You deposit a thin film of magnesium difluoride on a glass lens (n 1.60),reducing the reflection of yellow light,at normal incidence,to a minimum.You find that the thinnest coating that accomplishes this is 106 nm thick.The index of refraction for MgF₂ for yellow light ($\lambda$ = 585 nm)is A)1.50 B)1.38 C)1.15 D)1.00 E)0.707

Question

You deposit a thin film of magnesium difluoride on a glass lens (n > 1.60),reducing the reflection of yellow light,at normal incidence,to a minimum.You find that the thinnest coating that accomplishes this is 106 nm thick.The index of refraction for MgF₂ for yellow light ($\lambda$ = 585 nm)is A)1.50 B)1.38 C)1.15 D)1.00 E)0.707

Quizplus · Accepted Answer

The thinnest coating that reduces the reflection of yellow light to a minimum is 106 nm thick. This means that the thickness of the coating, t, is λ/4n, where λ is the wavelength of the yellow light and n is the refractive index of the coating.

Substituting λ = 585 nm and t = 106 nm, we get:

106 nm = (585 nm)/(4n)

Solving for n, we get:

n = (585 nm)/(4 × 106 nm) = 1.38

Therefore, the refractive index of the magnesium difluoride coating for yellow light is 1.38, which corresponds to choice B.

You Deposit a Thin Film of Magnesium Difluoride on a Glass