If a substance is behaving as convex lens in air and concave lens in water then which one of the following is its refractive index?

The behavior of a lens (converging or diverging) depends on its refractive index relative to the surrounding medium. According to the lensmaker's formula, the focal length's sign depends on the term (n_lens / n_medium - 1) [t5]. A lens behaves as a convex (converging) lens when its refractive index is greater than the surrounding medium [t5]. Since the substance acts as a convex lens in air (n ≈ 1.00), its refractive index must be greater than 1.00 [c4][t6]. Conversely, a convex lens reverses its behavior and acts as a concave (diverging) lens when placed in a medium with a higher refractive index than the lens material itself [t3][t5]. For the substance to behave as a concave lens in water (n ≈ 1.33), its refractive index must be less than that of water [t1][t4]. Therefore, the substance's refractive index is greater than air but lesser than water.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.2 The Refractive Index > p. 149
2. [2] https://www.sciencedirect.com/topics/biochemistry-genetics-and-molecular-biology/refraction-index