Question

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

Answer 1

Answer is: 54  

Maxima condition

\(2 \mu \mathrm{t}=\mathrm{n} \lambda \Rightarrow \mathrm{t}=\frac{\mathrm{n} \lambda}{2 \mu} \Rightarrow \mathrm{t}=\frac{\lambda}{2 \mu}, \frac{2 \lambda}{2 \mu}, \ldots \ldots\)

Minima condition \(2 \mu \mathrm{t}=(2 \mathrm{n}-1) \lambda / 2\)

\(\Rightarrow \mathrm{t}=\frac{(2 \mathrm{n}-1) \lambda}{4 \mu} \Rightarrow \mathrm{t}=\frac{\lambda}{4 \mu}, \frac{3 \lambda}{4 \mu}, \ldots \ldots\)

\(\Delta t=\frac{2 \lambda}{4 \mu}\)

Rate of evaporation \(=\frac{\mathrm{A}(\Delta \mathrm{t})}{\text { time }}=54 \times 10^{-13} \mathrm{~m}^{3} / \mathrm{s}\)