Question

When a thin oil film spreads out on a puddle of water, the thinnest part of the film looks dark in the resulting interference pattern. What does this tell you about the relative magnitudes of the refractive indexes of oil and water?

Short answer

the refractive index of oil is greater than water.

Step-by-step solution

(a) Concept of refractive index.

The concept of refractive index is related to the refraction of light.The refractive index is a dimensionless quantity which gives the measure by which a medium can bend light travelling through it compared to other mediums. The light will bend more in the medium having a higher refractive index.

(b) Explanation of the argument.

Destructive interference occurs at the oil-water interface. This is only possible if; the reflected beams must have different phases. When the refractive index of oil is larger than water, the speed of light will decrease and the phase will change. This is the cause for the dark appearance of the film.