Answer
The oil’s index of refraction must be greater than that of air, and greater than that of water.
Work Step by Step
This is explained using the principles on page 1172. Reflected light undergoes a phase change of $\pi$ rad at the air-oil interface, and no phase change at the subsequent oil-water interface.
We know this because the thinnest part of the film looks black, indicating that the 2 reflected beams destructively interfere.
Because no phase change occurs at the second interface, between oil and water, light must travel more slowly in oil than in water.
