A 360-nm thick oil film floats on the surface of a pool of water water. The indices of refraction of the oil and the water are 1.5 and 1.33, respectively. When the surface of the oil is illuminated from
Above at normal incidence with white light, what are the two wavelengths of light between 400 nm
To 800 nm wavelength that are most strongly reflected?

Question

Quizplus · Accepted Answer

The condition for constructive interference in thin films is given by $2nt = m\lambda$, where $n$ is the refractive index, $t$ is the thickness, and $m$ is an integer. For the oil film, $2(1.5)(360 \text{ nm}) = m\lambda$. Solving for $m = 1$ and $m = 2$ within the 400-800 nm range gives approximately 430 nm and 720 nm.

A 360-Nm Thick Oil Film Floats on the Surface of a Pool