Washing dishes one evening, you admire the swirling colors visible in the soap bubbles. You hold up a cup and peer into its soap-covered mouth. As you hold the cup still and examine it in the light of a lamp behind you, you notice that the colors begin to form horizontal bands, as in the figure below. You observe that the film appears black near the top, with stripes of color below.
Approximately how thick is the film of soap in the reddish region of the fourth stripe indicated? Assume that the film is nearly perpendicular both to your line of sight and to the light rays from the lamp, For simplicity, assume that the region specified corresponds to the fourth maximum of the intensity of reflected red light with a 645-nm wavelength. The index of refraction of the soap film is 1.34.
