BASIC OPTICS OF EFFECT MATERIALS 87 refl ected at the interface is determined by the Fresnel equations. At normal incidence, the Fresnel equation simplifi es to equation 3: R n n n n 2 1 2 1 2 = − + [( )/( )] (3) The equation becomes more complicated for non-normal incidence. Regardless of the form, the point is the same: the larger the difference between n1 and n2, the higher the refl ection will be. For example, at the interface between media with an index of refraction of 1 (air) and 2.7 (rutile titanium dioxide), the % refl ection (at normal incidence) is 21%, while the % refl ection (at normal incidence) at the interface between media with an index of refraction of 1 (air) and 1.5 (silica) is only 4%. Light that is not refl ected at the interface enters the medium and is refracted. The refrac- tion angle θ2 is determined by Snell’s law in equation 4: n Sin n Sinθ 1 1 2 2 θ = (4) The velocity of light through a medium that is denser than space (or air) is slower than the maximum value for the speed of light. Equation 2 can be rearranged to solve for ve- locity as in equation 5: v c n = / (5) This equation means that the higher the refractive index of a medium, the slower the velocity of light through that medium. If equation 5 is substituted into equation 1, the result is equation 6: c /n = νλ (6) Since the frequency of a wave and the speed of light remain constant, the wavelength of light changes according to equation 7: λ λ 2 1 1 2 n = ( / ) n (7) Figure 2. Refl ection and refraction of incident light at the interface between media with refractive indexes of n1 and n2.

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