White light is shone on a very thin layer of mica ( $\mathrm{n}=1.57)$, suspended in air, at normal incidence. When the mica layer is observed from the illuminated side, constructive interference is observed for wavelengths of violet $(400 \mathrm{~nm})$ and yellow $(560 \mathrm{~nm})$ light. What is the thickness of the mica layer?
A) $446 \mathrm{~nm}$
B) $892 \mathrm{~nm}$
C) $700 \mathrm{~nm}$
D) $382 \mathrm{~nm}$
E) $764 \mathrm{~nm}$
F) $600 \mathrm{~nm}$

Question

Quizplus · Accepted Answer

Constructive interference occurs when the path length difference between two waves is an integer multiple of the wavelength. In this case, the path length difference is twice the thickness of the mica layer, since the light travels through the mica layer twice. Therefore, the thickness of the mica layer is half the wavelength of the light that is constructively interfering. For violet light, the wavelength is 400 nm, so the thickness of the mica layer is 200 nm. For yellow light, the wavelength is 560 nm, so the thickness of the mica layer is 280 nm. The correct answer is therefore A) 446 nm, which is the average of 200 nm and 280 nm.

White Light Is Shone on a Very Thin Layer of Mica