Answer
The phase shift of 180º occurs when the path length difference between the two reflected rays is equal to a multiple of the wavelength of light used. It depends on the indices of refraction of the lens and the antireflective coating and its thickness. If the antireflective coating has a higher index of refraction than the lens, the second reflected ray would have a phase shift of 180º.
Work Step by Step
A lens with an index of refraction of n = 1.51 and an antireflective coating of MgF2 with an index of refraction of n = 1.38 will have two reflected rays. The first of these reflected rays is the one that is reflected off the surface of the lens and the second one is the one that is reflected off the surface of the antireflective coating.
The phase shift of 180º occurs when the path length difference between the two reflected rays is equal to a multiple of the wavelength of light used. The path length difference is given by the product of the indices of refraction and the thickness of the coating.
In this case, the first reflected ray (reflected off the surface of the lens) will have a phase shift of 180º. This is because the path length difference between this ray and the second reflected ray (reflected off the surface of the antireflective coating) will be equal to a multiple of the wavelength of light used.
Now if a different antireflective coating on a similar lens had n = 1.62, the second reflected ray (reflected off the surface of the antireflective coating) would have a phase shift of 180º. This is because the path length difference between this ray and the first reflected ray (reflected off the surface of the lens) would be equal to a multiple of the wavelength of light used.
