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The rhinestones in costume jewelry are glass with index of refraction 1.50. To make them more reflective, they are often coated with a layer of silicon monoxide of index of refraction 2.00. What is the minimum coating thickness needed to ensure that light of wavelength 576 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference

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okpalawalter8

Answer:

[tex]T=62.9*10^{-9}[/tex]

Explanation:

From the question we are told that:

Index of refraction of Rinestones [tex]\gamma_1 =1.5[/tex]

Index of refraction of silicon [tex]\gamma_2 =2.0[/tex]

Wavelength  [tex]\lambda=576nm=576*10^{-9}[/tex]

Let each layer have thickness T

Therefore

Total Thickness =2T

Generally the equation for  Constructive interference is mathematically given by

[tex]2T=(m+0.5)\frac{l\lambda}{\gamma_2}[/tex]

Where

 [tex]M=0[/tex]

 [tex]2T=(0+0.5)\frac{576*10^{-9}}{2*2.0}[/tex]

 [tex]T=62.9*10^{-9}[/tex]

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