A water tank is filled to a height of 16 cm with water (refractive index = 4 3 ). A plane mirror is placed horizontally at the bottom of the tank. A small object is placed in air, 12 cm above the water surface. An observer looks vertically downwards from the air above the object. The apparent depth of the image formed by the mirror, as measured from the water surface, is:

Step-by-step solution

First, we find the apparent position of the object as seen by the mirror at the bottom of the tank. The actual height of the object above the water surface is 12 cm . Since light travels from air ( n = 1 ) to water ( n = 4 3 ), the apparent height of the object from the water surface is: h_ app = 12 4/3 1 = 16 cm The total apparent distance of the object from the mirror is the depth of the water plus this apparent height: u = 16 cm + 16 cm = 32 cm The plane mirror forms an image at the same distance behind it. Ther