An uncut lens must be at least how many mm in diameter to allow the cutting of a 48mm round lens, decentered 4mm in?

To determine the minimum diameter of an uncut lens required to produce a 48mm round lens that is decentered by 4mm, it's essential to consider the impact of decentering on the overall size of the uncut lens.

When the lens is decentered, it means that the optical center of the lens is moved from its standard position. In this scenario, a 4mm decentering implies that the center of the lens will be shifted inward. To maintain the circular shape of the final 48mm lens while accounting for this shift, the uncut lens needs to have additional diameter on one side to accommodate the decenter.

If the finished lens has a diameter of 48mm and is decentered by 4mm, the effective width needed on the side shifted inward increases by 4mm, plus the radius of the original lens. The radius of a 48mm lens is 24mm, and by adding the 4mm required for decentering, the total distance from the optical center to the edge of the lens becomes 28mm (24mm + 4mm). Since this is the radius, the diameter of the uncut lens must be at least double this measurement, which is 56