Two convex lenses with power 2 dioptre are kept in contact with each other. The focal length of the combined lens system is

The power of a lens is defined as the reciprocal of its focal length (P = 1/f), where focal length is measured in meters [1]. When two thin lenses are placed in contact with each other, their combined power (P) is the algebraic sum of their individual powers (P = P1 + P2) [4]. In this problem, both convex lenses have a power of 2 dioptres. Therefore, the total power of the combined system is 2 D + 2 D = 4 D. To find the combined focal length (f), we use the relationship f = 1/P. Substituting the total power, we get f = 1/4, which equals 0.25 meters. Since convex lenses have positive power and focal length, the result is +0.25 m [2]. Thus, the focal length of the combined lens system is 0.25 m.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.8 Power of a Lens > p. 157
2. [2] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.6 Sign Convention for Spherical Lenses > p. 155
3. [4] https://en.wikipedia.org/wiki/Dioptre