Cut Lens Focal Length · CAP 2025 #4
Physics · optics
Problem
A thin lens of focal length f = 10 cm is cut into two equal halves. What is the new focal length of each half? A. 2.5 cm B. 5 cm C. 10 cm D. 20 cm E. 40 cmIntuitive explanation
When you cut a lens in half, you're not changing the curvature of its surfaces—each piece still has the same radius of curvature. The lensmaker's equation tells us that focal length depends on surface curvature and refractive index, not on the lens's size or shape. Think of it this way: a smaller piece of glass with the same curved surfaces bends light the same way as the original. The key insight is that focal length is a property of the optical power per unit area, and cutting the lens doesn't alter that fundamental property.
Intuitive explanation
When you cut a lens in half, you're not changing the curvature of its surfaces—each piece still has the same radius of curvature. The lensmaker's equation tells us that focal length depends on surface curvature and refractive index, not on the lens's size or shape. Think of it this way: a smaller piece of glass with the same curved surfaces bends light the same way as the original. The key insight is that focal length is a property of the optical power per unit area, and cutting the lens doesn't alter that fundamental property.