Question

A thin transparent film with refractive index 1.4 is held on a 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:

Hint:

For thin film interference, use the relationship between film thickness, wavelength, and time to calculate the rate of evaporation or thickness change.

Answer 1

Correct Answer: 1.67

Given Data:

Refractive Index of Film (μ): 1.4

Wavelength (λ): 560 nm = 560 × 10⁻⁹ m

Time for minimum transmission (T): 12 seconds

Effective Wavelength in the Film:

λ' = λ / μ = (560 × 10⁻⁹) / 1.4 = 400 × 10⁻⁹ m

Change in Thickness for One Minimum:

Δd = λ'/2 = (400 × 10⁻⁹) / 2 = 200 × 10⁻⁹ m

Rate of Evaporation:

Rate = Δd / T = (200 × 10⁻⁹) / 12 ≈ 1.67 × 10⁻⁸ m/s

Answer:

The rate of evaporation is approximately 1.67 × 10⁻⁸ m/s.