Some problems involving thin films

1. A layer of oil (n=1.75) lies on top of a puddle of water. Consider light reflected normally from the surface ...
   1. Find three thicknesses of the oil that will give constructive interference for red light (600 nm)
   2. Find three thicknesses of the oil that will give destructive interference for blue light (400 nm)
   If you have time
   3. Can you find a thickness for the oil which will cause BOTH red light and blue light to undergo constructive interference?
2. Good camera lenses have anti-reflection coatings which prevent light from bouncing off their outer surfaces. One material used in these coating is MgF, which has an index of refraction n=1.38.
   1. How thick should Nikon make a film of MgF on a glass lens in order to transmit as much visible light as possible through the lens? A round number for the middle of the range of visible wavelengths is 550 nm.
   2. Little Billy plays with his grandfather's old Nikon lens. He peels off the coating from the front surface of the lens and examines it, holding one edge of the film so that it hangs down in front of his eyes. Does the film appear transparent or opaque to Billy? Explain.
3. Tim dips a circular wand into a mixture of soapy water. He pulls the wand out and sees a thin, flat film filling the circle. It is very colorful.
   1. What thickness of soapy water will make the film appear bright at a wavelength of 550 nm (which is yellowish light)
   2. What thickness of soapy water will make the film appear dark at 550 nm?
   3. As Tim watches, some of the water slowly evapoates, making the film thinner and thinner. What sort of interference occurs last before the film becomes too thin and breaks?