Question

PART 2: Quantitative Questions. Show your work, especially diagrams. Explairn your reasoning. 1.) A coating is being applied on a pane of glass (for a window) to reduce the reflectivity of light with a wavelength of 522 nm at near normal incidence from the air. The coating material has an index of refraction of 1.375. (a) How thick should the coating be if the light is incident from the air and hits the coating side first? (b) How would your answer change if the light is incident from the glass side first. For (a) and (b), explain your reasoning and justify your answer using the fundamental physics principles and definitions we learned in class.

Answer 1

(a) How thick should the coating be if the light is incident from the air and hits the coating side first?

For destructive interference condition, we have

2 t = [m + (1/2)] ( $\lambda$ / n)

t = (1/2) [m + (1/2)] ( $\lambda$ / n)

At m = 0, we get

t = $\lambda$ / 4n

where, n = refractive index of coating material = 1.375

$\lambda$ = wavelength of light = 522 x 10^-9 m

t = (522 x 10^-9 m) / [4 (1.375)]

t = 9.49 x 10^-8 m

converting m into nm :

t = 95 nm