Glass, despite being transparent, still reflects a little bit of light. When making lenses and such, you'd rather not waste any light with stray reflections. Fortunately, you can use destructive interference to suppress those reflections. The picture below shows a piece of glass with a coating of magnesium fluoride (MgF2). The arrows represent incoming light. Some of the light will reflect off the air-MgF2 interface. Some of the light will reflect off the MgF2-glass interface. If you can get these two portions of light to interfere destructively, there won't be any visible reflections. Use what you know about path length differences and interference to figure out how thick the coating of MgF2 needs to be for an anti-reflective coating for light of wavelength 640 nm. Use the thinnest coating possible. MgF2 has an index of refraction of 1.38 and the glass has an index of 1.58.
Glass, despite being transparent, still reflects a little bit of light. When making lenses and such, you'd rather not waste any light with stray reflections. Fortunately, you can use destructive interference to suppress those reflections. The picture below shows a piece of glass with a coating of magnesium fluoride (MgF2). The arrows represent incoming light. Some of the light will reflect off the air-MgF2 interface. Some of the light will reflect off the MgF2-glass interface. If you can get these two portions of light to interfere destructively, there won't be any visible reflections. Use what you know about path length differences and interference to figure out how thick the coating of MgF2 needs to be for an anti-reflective coating for
Note: the wavelength given is the wavelength of the light in air.
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