Green light having a wavelength of 550 nm (in air) is vertically incident on a thin film of water that has an index of refraction of 1.30. The film of water rests above a plastic pane (having an index of refraction of 1.22). No green light is reflected. The minimum (nonzero) thickness of the film of water is
A) 212 nm.
B) 450 nm.
C) 423 nm.
D) 108 nm.

Question

Quizplus · Accepted Answer

For destructive interference (no reflection) in a thin film, the condition is $2nt = (m + \frac{1}{2})\lambda$, where $n$ is the refractive index of the film, $t$ is the thickness, $\lambda$ is the wavelength in the film, and $m$ is an integer. The wavelength in the film is $\lambda/n$. For minimum thickness, $m = 0$, so $2(1.30)t = \frac{1}{2}(550/1.30)$. Solving gives $t = 212$ nm.

Green Light Having a Wavelength of 550 Nm (In Air)