In terms of the wavelength of the pertinent light how thick must the layer of transparent optical coating on a transparent medium be in order to create maximum destructive interference of the reflected light therefore maximizing transmission? (select the answer that is appropriate for the case in which light that is travelling in air is approaching a piece of glass along a path that is normal to the surface of the glass and the coating whose index of refraction is between that of air and that of glass is to be placed on the first surface of the glass to be encountered by the light in order to minimize reflection from that surface.)

Answer:

We require the path length difference between light that bounces off the air-coating interface and the light that bounces off the coating-glass interface to be one-half a wavelength in order to get destructive interference. The light that goes throughout the first interface (the air-coating interface) travels through the width of the coating bounces off the coating-glass interface and travels back through the thickness of the coating again prior to passing back out through the air-coating interface to join the light that bounced off the air-coating interface. The additional distance that the light that goes through the first interface travels is thus twice the thickness of the coating. For that distance to be half a wavelength the width of the coating must be a quarter of a wavelength. Since the additional travelling that the light that goes through the air-coating interface does is in the coating material it is the wavelength that the light has when it is in the coating material that matters not the wavelength that the light has when it is in the air.