An oil film covers the surface of a small pond. The refractive index of the oil is greater than that of water. At one point on the film, the film has the smallest non-zero thickness for which there will be destructive interference in the reflected light when infrared radiation with wavelength 800 nm is incident normal to the film. When this film is viewed at normal incidence at this same point, for what visible wavelengths, if any, will there be constructive interference? (Visible light has wavelengths between 400nm and 700 nm )

Explanation

To solve the problem, we need to determine the conditions for destructive and constructive interference for the oil film on the pond. Here’s a step-by-step solution:

### Step 1: Understanding Destructive Interference
For destructive interference in a thin film, the condition is given by:
\[ 2 \mu t = (n + \frac{1}{2}) \lambda \]
where:
- \( \mu \) is the refractive index of the oil,
- \( t \) is the thickness of the oil film,
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