An oil film with refractive index 1.48 and thickness 290 nm is floating on water and illuminated with white light at normal incidence. What is the wavelength of the dominant color in the reflected
Light?

Question

Quizplus · Accepted Answer

The dominant color in the reflected light is the one that undergoes constructive interference. For normal incidence, the condition for constructive interference is 2nt = mλ, where n is the refractive index of the film, t is the thickness of the film, m is an integer (1, 2, 3, ...), and λ is the wavelength of the light. For m = 1, we have λ = 2nt = 2(1.48)(290 nm) = 862.4 nm. This wavelength corresponds to the color red. However, the question asks for the dominant color, which is the one that undergoes the strongest constructive interference. This occurs when m = 2, which gives λ = 431.2 nm. This wavelength corresponds to the color blue-green.

An Oil Film with Refractive Index 1