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Electronic, magnetic and optical materials

When light from air strikes the surface of a transparent material with a refractive index of 2.4 (close to diamond) at normal incidence, which value is closest to the reflectance at the surface? Neglect absorption.

  1. AAbout 17%
  2. BAbout 41%
  3. CAbout 4%
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Answer: A. About 17%

The reflectance at normal incidence is R = [(n − 1)/(n + 1)]², so for n = 2.4 it is (1.4/3.4)² = 0.412² ≈ 0.17, about 17%. About 41% forgets to square and gives (n − 1)/(n + 1). About 4% is the reflectance of glass with a refractive index of 1.5, (0.5/2.5)², the mistake of applying the value for glass. The higher the refractive index, the stronger the surface reflection, which is one reason for the brilliance of diamond. Silicon, with a refractive index of about 3.5, reflects as much as about 30%, so solar cells reduce reflection with antireflection coatings and surface texturing.

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