A small object is located at the centre of the bottom of a cylindrical vessel of radius 3 cm and height 4 cm , which is completely filled with water. Consider a ray that leaves the vessel through a corner. Suppose this ray, along with the ray travelling along the axis of the vessel, is used to trace the image. Determine the apparent depth of the image and the ratio of the real depth to the apparent depth under these

Step-by-step solution

Let the real depth of the vessel be H = 4 cm and its radius be R = 3 cm . The object is at the centre of the bottom. A ray travelling from the object to the corner of the vessel has an angle of incidence i at the water surface. From the geometry of the vessel: i = R H = 3 4 This gives i = 3 5 . Applying Snell's law at the corner of the vessel: n i = 1 r 4 3 3 5 = r r = 4 5 This implies r = 4 3 . The refracted ray emerges at an angle r with the normal. When this ray is traced backward, it intersects the normal (the