The refractive index of a medium x with respect to y is 2/3 and the refractive index of medium y with respect

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The refractive index of a medium x with respect to y is 2/3 and the refractive index of medium y with respect to z is 4/3 Calculate the refractive index of medium z with respect to medium x

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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 .$\frac98$