A student focuses sunlight to a point with a thin converging (convex) lens. Which direct measurement can the student make?

• A. The diameter of the lens
• B. The approximate focal length of the lens
• C. The refractive index of the lens
• D. The focal ratio of the lens

Answer: (B)

When a thin converging lens forms an image of distant light, the rays converge at the lens’s focal point. The sun is effectively at infinity, so the spots you see on a screen after focusing light will come to a point at a distance equal to the focal length from the lens. By placing a screen and moving it along the axis until the focused spot is smallest and sharpest, you can directly measure that distance—the focal length.

The diameter of the lens can be measured, but that’s not obtained from where the sun’s image focuses. The refractive index isn’t read directly from this setup, since it requires knowing how much light bends at the interface, not just where the focus occurs. The focal ratio involves both focal length and diameter, so you’d need to know the diameter separately to compute it; it isn’t a single direct measurement from the focusing observation.