Magnesium fluoride (MgF') is a transparent solid with an index of refraction of 1.38, and can be deposited in very thin layers to create coatings. (a) [4 pts] Suppose that you want to create an anti-reflection coating on a piece of glass (index of refraction 1.45) using a thin layer of MgF', choosing a thickness such that reflections off the top and bottom surface of the MgF' interfere destructively. If you are designing the coating for light of wavelength 532 nm (in vacuum) at normal incidence (i.e. incident perpendicular to the surface), what are the three smallest thicknesses you could choose for your coating? (b) Bonus point [ 1]: which of those three thicknesses would give you the widest bandwidth anti-reflection coating - that is, the largest range of wavelengths on either side of 532 nm before you get to a wavelength whose reflections off the two MgF' surfaces interfere constructively? Explain or derive your