and focal length are reciprocals, small changes in diopters swing the focal length a lot at low powers and little at high powers. A 1 D lens focuses at 1 m, a 2 D lens at 0.5 m, and a 4 D lens at 0.25 m. Seeing the focal length in centimeters, as this tool shows, makes the practical working distance concrete. That is often more intuitive than the diopter label alone when choosing a strength.
Why stacked lenses add
When two thin lenses sit right against each other, their powers add directly, which is the rule the combine mode applies. Clip a +1 close-up filter onto a +2 lens and the pair behaves like a +3 lens with a shorter focal length. The same logic lets an optician think in additive steps when layering corrections. The approximation holds best when the lenses are genuinely thin and touching, with negligible gap between them.
Where the simple model stops
The reciprocal and additive rules describe ideal thin lenses. Real spectacle and camera lenses have thickness, and a meaningful air gap between two lenses changes the combined power beyond a plain sum. Prescriptions also carry cylinder and axis terms for astigmatism that a single power cannot capture. For everyday estimates and physics homework the thin-lens math here is accurate, but precision optical design needs the fuller lensmaker's equations.