A silicon monoxide thin film (n = 1.45)of thickness 73.9 nm is applied to a camera lens made of glass (n = 1.55).This will result in destructive interference for reflected light of what wavelength?

Question

Quizplus · Accepted Answer

When light reflects from the surface of the thin film, the reflected waves interfere with the incident waves. The condition for destructive interference is given by: 
2nt = (m + 1/2)λ
where n is the refractive index of the film, t is its thickness, m is an integer, and λ is the wavelength of the light. 
Plugging in the values given, 
2(1.45)(73.9 nm) = (m + 1/2)λ
Solving for λ, 
λ = 2(1.45)(73.9 nm) / (m + 1/2)
We want to find the wavelength for which the interference is destructive, which corresponds to m = 1 (the first minimum). Plugging in m = 1, we get 
λ = 429 nm. 
Therefore, the answer is C) 429 nm.

A Silicon Monoxide Thin Film (N = 1