A coin rests at the bottom of a swimming pool of depth d. A layer of clear oil of thickness t floats on top of the water. The indices of refraction are noil=1.40 for the oil and nwater=1.33 for the water; air above the oil has index nair≈1.00.
A swimmer standing on a diving board looks down at the coin. The swimmer’s eye is located directly above the coin along a line that is nearly, but not exactly, normal to the liquid surfaces. Neglect surface curvature and assume each interface is perfectly flat.
(a) When the swimmer’s line of sight is essentially normal to the surfaces, describe qualitatively whether the apparent depth of the coin is greater than, less than, or equal to the actual depth d+t. Provide reasoning based on the indices of refraction of the three media.
(b) The swimmer pours additional oil so that the thickness of the oil layer increases while d remains fixed. Predict qualitatively how the apparent depth observed along the same near-normal line of sight changes as t increases. Explain your reasoning.
(c) Now the swimmer tilts their head so that the line of sight makes a significant angle with the normal. Describe qualitatively how the lateral (sideways) position of the coin’s apparent image shifts relative to its actual position on the pool bottom. Explain how refraction at the two interfaces produces this effect.
(d) Consider the limiting case t→0 (no oil). Explain how your answers to parts (a)–(c) reduce to the familiar single-interface situation of air–water refraction.