Question

The refractive index of a medium ‘x’ with respect to medium ‘y’ is 2/3 and the refractive index of medium y with respect to medium ‘z’ is 4/3. find refractive index of medium ‘z’ with respect to medium ‘x’. Calculate speed of light in medium ý’.

Answer 1

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Answer 2

Given info : The refractive index of a medium ‘x’ with respect to medium ‘y’ is 2/3 and the refractive index of medium y with respect to medium ‘z’ is 4/3.

To find : refractive index of medium ‘z’ with respect to medium ‘x’ and also the speed of light in medium y if the speed of light in medium x is 3 × 10^8 m/s [ you forgot to mention it ] is ..

solution : refraction index of x with respect to y = x/y = 2/3

and refractive index of y with respect to z = y/z = 4/3

so, refractive index of x with respect to z = x/z = (x/y) × (y/z) = 2/3 × 4/3 = 8/9

so, the refractive index of z with respect to x = z/x = 9/8

we know, speed of light in a medium ∝ 1/refractive index of that medium.

⇒v₁/v₂ = μ₂/μ₁

let v₁ is speed of light in medium x , v₂ is speed of light in medium y and μ₂/μ₁ is refractive index of y with respect to x.

⇒(3 × 10^8 m/s)/v₂ = y/x = 1/(x/y) = 1/(2/3) = 3/2

⇒v₂ = 2 × 10^8 m/s

Therefore the speed of light in medium y is 2 × 10^8 m/s.