A one-rupee coin is placed at the bottom of a vessel. Water is then poured into the vessel such that the depth of water becomes 20 cm. If water has refractive index 4/3, the coin would be seen at a depth of

The phenomenon where a submerged object appears closer to the surface is due to the refraction of light as it travels from a denser medium (water) to a rarer medium (air) [t2, t5]. According to Snell's Law, light rays bend away from the normal at the interface, creating an optical illusion of reduced depth [c1, t3]. The relationship between the real depth (D), the refractive index (μ), and the apparent depth (d) is given by the formula: d = D / μ [t2, t6]. In this problem, the real depth of the water is 20 cm and the refractive index of water is 4/3 [t1]. Substituting these values into the formula: d = 20 / (4/3) = 20 * (3/4) = 15 cm. Therefore, the coin at the bottom of the vessel will be seen at an apparent depth of 15 cm [t4, t6].

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > Activity 9.10 > p. 148