Question:
How is the refractive index of a medium related to the speed of light ?
Obtain an expression for refractive index of a medium with respect to another in terms of speed of light in these two media.
Solution:
Refractive index of a medium
$=\frac{\text { speed of light in air }}{\text { speed of light in medium }}$
i.e. $n=\frac{c}{v}$
For medium $\mathrm{I}, n_{1}=\frac{c}{v_{1}}$
For medium II, $n_{2}=\frac{c}{v_{2}}$
$\therefore n_{21}=\frac{n_{2}}{n_{1}}=\frac{c}{v_{2}} \times \frac{v_{1}}{c}=\frac{v_{1}}{v_{2}}$
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