The LENSMAKER'S formula for a thin lens of refractive index $n$ (in air) with radii of curvature $R_1$ and $R_2$ is

1. NCERT §9.6.2 derives the Lensmaker's formula by combining the refraction-at-spherical-surface formulas for both surfaces of a thin lens. 2. Result: $\dfrac{1}{f} = (n - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$ — where $n$ is the lens material's refractive index relative to the surrounding medium. 3. Sign convention: $R$ is positive if the surface is convex toward the incoming light, negative if concave. 4. Examples: - Biconvex symmetric lens ($R_1 = +R$, $R_2 = -R$): $1/f = (n-1)(2/R)$, so $f = R/[2(n-1)]$. - Plano-convex ($R_1 = +R$, $R_2 = \infty$): $f = R/(n-1)$. 5. Options B, C, D have wrong functional forms. _Source: NCERT Class 12 Physics Part 2, Ch 9, §9.6.2 (Lensmaker's Formula, Eq. 9.20), p. 17–18._