Chapter 24 & 25 Geometrical Optics & Physical Optics   Thin-Film Interference Light reflected from the top and bottom of the film interferes to create a fringe pattern. Optical Path Length: The optical path length is the actual length of the path taken by light, multiplied by the index of refraction of the medium through which it travels. The optical path length divided by the vacuum wavelength () equals the number of wavelengths corresponding to the route taken. The phase difference between the waves is given by: (13)   Case 1 applies when the index of the film lies between the indices of the surrounding two media: or . Maxima: (14) where: m = 1, 2, 3, ...     Case 2 applies when the index of the film is greater or less than the indices of the surrounding two media: or . Maxima: (15)   Example 19 A beam consisting of red light () and blue light () is directed at right angles onto a thin soap film. If the film has an index of refraction n = 1.33 and is suspended in air (n = 1.00), find the smallest nonzero thickness for which it appears red in reflected light.   Solution:   Example 20 Camera lenses (n = 1.52) are often coated with a thin film of magnesium flouride (n = 1.38). These "nonreflective coatings" use destructive interference to reduce unwanted reflections. Find the condition for destructive interference in this case, and calculate the minimum thickness required to give destructive interference for light in the middle of the visible spectrum (yellow-green light, ).     Solution: The rays need to be out of phase: (Maxima in normally reflected light occur when the film thickness is a whole number multiple of half the wavelegth (). Minima occur when the thickness is an odd multiple of one-quarter of the wavelength ().)     Michelson Interferometer   On to Diffraction