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.

A) What is the minimum thickness of film that is needed ( in nm) ?

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.

Answer 1

A) Minimum thickness of the film can be determined by the formula 2nt-mi For destructive interference For minimum thickness, m-1 λ wavelength of light used 500nm 2x1.38 t-181.159nm B) Layeris thicker than 200nm t> 200nm Applying condition for interference tmx_ t-mx181.159 m-2, t,-2x181.159-362.318nm m-3, t-3x181.159-543.478nm m = 4,ち= 4× 18 1.159 = 724.637mm Therefore the three thickness is given by 362.318nm,543.478nm,724.637nm