What is the minimum diameter in millimeters for an uncut lens to allow cutting a 48 mm round lens decentered 4 mm?

What is the minimum diameter in millimeters for an uncut lens to allow cutting a 48 mm round lens decentered 4 mm?

• A. 48
• B. 60
• C. 52
• D. 56

Answer: (D)

When cutting an off-center lens from a circular blank, the blank must be large enough to cover the finished lens at its offset position. The finished lens has a diameter of 48 mm, so its radius is 24 mm. If the cut is decentered by 4 mm, the far edge of the finished lens from the blank’s center can extend 4 mm beyond the lens center, giving a maximum distance of 24 + 4 = 28 mm from the blank center. Therefore the blank must have at least this radius, meaning a diameter of 2 × 28 = 56 mm. Any larger blank would work, but 56 mm is the smallest that accommodates the off-center cut.

When cutting an off-center lens from a circular blank, the blank must be large enough to cover the finished lens at its offset position. The finished lens has a diameter of 48 mm, so its radius is 24 mm. If the cut is decentered by 4 mm, the far edge of the finished lens from the blank’s center can extend 4 mm beyond the lens center, giving a maximum distance of 24 + 4 = 28 mm from the blank center. Therefore the blank must have at least this radius, meaning a diameter of 2 × 28 = 56 mm. Any larger blank would work, but 56 mm is the smallest that accommodates the off-center cut.