A surface is coated with a material having index of refraction 1.69.If light in air has a wavelength of 388 nm and is normally incident on this surface,and it is found through interference effects with this light that the surface is 19 wavelengths thick,which of the following is the thickness of the surface?
A) 0.012 μm
B) 4.4 μm
C) 2.2 μm
D) 1.1 μm
E) 35 μm

Question

A surface is coated with a material having index of refraction 1.69.If light in air has a wavelength of 388 nm and is normally incident on this surface,and it is found through interference effects with this light that the surface is 19 wavelengths thick,which of the following is the thickness of the surface?
A) 0.012 μm
B) 4.4 μm
C) 2.2 μm
D) 1.1 μm
E) ​35 μm

Quizplus · Accepted Answer

The thickness of the surface is equal to the product of the wavelength of light in the material and the number of wavelengths that fit into the thickness. In this case, the wavelength of light in the material is 388 nm / 1.69 = 230 nm, and the number of wavelengths that fit into the thickness is 19. Therefore, the thickness of the surface is 230 nm * 19 = 4.4 μm.

A Surface Is Coated with a Material Having Index of Refraction