A thin transparent film with refractive index \( 1.4 \), is held on 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 \( 12 \, \text{seconds} \). Assuming that the film is flat on its two sides, the rate of evaporation is __________ \( \pi \times 10^{-13} \, \text{m}^3/\text{s} \).
