The lead architect on the design team of a new skyscraper decides that the outer

Question

The lead architect on the design team of a new skyscraper decides that the outer surface of the building’s windows need to be coated with a reflective layer in order to lower airconditioning costs. MgF2 is chosen for the reflective layer, which has a refractive index n=1.38. Assume that the refractive index of the window glass is 1.5 and that the reflective coating should work optimally at the peak of the sunlight spectrum,500 nm.

Part A) What is the minimum thickness of film that is needed?Express your answer in nanometers to three significant figures. t=? nm

Part B). Suppose the layer needs to be thicker than 200 nm in order to hold up to the weather. What other thicknesses would also work? Give only the three thinnest ones.Enter your answers in nanometers, separated with commas, to three significant figures. t2,t3,t4=? nm

Explanation / Answer

A) condition for constructive interefernce,

2*t = m*lamda/n (m = 1,2,3,....)

for minimum thuckness, m = 1

so, t = lamda/(2*n)

= 500 nm/(2*1.38)

= 181 nm

B) t2 = 2*t1 = 2*181 = 362 nm

t3 = 3*t1 = 543 nm

t4 = 4*t1 = 4*181 = 724 nm

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