The thin-lens formula for a thin lens in air is 1/f = (n - 1)(1/R1 - 1/R2). For a symmetric bi-convex lens with R1 = +12 cm and R2 = -12 cm and n = 1.50, what is f?

• A. -24 cm
• B. +6 cm
• C. +12 cm
• D. +48 cm

Answer: (C)

Understanding how the thin-lens equation works in air with the sign convention for radii of curvature is key. The formula 1/f = (n − 1)(1/R1 − 1/R2) uses radii with positive or negative signs depending on the direction of the center of curvature relative to the light’s travel. For a symmetric bi-convex lens, the first surface is convex toward the incoming light, giving R1 = +12 cm. The second surface is convex toward the outgoing light, so its center of curvature lies to the left of that surface, giving R2 = −12 cm. The index contrast is n − 1 = 1.50 − 1 = 0.50.

Compute the curvature term: 1/R1 − 1/R2 = 1/12 − 1/(−12) = 1/12 + 1/12 = 1/6. Multiply by the index contrast: 0.50 × 1/6 = 1/12.

Thus 1/f = 1/12, so f = 12 cm. The positive focal length confirms a converging lens, as expected for a bi-convex lens.