The radii of cui-vature of the faces of a double convex lens are 10 cm and . 20 cm. The refractive index of the glass is 1-5. What is the power of this lens {in units of dioptre) ? .

To find the power of a double convex lens, we use the Lensmaker's formula: P = 1/f = (n - 1) * (1/R1 - 1/R2) [1]. For a double convex lens, the first surface is convex (R1 = +10 cm = +0.1 m) and the second surface is concave relative to the incoming light (R2 = -20 cm = -0.2 m) according to standard sign conventions. Given the refractive index n = 1.5, the calculation is: P = (1.5 - 1) * (1/0.1 - 1/(-0.2)). This simplifies to P = 0.5 * (10 + 5) = 0.5 * 15 = 7.5 Dioptres. Since the focal length of a convex lens is positive, the power is +7.5 D. This aligns with the principle that convex lenses are converging lenses with positive power.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.6 Sign Convention for Spherical Lenses > p. 155