A common way of specifying the refractive index properties of glass used for opt

Question

A common way of specifying the refractive index properties of glass used for optical components is in terms of two numbers, a refractive index and a dispersion index. Refractive indexes are measured at certain standard wavelengths, corresponding to strong spectral line emissions from gases such as hydrogen, helium, cadmium and mercury. The three most commonly used wavelengths are: The refractive indexes at these wavelengths arc designated nc,n4 and nF respectively. Dispersion is specified in terms of the Abbe value Vd defined by A very common type of glass is BK7. which has n4 = 1.51680 and Vd = 64.17 From this information, calculate an approximate value for the group refractive index ng. of BK7 at 588 nm.

Explanation / Answer

A very common tyoe glass is B K7 has n_d = 1.51680         velocity v_d = 64.17 , = 588*10^-9 m     group refractive index is   n_g = c / v_g                      group velocity v_g = ( v - ) d v / d                                    = ( 64.17 - 588*10^-9 m ) d ( 64.17 m/s /588*10^-9 m )                                    = 7.003*10^9 m/s                          n_g = 3.00*10^8 m/s / 7.003*10^9 m/s                                  = 4.283                                         

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