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

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.

Explanation / Answer

A) By thin film interference for destructive interference,

2nt = (m+1/2)

2*1.38*t = (0+1/2)*500

Gives, t=90.6nm

B) For m=1,

2nt = (m+1/2)

2*1.38*t = (1+1/2)*500

Gives, t=271.7nm

For m=2,

2nt = (m+1/2)

2*1.38*t = (2+1/2)*500

Gives, t=453nm

For m=3,

2nt = (m+1/2)

2*1.38*t = (3+1/2)*500

Gives, t=634nm

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