The refractive index of a medium 'x' with respect to a medium y is 2/3 and the refractive index of medium with respect to medium 'z' is 4/3. Find the refractive index of medium 'z' with respect to medium 'x'. If the speed of light in medium 'x' is `3 xx 10^(8) m s^(-1)` , into to calculate the speed of light in medium 'y'.

Explanation

As per question, refractive index of medium x w.r.t medium y, `n_(xy) = (2)/(3)`
and refractive index of medium y w.r.t. medium z, `n_(yz) = (4)/(3)`
and speed of light in medium x, `V_(x) = 3 xx 10^(8) m s^(-1)`
`:.` Refractive index of medium z w.r.t. medium x will be
`n_(zx) = (n_(zy))/(n_(xy)) = (1)/((n_(yz)) xx (n_(xy))) = (1)/((4)/(3) xx (2)/(3)) = (9)/(8)`
As `n_(xy) = (V_(y))/(V_(x))`, hence `V_(y) = V_(x) xx n_(xy) = (3 xx 10^(8)) xx (2)/(3) = 2 xx 10^(8) m s^(-1)`