An optical designer is asked to eliminate the bright reflection seen from a transparent window whose substrate index of refraction is 1.60. Light is incident normally from air.
The designer will deposit a single uniform layer of an as-yet-unspecified transparent material on the window.
(a) Derive an expression, in symbolic form, for the index of refraction of the coating that will cause the two first-order reflected rays (one from the air-to-coating interface and the other from the coating-to-substrate interface) to cancel each other at a chosen design wavelength.
(b) Using your result from part (a), determine a numerical value for the required coating index when the surrounding medium is air.
(c) Identify one common optical material whose index is close to the value found in part (b) and discuss one practical consideration (such as durability or adhesion) in choosing this material for large outdoor windows.