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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 .\(\frac98\)

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