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 miniumum every 12 seconds. Assuming that the film is flat

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Solution

Q.
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 _________ $π \times 10^{- 13} m^{3} / s$ . [2025]

Ans.
(54)

Maxima condition, $2 μ t = n λ$

$\Rightarrow t = \frac{n λ}{2 μ} \Rightarrow t = \frac{λ}{2 μ}, \frac{2 λ}{2 μ}, . . .$

Minima condition, $2 μ t = \frac{(2 n - 1) λ}{2}$

$\Rightarrow t = \frac{(2 n - 1) λ}{4 μ} \Rightarrow t = \frac{λ}{4 μ}, \frac{3 λ}{4 μ}, . . .$

$△ t = \frac{2 λ}{4 μ}$

Rate of evaporation $= \frac{Area (△ t)}{Time} = 54 π \times 10^{- 13} m^{3} / s$

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