Refractive index of air, μair = 1;
Given;
Refractive index of medium x w.r.t medium y, μxy = \(\frac23\)
Refractive index of medium y w.r.t medium z, μyz = \(\frac43\)
Refractive index of medium z w.r.t medium x = μzx = \(\frac{μ_z}{μ_x} = \frac{μ_z}{μ_y}\times\frac{μ_y}{μ_x}\)
⇒ μzx = \(\frac{1}{\frac{μ_y}{μ_z}}\times\frac{1}{\frac{μ_x}{μ_y}}\)
⇒ μzx = \(\frac{1}{μ_{yz}}\times\frac{1}{μ_{xy}}\)
⇒ μzx = \(\frac{1}{\frac{4}{3}}\times\frac{1}{\frac{2}{3}}\)
⇒ μzx = \(\frac{3}{4}\times\frac32\)
⇒ μzx = \(\frac98\)
∴ Refractive index of medium z w.r.t medium x is .\(\frac98\)