Thin films: Light of frequency 6.00 × 10¹⁴ Hz illuminates a soap film (n = 1.33) having air on both sides of it. When viewing the film by reflected light, what is the minimum thickness of the film that will give an interference maximum when the light is incident normally on it? (c = 3.00 × 10⁸ m/s) A) 24.0 nm B) 94.0 nm C) 188 nm D) 279 nm E) 376 nm

Question

Quizplus · Accepted Answer

For constructive interference in a thin film with air on both sides and light incident normally, the path difference must be an integral multiple of the wavelength in the medium (mλ_n, where m is an integer and λ_n is the wavelength in the medium). The minimum thickness for a maximum (first order, m=1) occurs when the path difference is equal to one wavelength in the medium. The wavelength in the medium (λ_n) is λ_0/n, where λ_0 is the wavelength in vacuum and n is the refractive index of the film. The thickness (t) for the first maximum is λ_n/2 (since the light travels back and forth through the film, doubling the path). Given frequency f = 6.00 × 10^14 Hz and speed of light c = 3.00 × 10^8 m/s, λ_0 = c/f = (3.00 × 10^8 m/s) / (6.00 × 10^14 Hz) = 5.00 × 10^-7 m = 500 nm. With n = 1.33, λ_n = 500 nm / 1.33 ≈ 376 nm. The minimum thickness for a maximum is therefore 376 nm / 2 ≈ 188 nm. However, due to a misunderstanding in the explanation process, the correct calculation for the minimum thickness that will give an interference maximum, considering the phase change upon reflection, should lead to a thickness that supports the condition for constructive interference differently. The correct approach involves recognizing that for the first constructive interference (m=0), the effective path difference should account for a half-wavelength shift due to reflection, leading to a minimum thickness calculation error in the explanation. The correct minimum thickness for the first constructive interference, considering the phase change, would indeed be half of the calculated wavelength in the medium, which is not correctly represented in the initial explanation provided.

Thin Films: Light of Frequency 6