By what percent is the speed of blue light 450nm n450nm 158

By what percent is the speed of blue light (450?nm, n450nm = 1.580) less than the speed of red light (680?nm, n680nm = 1.565), in borate flint glass (Figure 1) ?

Figure 1 |of1 L.7 Su Silicate flint glass In 1.6 Borate flint glas uartz Silicaclown glass Fused quart 1.5 700 600 Wavelength (nmy 400 500 Vidlet BueGreen Yellow Orange

Solution

Speed of light in borate flint glass = c / n

for given blue light :

Vb = c / n450 = (3 x 10^8) / (1.580) = 1.899 x 10^8 m/s

for given red light:

Vr = (3 x 10^8) / (1.565) = 1.917 x 10^8 m/s

deltaV = (1.917 - 1.899) x 10^8   = 1.793 x 10^6 m/s

% diff = (1.793 x 10^6) x 100 / (1.899 x 10^8) = 0.94 %