As the radius of curvature of a curved lens is increased, the focal length of the lens will:

• A. Increase
• B. Decrease
• C. Remain the same
• D. Be indeterminate unless the frequency is known

Answer: (A)

The main idea is that a lens’s focal length is set by how strongly it bends light, which depends on its curvature and the material’s index. Increasing the radius of curvature makes the lens surfaces less curved (flatter). Less curvature means less bending power, so the lens converges light less aggressively, and the focal point moves farther away — the focal length increases.

For a symmetric bi-convex lens, the thin-lens formula shows this directly: 1/f = (n − 1)(1/R1 − 1/R2). If the surfaces share equal but opposite curvatures, R1 = R and R2 = −R, giving 1/f = 2(n − 1)/R, so f = R/[2(n − 1)]. Here, as R grows, f grows proportionally. Frequency (or wavelength) isn’t needed to determine this basic relationship, though dispersion can slightly change n with wavelength.

So, increasing the radius of curvature increases the focal length.