Physics Question from JEE Main 2025 · 28 January, Shift 2

A thin transparent film with refractive index $1.4$ is held on a circular ring of radius $1.8 \, \text{cm}$. The fluid in the film evaporates such that transmission through the film at wavelength $560 \, \text{nm}$ goes to a minimum every $12 \, \text{s}$. Assuming that the film is flat on its two sides, the rate of evaporation is _____ $\pi \times 10^{-13} \, \text{m}^3/\text{s}$.