To reduce the loss of light by reflection from the surface of lenses in modern optical instruments, wide use is made of the method of "blooming" developed by Academicians I. V. Grebenshikov, A. A. Lebedev, and A. N. Terenin. The following phenomenon lies at the basis of this method. If the surface of glass is covered with a thin transparent film whose refractive index is smaller than that of the glass and whose thickness is equal to one-quarter wavelength of the incident light, then the intensity of the light reflected from such a layer will be zero, and all the light will pass through the layer.
Consider the interaction between the light pencils reflected from the upper and lower surfaces of such a film and explain why, when the film is applied, the surface ceases to reflect light. Why should the thickness of the film be equal to a quarter wavelength of the incident light? Why should the refractive index of the film be smaller than the refractive index of the glass?