The focal length of a lens depends on

The correct answer is Option (1) → The radii of curvature of its surfaces and the refractive index of the lens with respect to surrounding medium.

The focal length of a thin lens is given by the lens maker's formula

    \( \displaystyle \frac{1}{f} = \left(n_{21} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right), \qquad n_{21} = \frac{n_2}{n_1} \)

where \( n_2 \) is the refractive index of the lens material and \( n_1 \) that of the surrounding medium. So \( f \) depends on the radii of curvature and on the relative refractive index of the lens with respect to the medium.

Option (2) Only the radii of curvature of its surface and the absolute refractive index of its material. — Incorrect. The absolute refractive index is enough only when the lens is in air; in another medium the focal length changes.

Option (3) Only the radii of curvature of its surface and the refractive index of the surrounding medium. — Incorrect. The refractive index of the lens material itself is left out.

Option (4) Only the radii of curvature of its surface. — Incorrect. Lenses of the same shape but different materials have different focal lengths.

NCERT (2026-27):
Refraction by a Lens – “… By the sign convention, BC₁ = + R₁, DC₂ = –R₂ So Eq. (9.20) can be written as

    \( \displaystyle \frac{1}{f} = (n_{21} - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \qquad \left(\because\ n_{21} = \frac{n_2}{n_1}\right) \qquad (9.21) \)

Equation (9.21) is known as the lens maker’s formula. It is useful to design lenses of desired focal length using surfaces of suitable radii of curvature.”