A cylindrical vessel with a diameter of 12 cm holds 800 cm ^3 of water. A cylindrical glass piece having a diameter of 8.0 cm and a height of 8.0 cm is placed inside the vessel. Determine the position of the image of the vessel's bottom under the glass piece, when viewed by paraxial rays from above, as shown in the figure. The refractive index of glass is 1.50 and that of water is 1.33 .

Step-by-step solution

Volume of water initially in the vessel, V_w = 800 cm ^3 . Radius of the cylindrical vessel, R = 12 2 = 6 cm . Radius of the glass piece, r = 8.0 2 = 4.0 cm . Height of the glass piece, h_g = 8.0 cm . Volume of the glass piece, V_g = r^2 h_g = (4)^2 (8) = 128 cm ^3 . When the glass piece is placed in the vessel, it sinks to the bottom. The total volume occupied up to the new water level H is: V_ total = V_w + V_g = 800 + 128 = 928 cm ^3 . The new height of the water level from the bottom is: H = V_ total R^2 = 928