SELLMEIER EQUATION AND DIAMOND The relevant Sellmeier coefficients for diamond are given in Table 9.2. Calculate its refractive index at 550 nm (green light) to three decimal places.

Question

Table 9.2 Sellmeier and Cauchy coefficients
Sellmeier
	[latex]A_{1}[/latex]	[latex]A_{2}[/latex]	[latex]A_{3}[/latex]	[latex]\lambda _{1} (\mu m)[/latex]	[latex]\lambda _{2} (\mu m)[/latex]	[latex]\lambda _{3} (\mu m)[/latex]
SiO[latex]_{2}[/latex] (fused silica)	0.6967490	0.4082180	0.8908150	0.0690660	0.1156620	9.9005590
86.5% SiO[latex]_{2}[/latex]–13.5% GeO[latex]_{2}[/latex]	0.711040	0.451885	0.704048	0.0642700	0.129408	9.425478
GeO[latex]_{2}[/latex]	0.80686642	0.71815848	0.85416831	0.068972606	0.15396605	11.841931
Sapphire	1.023798	1.058264	5.280792	0.0614482	0.110700	17.92656
Diamond	0.3306	4.3356		0.1750	0.1060
Cauch
	Range of [latex]hf[/latex] (eV)	[latex]n_{−2} (eV^{2} )[/latex]	[latex]n_{0}[/latex]	[latex]n_{2} (eV^{−2})[/latex]	[latex]n_{4} (eV^{−4})[/latex]
Diamond	0.05–5.47	−1.07 × [latex]10^{−5}[/latex]	2.378	8.01 × [latex]10^{−3}[/latex]	1.04 × [latex]10^{−4}[/latex]
Silicon	0.002–1.08	−2.04 × [latex]10^{−8}[/latex]	3.4189	8.15 × [latex] 10^{−2}[/latex]	1.25 × [latex]10^{−2}[/latex]
Germanium	0.002–0.75	−1.0 × [latex]10^{−8}[/latex]	4.003	2.2 × [latex]10^{−1}[/latex]	1.4 × [latex]10^{−1}[/latex]

Accepted Answer

The Sellmeier dispersion relation for diamond is

[latex] n^{2}=1+\frac{0.3306 \lambda^{2}}{\lambda^{2}-(175 nm )^{2}}+\frac{4.3356 \lambda^{2}}{ \lambda^{2}-(106 nm )^{2}} [/latex]

[latex] =1+\frac{0.3306(550 nm )^{2}}{(550 nm )^{2}-(175 nm )^{2}}+\frac{4.3356(550 nm )^{2}}{(550 nm )^{2}-(106 nm )^{2}}=5.8707 [/latex]

So that [latex]n[/latex] = 2.423

which is about 0.1 percent different than the experimental value of 2.426.

Question 9.3: SELLMEIER EQUATION AND DIAMOND The relevant Sellmeier coeffi...

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