Question

write the expression relating the refractive index of medium A with respect to medium B to the speed of light in the two media A& B.
name the constant when medium B is vacuum.

Answer 1

$$\begin{gathered} \mathbf{Case}\mathbf{}\mathbf{I}\mathbf{:} \\ {\mathrm{\mu }}_{\mathrm{A}}^{\mathrm{B}}=\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{the}\mathrm{medium}\mathrm{A}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{B} \\ =\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{medium}\mathrm{B}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{medium}\mathrm{A}} \\ \mathbf{Case}\mathbf{}\mathbf{II}\mathbf{:} \\ {\mathrm{\mu }}_{\mathrm{A}}^{\mathrm{vacuum}}=\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{the}\mathrm{medium}\mathrm{A}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{vacuum} \\ =\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{medium}\mathrm{A}} \\ =\mathbf{Absolute}\mathbf{}\mathbf{refractive}\mathbf{}\mathbf{index}\mathbf{}\mathbf{of}\mathbf{}\mathbf{the}\mathbf{}\mathbf{medium} \end{gathered}$$