Antireflection coatings can be used on the inner surfaces of eyeglasses to reduce the reflection of stray light into the eye, thus reducing eyestrain.

a. A 90-nm-thick coating is applied to the lens. What must be the coating's index of refraction to be most effective at \(480 \mathrm{~nm}\) ? Assume that the coating's index of refraction is less than that of the lens.

b. If the index of refraction of the coating is 1.38 , what thickness should the coating be so as to be most effective at \(480 \mathrm{~nm}\) ? The thinnest possible coating is best.