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A soap film(n=1.33) in air is 320nm thick.if it is illuminated with white light at normal incidence,what colour will it appear to be in reflected light??? |
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Answer» ht ray's wavelength : 380 nm to 760 nm for visible light (white rays). μ_film = 1.33 thickness of film = d = 320 nm θ1 = 0° = angle of incidence at the top layer of film μ_air = 1 θ2 = angle of REFRACTION into the soap film = angle of reflection at the film-air interface. μ_air Sin θ1 = μ_film Sin θ2 --- (1) There is a phase shift of 180 DEG. when light rays are reflected at the top surface of the film, as μ_air < μ_film. There is no phase shift when rays are reflected at the film-to-air interface. The OPD (optical path difference) is: 2 μ_film d Cos θ2 = (m - 1/2) λ for constructive interference. --(2) 2 μ_film d Cos θ2 = m λ for destructive interference. -- (3) here m = an integer. As θ1 = 0°, θ2 = 0°. 2 * 1.33 * 320 nm = Optical path difference OPD = 661.12 nm In equations (2) and (3), the RHS is λ/2, λ, 3λ/2 ... We have the range of white light wavelengths mentioned above. 661.12 = λ for red color satisfies equation (3). So red color is destroyed. 661.12 = 1.5 λ for λ = 440.7 nm satisfies equation (4), ie., violet color is constructively added. |
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