Question

A thin film with index of refraction nf separates two materials, each of which has an index of refraction less than nf. A monochromatic beam of light is incident normally on the film. If the light has a wavelength lambda within the film, maximum constructive interference occurs for which of the following film thicknesses?

a) λ / 4nf
b) λ / 2nf
c) λ / nf
d) λ / (2nf + λ)

Answer 1

For maximum constructive interference in a thin film with light incident normally, the film thickness should be an integral multiple of the wavelength within the film divided by twice the refractive index, hence λ/(2nf).

Step-by-step explanation:

The question is regarding constructive interference in a thin film. Constructive interference occurs when the thickness of the film is such that the path length difference for the two rays is an integral multiple of the wavelength within the film. Assuming the light is incident normally and there is no phase change upon reflection, constructive interference occurs at film thicknesses of λ/(2nf), where λ is the wavelength of light within the film and nf is the index of refraction of the film. Therefore, the correct answer is b) λ/(2nf).