Example 17.5 showed that a thin film whose thickness is one quarter of the wavelength of light in the film serves as an antireflection coating when coated on glass. In Example 17.5, \(n_{\text {film }}n_{\text {glass }}\) were used instead, would the film still serve as an antireflection coating? Explain.<_>

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EXAMPLE 17.5 Designing an antireflection coating To keep unwanted light from reflecting from the surface of eyeglasses or other lenses, a thin film of a material with an index of refraction n = 1.38 is coated onto the plastic lens (n = 1.55). It is desired to have destructive interference for A = 550 nm because that is the center of the visible spectrum. What is the thinnest film that will do this? The glasses on the top have an antireflection coating on them. Those on the bottom do not. PREPARE We follow the steps of Tactics Box 17.1. As the light traverses the film, it first reflects at the front surface of the coating. Here, the index of refraction increases from that of air (n = 1.00) to that of the film (n = 1.38), so there will be a reflective phase change. The light then reflects from the rear surface of the