A concave mirror has radius of curvature of 40 c m . It is at the bottom of a glass that has water filled up to 5 c m (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33 )

Step-by-step solution

Given u = - 5   c m f = - R 2 = - 40 2 = - 20   c m   Now 1 v + 1 u = 1 f 1 v = 1 - 20 = 1 - 5 ∴  v = + 20 3   c m Then Object distance d = 5 + 20 3 = 35 3   c m (below water surface) The image after refraction d ' = d μ 2 μ 1 = 35 3 1 1.33 = 8.77 d ' ≃ 8.8   c m