Final answer:
An object appears to be displaced when light passes from one medium to another due to refraction. Snell's law can be used to mathematically calculate the displacement by comparing the angles of incidence and refraction.
Step-by-step explanation:
The object in the bathtub appears to be displaced due to refraction. When light passes from one medium to another, it changes direction, and this apparent shift in position is called refraction. The amount of displacement can be calculated using Snell's law, which relates the angles of incidence and refraction to the refractive indices of the two media.
Mathematically, Snell's law is given by: n1 * sin(theta1) = n2 * sin(theta2), where n1 and n2 are the refractive indices of the two media, and theta1 and theta2 are the angles of incidence and refraction, respectively.
In this case, if the object is at the bottom of the tub and water is poured on it, the refractive index of water (n2) is 1.33. By comparing the angles of incidence (which can be assumed to be 90 degrees) and the angle of refraction (which can be calculated using Snell's law), the displacement of the object can be determined.