Question

The refractive index of a medium 'a' with respect medium 'b' is 2+3 and the refractive index of medium 'b' with respect to medium 'c' is 4+3 . Find the refractive index of medium 'c' with respect to medium 'a' .

Answer 1

Dear Student,

Given that,

n_ab = 2/3

n_bc = 4/3

n_ca = ?

$$\begin{gathered} {\mathrm{n}}_{\mathrm{ca}}=\frac{{\mathrm{n}}_{\mathrm{c}}}{{\mathrm{n}}_{\mathrm{a}}}=\frac{{\mathrm{n}}_{\mathrm{c}}}{{\mathrm{n}}_{\mathrm{b}}}\times \frac{{\mathrm{n}}_{\mathrm{b}}}{{\mathrm{n}}_{\mathrm{a}}} \\ {\mathrm{n}}_{\mathrm{ca}}=\frac{1}{{\mathrm{n}}_{\mathrm{bc}}}\times \frac{1}{{\mathrm{n}}_{\mathrm{ab}}} \\ {\mathrm{n}}_{\mathrm{ca}}=\frac{1}{{\displaystyle \raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\times \frac{1}{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}=\frac{9}{8} \end{gathered}$$