Question

The index of refraction of glass for violet light is 1.665 and for red light 1.618. Compute the difference in the speed of light in glass for the two colours.

Answer 1

Given,

Refractive index for violet, ${\mu }_v=1.665$

Refractive index for red; ${\mu }_r=1.618$

We know,

$\mu =\frac{c}{v}$

$v=\frac{c}{\mu }$

$\Rightarrow$ $V_v=\frac{c}{{\mu }_v}=\frac{3\times {10}^8}{1.665}$

$V_r=\frac{c}{{\mu }_r}=\frac{3\times {10}^8}{1.665}$

Difference $=|V_v-V_r|$

$=|\frac{3\times {10}^8}{1.665}-\frac{3\times {10}^8}{1.618}|=0.05\times {10}^8$

$\Delta V=5\times {10}^{6}m/s$