A thin film of magnesium fluoride (n = 1.38) is applied to glass (n = 1.50). If the thickness of the film is 100 nm, for what visible wavelength will it be nonreflecting?
A) 600 nm
B) 578 nm
C) 552 nm
D) 504 nm
E) 491 nm

Question

Quizplus · Accepted Answer

For a thin film to be nonreflecting, the reflected waves from both sides of the film must be in phase and cancel each other out. This means that the path difference between the two reflected waves must be equal to an odd multiple of half the wavelength:

2nt = (2m + 1)λ/2

where n is the refractive index of the film, t is the thickness of the film, m is an integer (0, 1, 2, 3...), and λ is the wavelength of the incident light.

Substituting the given values, we get:

2(1.38)(100 nm) = (2m + 1)λ/2

Solving for λ, we get:

λ = 4t/n(2m + 1) = 552 nm (for m = 0)

Therefore, the best choice is C (552 nm).

A Thin Film of Magnesium Fluoride (N = 1