A surface is coated with a material having index of refraction 1.41.If light in air has a wavelength of 701 nm and is normally incident on this surface,and it is found through interference effects with this light that the surface is 11 wavelengths thick,which of the following is the thickness of the surface?
A)4.5E-8 m
B)5.5E-6 m
C)2.7E-6 m
D)1.4E-6 m
E)2.1E-5 m

Question

Quizplus · Accepted Answer

The thickness of the surface can be calculated by first finding the wavelength of light within the material using the formula $\lambda' = \lambda / n$, where $\lambda$ is the wavelength in air (701 nm) and $n$ is the index of refraction (1.41). This gives $\lambda' = 701 nm / 1.41 = 497 nm$. The thickness of the surface is then found by multiplying this wavelength by the number of wavelengths the surface is thick (11), giving a thickness of $497 nm * 11 = 5467 nm = 5.5E-6 m$.

A Surface Is Coated with a Material Having Index of Refraction