A cylindrical vessel, having both its diameter and height equal to 30 cm , rests on a horizontal surface. A small particle P is located inside it at a distance of 5.0 cm from the centre. An eye is situated such that the edge of the bottom is just visible, as shown in the figure. The particle P lies in the plane of the drawing. Determine the minimum height to which water must be poured into the vessel so that the part

Step-by-step solution

Let the bottom-left corner of the vessel be the origin (0,0) . The top-right corner is at (30, 30) . The eye is positioned such that the line of sight passes through (30, 30) and (0,0) . The angle of refraction r with the vertical is given by r = 30 30 = 1 , so r = 45^ . The center of the vessel's bottom is at x = 15 cm . The particle P is at a distance of 5 cm from the center. From the figure, it is closer to the origin, so its position is x = 15 - 5 = 10 cm . Let water be filled to a height h . The ray from P (10