3. A glass lens is coated with a non-reflecting coating of thickness one quarter of a wavelength (in the coating) of light whose wavelength in air is 10. The index of refraction of the glass is n, and that of the coating is √√n. The refractive index of air can be taken to be unity. Show that the coefficient of reflection for light normally incident on the lens from air is R = (n-1) cos² [(/2) (1/1)] 4n+ (n-1)2 cos²[(л/2) (o/λ)]' where is the wavelength of the incident light in air. Assume that n = 1.5, and that this value remains approximately constant for light whose wavelengths lie in the visible band. Suppose that 550 nm, which corresponds to green light. It follows that R = 0 for green light. What is R for blue light of wavelength = 450 nm, and for red light of wavelength 650 nm? Comment on how effective the coating is at suppressing unwanted reflection of visible light incident on the lens. (Warning: This question is very difficult.) 4. A glass lens is coated with a non-reflective coating whose thickness is one quarter of a wavelength (in the coating) of light whose frequency is fo. Demonstrate that the coating also suppresses reflection from light whose frequency is 3 fo, 5 fo, et cetera, assuming that the refractive index of the coating and the glass is frequency independent.