You are designing a thin transparent reflective coating for the front surface of a sheet of glass. The index of refraction of the glass is 1. 52 , and when it is in use the coated glass has air on both sides. Because the coating is expensive, you want to use a layer that has the minimum thickness possible, which you determine to be \(104 \mathrm{~nm}\). What should the index of refraction of the coating be if it must cancel \(550-\mathrm{nm}\) light that hits the coated surface at normal incidence?