2] 21 5] 3] 4] C.3 Consider the reflection of light at near normal incidence from a glass surface coated with a thin fil

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2 21 5 3 4 C 3 Consider The Reflection Of Light At Near Normal Incidence From A Glass Surface Coated With A Thin Fil 1 (105.96 KiB) Viewed 40 times

2] 21 5] 3] 4] C.3 Consider the reflection of light at near normal incidence from a glass surface coated with a thin film, as illustrated below. 1234 a) Explain qualitatively how the presence of a "quarter wave" titanium dioxide (TiO₂) film on the surface of glass gives rise to a greater reflectivity than that of glass or of the film alone. air [4] film (The refractive indicies of glass and TiO₂ are 1.50 and 2.40 respectively.) glass The Fresnel amplitudes for reflection and transmission for light travelling (at normal incidence) from medium 1 towards medium 2 are T12 = n1n₂ n₁ + 1₂ t12 = 2n₁ n₁ + n₂ where the n are the refractive indices. b) Calculate the amplitudes of rays 1 and 2 (in the image above) for a TiO₂ quarter wave film, taking care to include the Fresnel transmission amplitudes for the air- film and film-air interfaces where appropriate. Hence estimate the total reflected amplitude and the reflectivity. [3] c) Write down expressions for the amplitudes of rays 3 and 4 in terms of r2, the amplitude of ray 2. [2] Hence show that the reflection amplitude for the air-film-glass (afg) system, ac- counting for all multiple reflections, is Taj - Tjg [raj + taftfa] Tafg= 1-Taft fg [Note that the sum of a convergent geometric series is given by a + ax + ax² + ... = a/(1-1).] d) Calculate the exact reflectivity of glass with a TiO2 quarter-wave coating. e) A quarter wavelength layer of Mg F2 with refractive index 1.38 is inserted between the glass and TiO2 quarter-wave coating. How will the reflectivity be affected?